Distorted Time Preferences and Structural Change in the Energy Industry: A Theoretical and Applied Environmental-Economic Analysis (Sustainability and Innovation)

Sustainability and Innovation Coordinating Editor: Jens Horbach Series Editors: Eberhard Feess Jens Hemmelskamp Joseph ...

Author: Christoph Heinzel

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Sustainability and Innovation Coordinating Editor: Jens Horbach

Series Editors: Eberhard Feess Jens Hemmelskamp Joseph Huber Ren´e Kemp Marco Lehmann-Waffenschmidt Arthur P.J. Mol Fred Steward

Sustainability and Innovation Published Volumes: Jens Horbach (Ed.) Indicator Systems for Sustainable Innovation 2005. ISBN 978-3-7908-1553-5 Bernd Wagner, Stefan Enzler (Eds.) Material Flow Management 2006. ISBN 978-3-7908-1591-7 Andreas Ahrens, Angelika Braun, Arnim v. Gleich, Kerstin Heitmann, Lothar Lißner Hazardous Chemicals in Products and Processes 2006. ISBN 978-3-7908-1642-6 Ulrike Grote, Arnab K. Basu, Nancy H. Chau (Eds.) New Frontiers in Enviromental and Social Labeling 2007. ISBN 978-3-7908-1755-3 Marco Lehmann-Waffenschmidt (Ed.) Innovations Towards Sustainability 2007. ISBN 978-3-7908-1649-5 Tobias Wittmann Agent-Based Models of Energy Investment Decisions 2008. ISBN 978-3-7908-2003-4 Rainer Walz, Joachim Schleich The Economics of Climate Change Policies 2008. ISBN 978-3-7908-2077-5 Barbara Praetorius, Dierk Bauknecht, Mark Carnes, Corinna Fischer, Martin Pehnt, Katja Schumacher, Jan-Peter Voß Innovation for Sustainable Electricity Systems 2008. ISBN 978-3-7908-2075-1

Christoph Heinzel

Distorted Time Preferences and Structural Change in the Energy Industry A Theoretical and Applied Environmental-Economic Analysis

Christoph Heinzel Center for Energy and Environmental Markets (CEEM) School of Economics Australian School of Business University of New South Wales Sydney 2052, NSW, Australia [email protected]

ISSN 1860-1030 ISBN 978-3-7908-2182-6 e-ISBN 978-3-7908-2183-3 DOI 10.1007/978-3-7908-2183-3 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009926006 c Physica-Verlag Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Physica-Verlag. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Meinen Eltern

Preface

The present study is a slightly revised version of my PhD thesis which was accepted at the Economics Department of Dresden University of Technology in July 2008. It has a long and a short history. For it began, as suggested theme, as a fundamental evaluation of evolutionary economics for ecological economics, asking, especially, for what the two fields actually constitutes and, eventually, relates. In several years of unfruitful dwelling, however, neither of these two young, non-mainstream fields proved as constituted at a fundamental level as yet. Rather, ecological economics, founded at the end of the 1980s as an attempt to combine social and natural science approaches (in particular economics and ecology) to study especially long-run environmental problems in an encompassing manner, has mainly developed into an interdisciplinary research forum on environmental-economic issues. Particularly unified by certain normative stances shared within its community, it constitutes, well understood, a new discpline of its own right, distinct from economics, with its own scientific standards, questions, methodologies and institutions (Baumg¨artner and Becker 2005). Modern evolutionary economics on the other hand has been a quarter of a century after its inception with Nelson and Winter (1982) still a mainly heterogeneous endeavor, linked by a (rather amorphous) common interest in economic “evolution” and a critical stance towards neoclassical mainstream economics, with a certain strength in applied studies on industrial dynamics (Heinzel 2004, 2006). Was the critizism of economics at the time of inception of the two fields more justified, the to a good part established, though still young discipline of economics – remaining necessarily both science and art at the same time – has in the mean time, in my view, been evolving to its best (leaving, of course, sufficient room for further research and improvement). At the same time, a doctoral dissertation is not the right place to postulate some kind of general foundations for an evolutionary approach to economics perceptive of environmental themes. The upshot was a complete revisioning of the initial project. The present work was then done in 18 months. It is my pleasure to thank Prof. Dr. Marco Lehmann-Waffenschmidt to have given the opportunity to write this thesis at the Economics Department of Dresden University of Technology. I am particularly grateful to Prof. Dr. Christian von Hirschhausen for his initiation to the German electricity industry and his support

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and encouragement for the present project. Moreover, I thank Prof. em. Dr. Malte Faber for his support and advice, also in difficult moments. Apart from them, my special thanks goes to Dr. Ralph Winkler for his support and advice on countless questions. His former work on time-lagged capital theory provided an excellent ground to clarify the theoretical argument of this study. I am similarly indebted to Dr. Normann Lorenz. In addition to them, I thank for valuable comments particularly Prof. Stefan Baumg¨artner, Prof. Christian Becker, Prof. Lucas Bretschger, Prof. Udo Broll, Prof. Martin Quaas, Dr. Grischa Perino, Prof. R¨udiger Pethig, Prof. Till Requate, Dr. Maik Schneider, Prof. Marcel Thum, and Dr. Christian Traeger. For comments on my earlier work I would moreover like to thank Prof. Kurt Dopfer, Dr. Alexander Ebner, Prof. Patrick Llerena, Dr. Jochen Luhmann, Prof. Andrea Maneschi, Dr. Reiner Manstetten, Prof. Stan Metcalfe, Dr. Thomas Petersen, Prof. Pier Paolo Saviotti, Prof. Raimund Schwarze, Prof. Yuichi Shionoya, and Prof. Ulrich Witt. I am particularly grateful to Prof. Hans Gersbach and Dr. Peter John for the opportunity to assist their courses as a teaching assistant. On institutional level, I thank the Interdisciplinary Institute for Environmental Economics at the University of Heidelberg and especially the PhD Program “Environmental and Resource Economics” of the German Research Foundation at the Universities of Heidelberg and Mannheim for support in multifarious ways. I thank for various conversations and support the co-organizers and members of the Heidelberg ecological-economics student group, especially Eva-Maria Eibel, Patrick Jochem, Eva Kiesele, Karoline Rogge, and Dr. Sheila Wertz-Kanounikoff, as well as my Dresden colleagues Dr. Robert B¨ohmer, Mag. Ferri Leberl, Dr. Anne Neumann, Dr. Serena Sandri, Tino Sch¨utte, Hannes Weigt, and Michael Zeidler. Finally, I gratefully acknowledge valuable comments and questions by participants of the (bi-)annual conferences of the European Association of Environmental and Resource Economists (EAERE), the European Economic Association (EEA), the European Society for Ecological Economics (ESEE), the European Society for the History of Economic Thought (ESHET) and the Verein f¨ur Socialpolitik (VfS), as well as by seminar and workshop participants at Buchenbach (near Freiburg i.Br.), Dresden University of Technology, the University of Heidelberg, the Helmholtz Centre for Environmental Research Leipzig, Schumpeter’s home town Trests (CZ), and the ETH Zurich. Apart from those among those already mentioned, I would once like to thank, in addition, my close friends, for their presence and unconditional being there, Dr. Sebastian Diehl, Nicole Nadine Hodek, H´el`ene Jobin, Christian Roeder, Dr. Wang Xiaodong, as well as, especially, Anneliese Junghans, in gratiam plenam for all she has done for me. Last, and the least to the contrary, I thank my parents for their everlasting presence and support. Sydney, February 2009

Christoph Heinzel

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Motivation and Research Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Analytical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Main Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 3 5

Part I Theoretical Analysis 2

3

Foundations of the Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Social versus Private Time Preferences . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 The Economic Discounting Debate: First-best Benchmark, Second-best Cases, and Some More Recent Issues . . . . . . . . . 2.1.2 Three Reasons Particularly Relevant for the Present Analysis 2.1.3 Summary and Treatment of the Assumption in the Model . . . 2.2 Time-Lagged Capital Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Its Evolution and the Basic Neo-Austrian Three-process Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 New Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Analytical Structure of the Model in Chapter 3 . . . . . . . . . . . . . . . . . . 2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Theoretical Model of Structural Change in the Energy Industry . . . 3.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Social Optimum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Necessary and Sufficient Conditions for Social Optimum . . . 3.2.2 Conditions for Investment and Replacement . . . . . . . . . . . . . . 3.3 Unregulated Competitive Market Equilibrium . . . . . . . . . . . . . . . . . . . 3.3.1 The Household’s Market Decisions . . . . . . . . . . . . . . . . . . . . . 3.3.2 The Firms’ Market Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Necessary and Sufficient Condition for Unregulated Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Conditions for Investment and Replacement . . . . . . . . . . . . . .

9 9 10 16 27 29 30 32 32 33 35 35 38 38 41 45 45 46 47 48

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3.4 Competitive Market Equilibrium with Emission Tax and Investment Subsidy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 The Household’s and Firms’ Market Decisions under Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Necessary and Sufficient Condition for Regulated Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Conditions for Investment and Replacement . . . . . . . . . . . . . . 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Summary of Results, Discussion of Assumptions, and Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Too Low Unit Costs of Energy of Established Technology as Compared to Social Optimum Due to Pollution . . . . . . . . . 4.1.2 Too High Unit Costs of Energy of New Technology as Compared to Social Optimum Because Private Time-Preference Rate Higher Than Socially Optimal . . . . . . 4.1.3 Time Lag of Capital Accumulation Reinforces Distortion from Split of Social and Private Time-Preference Rates . . . . 4.1.4 Distortions Imply in Mutually Reinforcing Way Less Favorable Circumstances for Innovation and Replacement . . 4.1.5 Social Optimum May Be Implemented by Setting Appropriate Emission Tax and Investment Subsidy . . . . . . . . 4.1.6 Environmental Policy Alone Biased Towards Gradual Change, Technology Policy Alone Independant of Environmental Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Discussion of Model Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Social Rate of Time Preference Below Private . . . . . . . . . . . . 4.2.2 Time Lag in Capital Accumulation . . . . . . . . . . . . . . . . . . . . . 4.2.3 Focus on Linear-limitational, General Energy Technologies . 4.2.4 Labor Only Primary Input, Energy Homogeneous Output . . . 4.2.5 Emissions as Flow Pollutant . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Abstraction from Peculiarities of Economics of Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 New Reason for Technology Policy . . . . . . . . . . . . . . . . . . . . . 4.3.2 No Support of Subsidies for Specific Technologies . . . . . . . . 4.3.3 Necessary Completion of Environmental by Technology Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Environmental Policy Alone Favors Gradual Change . . . . . . 4.3.5 Substantiation of Win-win Hypothesis of Environmental Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Conclusions to Theoretical Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51 51 52 54 58 59 59 59

60 61 61 62

62 63 63 63 64 64 65 65 65 66 66 66 67 67 67

Contents

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Part II Applied Analysis 5

6

Foundations of the Applied Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Analytical Setting and Specifics of the Applied Investigation . . . . . . 5.1.1 Analytical Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Focus on Germany Around 2015 and Conventional Generation Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Previous Literature, Contribution, and Data Sources . . . . . . . 5.1.4 Relationship to Theoretical Part . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Financial Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Capital Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Costs During Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Unit Costs of Electricity of the New Technologies . . . . . . . . . 5.2.4 Unit Costs of Electricity of the Established Technology . . . . 5.3 Technical and Economic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Old and New Coal-fired Reference Power Plants . . . . . . . . . . 5.3.2 Gas-fired Reference Power Plant . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Nuclear Reference Power Plant . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Policy Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Environmental Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Technology Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71 71 72 73 74 77 78 78 80 81 82 83 83 88 91 96 96 97 99

Technology Choice Under Environmental and Technology Policies . . . 101 6.1 No-policy Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2 Technology Choice Without Abatement Technology . . . . . . . . . . . . . 102 6.2.1 Sensitivity Under Environmental Policy . . . . . . . . . . . . . . . . . 102 6.2.2 Sensitivity Under Technology Policy . . . . . . . . . . . . . . . . . . . . 104 6.2.3 Sensitivity Under Environmental and Technology Policies Combined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.3 Technology Choice With Abatement Technology . . . . . . . . . . . . . . . . 109 6.3.1 Sensitivity Under Environmental Policy . . . . . . . . . . . . . . . . . 109 6.3.2 Sensitivity Under Environmental and Technology Policies Combined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.4 Summary and Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.4.1 No-policy Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.4.2 Results Under Environmental Policy Without and With Abatement Option . . . . . . . . . . . . . . . . . . . . 113 6.4.3 Results in Cases with Technology Policy . . . . . . . . . . . . . . . . 114 6.4.4 Results According to Nl and Nh Scenarios . . . . . . . . . . . . . . . 115 6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

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7

Optimal Moments of Transition Under Environmental and Technology Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.1 Determination of the Optimal Moment of Transition . . . . . . . . . . . . . 119 7.2 No-policy Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.3 Optimal Moments of Transition Without Abatement Technology . . . 122 7.3.1 Sensitivity Under Environmental Policy . . . . . . . . . . . . . . . . . 122 7.3.2 Sensitivity Under Technology Policy . . . . . . . . . . . . . . . . . . . . 124 7.3.3 Sensitivity Under Environmental and Technology Policies Combined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.4 Optimal Moments of Transition With Abatement Technology . . . . . . 129 7.4.1 Sensitivity Under Environmental Policy . . . . . . . . . . . . . . . . . 129 7.4.2 Sensitivity Under Environmental and Technology Policies Combined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7.5 Summary and Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.5.1 No-policy Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.5.2 Results Under Environmental Policy Without and With Abatement Option . . . . . . . . . . . . . . . . . . . . 133 7.5.3 Results in Cases with Technology Policy . . . . . . . . . . . . . . . . 135 7.5.4 Results According to Nl and Nh Scenarios . . . . . . . . . . . . . . . 137 7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

8

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 8.1 Putting the Analysis in Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 8.2 Policy Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 8.3 Issues for Further Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

A

Appendix to Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 A.1 Concavity of Hamiltonian Along Optimal Path . . . . . . . . . . . . . . . . . . 147 A.2 Optimal Transition Dynamics and Stationary States . . . . . . . . . . . . . . 148 A.3 Saddle-Point Stability of Interior Solution . . . . . . . . . . . . . . . . . . . . . . 149

B

Appendix to Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 B.1 Summary of Technical, Financing, and Cost Parameters . . . . . . . . . . 155

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Acronyms

a AC ACsp AUC b B c Δc C C CC CCGT CCS CRI D D(t) DC DCsp DM e E EC EPR EU ETS exp(.) f(.) fem FC FCs FOAK g

Abatement effort Abatement cost Specific abatement cost per mass unit of emission Abatement unit costs Bond (in Grant and Quiggin 2003) Boom state (in Grant and Quiggin 2003) Consumption Variation of c (in Gollier 2002a) Consumption (in Weitzman 1994) Hard-coal fired power plant Capital-investment costs Combined cycle gas turbine Carbon capture and storage Consumption rate of interest Disutility Annual amount of depreciation Decommissioning cost Specific decommissioning costs Deutsche Mark Net emissions Annual amount of emissions generated Emission cost European pressurised water reactor European Union emissions trading scheme Exponential function Production function Emission factor of a technology Fuel costs Annual fuel consumption First of a kind Per-capita consumption growth rate

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G G(.) GDP GJ GW GWe h(.) H hfl Hi hi i i I Ic ip is Isp ICnet IGCC IIP(t) j k k kWe l l1 , l2 , l3 LCOE LWR MWh j Nh nj Nl NOAK O&M OMC OMC f ix OMCvar p pe p f uel PHWR pstate PWR

Acronyms

Gas fired power plant Abatement function per unit of joint output Gross domestic product Gigajoules Gigawatt Gigawatt installed capacity Binary function (in Gollier 2002a) Present-value Hamiltonian function Hours of full-load operation Set of individuals with hi (in Grant and Quiggin 2003) Individual quality of human capital (in Grant and Quiggin 2003) Investment effort Market interest rate Gross investment (in Weitzman 1994) Construction-investment costs Private rate of return to investment, marginal productivity of capital Social rate of return to investment Specific (construction) investment costs Net installed capacity Integrated gasification combined cycle Annual imputed interest payment Unwanted and harmful joint output of technology Capital 1,000 Euro Kilowatt installed capacity Fixed amount of labor Labor input in production processes 1–3 Levelised cost of electricity Light water reactor Megawatt hour Index for state of employment (in Grant and Quiggin 2003) Nuclear in nuclear high-cost scenario State of unemployment (in Grant and Quiggin 2003) Nuclear in nuclear low-cost scenario Nth of a kind Operation and maintenance Operation and maintenance costs Fixed specific annual O&M costs Variable specific O&M costs Market price of energy Price of a unit of equity (in Grant and Quiggin 2003) Fuel price Pressurised heavy water reactor State-contingent claim price (in Grant and Quiggin 2003) Pressurised water reactor

Acronyms

q qk qx , qe , qi , ql1 r r rp rs PVbd R R&D RLC UCel t t1 ,tn tcom tend trepl T T1 , T2 TL Td TWh UCT1 ,UCT2 u, v U ui w W Wp x x1 , x2 Y ystate Z

δ δp φ γ Γ (.) ηi ηnet

xv

Risk premium for equity (in Grant and Quiggin 2003) Costate variable or shadow price of k Kuhn-Tucker parameters of x, e, i, l1 Market price of capital Real imputed interest rate Real imputed interest rate at private level Real imputed interest rate at social level Present value of costs incurred before decommissioning Recession state (in Grant and Quiggin 2003) Research and development Real levelised cost Unit costs of electricity Time First year of analysis, last year of analysis Year of commissioning of established plant End of expected economic life of established plant Replacement time Planning horizon Technology 1, technology 2 Expected economic lifetime of established plant Cost-accounting term of depreciation Terawatt hour Unit costs of energy of T1 , unit costs of energy of T2 Utility (in Gollier 2002a) Utility Von Neumann-Morgenstern utility index of individual i (in Grant and Quiggin 2003) Market price of labor Social welfare Private welfare Energy (in Part 1), electricity (in Part 2) Energy from technology 1, energy from technology 2 National income (in Weitzman 1994) State-contingent income (in Grant and Quiggin 2003) Proportion of Y spent on environmental improvement (in Weitzman 1994)

Social rate of time preference Private rate of time preference Coefficient of relative risk aversion (in Gollier 2002a) Deterioration rate of capital Relative environmental damage function (in Weitzman 1994) Individual holding of equity (in Grant and Quiggin 2003) Net thermal efficiency

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Acronyms

ι κ λ λ3 Λ ν π π1 , π2 θ Θ ρ ρp σ τe τi Ψ

Share of risky firms (in Grant and Quiggin 2003) Coefficient of capital Coefficient of labor Labor coefficient of capital good production Elasticity of environmental improvement (in Weitzman 1994) Relative riskiness of returns to physical capital versus human capital (in Grant and Quiggin 2003) Probability of recession (in Grant and Quiggin 2003) Profits of firm 1, profit of firm 2 Elasticity of the marginal utility of consumption Environmental damage (in Weitzman 1994) Social rate of pure time preference Private rate of pure time preference Time lag in capital accumulation Tax per unit of emission Investment subsidy (if negative) Environmental spending (in Weitzman 1994)

¤ ¤/t $ .. ..

Euro Euro per tonne CO2 US Dollar Mean value of a variable (unless differently indicated) Stochastic variable (in Gollier 2002a)

Chapter 1

Introduction

1.1 Motivation and Research Question How to accomplish the transition to a low-carbon energy industry in a socially optimal way is one of the major subjects in ongoing debates on climate and energy policy. Diffe- rent abatement options, such as demand reduction, efficiency increases, the substitution of polluting energy sources, and emission capture and sequestration, side in these discussions with different policy approaches. Common among the latter are environmental regulations that price emissions, and technology policies to foster energy efficiency and progress in green technologies. However, the transformation of the established polluting into a new less polluting, or even clean, system of energy generation has been proving as inherently time-consuming. One important reason is that conventional power plants, on which production is still mainly based, are particularly long-lived and cost-intensive capital goods with long construction times. At the same time, due to finite lifetimes their renewal in the course of reinvestment cycles constitutes a recurrent phenomenon. Usually associated with structural change, i.e. a shift in the relative use of different generation technologies, these cycles constitute a particular point at which various technological innovations may materialise. Under environmental policy, utilities face at this point a threefold trade-off. They do not only have to decide which new technology to introduce and when, but eventually also whether first, or never, to gradually refine in addition their existing plants, e.g., by enactment of an end-of-pipe abatement technology. As for any investment, investments in the energy industry are particularly dependent on the firms’ owners’ time preferences, determining their intertemporal consumption plans. Were investments in the energy sector formerly made by state-owned companies, and thus, at least ideally, evaluated at the social rate of time preference (e.g., Lind 1982), after the liberalisation of energy markets such investment decisions are now mainly governed by private actors. In economics, the correct determination and relationship of the social and private rates of time preference has been the object of a long-standing debate. As an C. Heinzel, Distorted Time Preferences and Structural Change in the Energy Industry, Sustainability and Innovation, DOI 10.1007/978-3-7908-2183-3 1, © Physica-Verlag Heidelberg 2009

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1 Introduction

outcome, it is now well recognised that private time preferences are, in general, systematically distorted. However, while the debate has especially been dealing with the optimal discounting of public projects, the welfare-theoretic implications for private investments – though occasionally alluded (e.g., Arrow and Lind 1970, Baumol 1968, Grant and Quiggin 2003, Hirshleifer 1966) – have, thus far, to the best of my knowledge, never been treated explicitly. Nor has the issue, apart from obvious cases, implicitly been resolved. In the context of energy-sector transformation this question is of a particular importance. The present study therefore addresses the following research question: What are the welfare-theoretic implications of (i) a social rate of time preference staying below the private and (ii) a time-to-build feature in capital accumulation for the conditions of structural change in the energy industry under the conditions of anthropogenic climate change and liberalised energy markets, if (iii) emissions are negatively valued and (iv) an end-of-pipe abatement technology is available? The deriving task splits in two parts. First, the theoretical status of the split of social and private rates of time preference and the time lag in capital accumulation is to be clarified. Second, the welfare-theoretic, i.e. welfare and policy, implications of these two assumptions for the conditions of investment and replacement in the energy industry are to be analysed under the given framework conditions.

1.2 Analytical Approach The analysis in this study proceeds on two levels, on theoretical level, based on a theoretical model of structural technological change in the energy industry, and, on applied level, in an explorative analysis of the implications of the theoretical findings at the particular case of the German electricity industry around 2015. The theoretical model developed in the first part of the study analyses the conditions of structural change between an established polluting and a new clean energy technology in an analytical setting where all above mentioned conditions, (i)–(iv), hold. In order to integrate and explore these features in a general-equilibrium model a particular strand of time-lagged capital theory is taken up which has been developed since the 1970s by authors such as, e.g., Bernholz et al. (1978), Faber (1979), Stephan (1995) and Winkler (2003, 2005, 2008). It is methodically further extended by the introduction of a complete market system, the specification of an (end-ofpipe) abatement function, and the consideration of diverging social and private rates of time preference. The thus extended modeling framework allows, first, to analyse the welfare and policy implications of a social rate of time preference staying below the private and a time lag in capital accumulation in the standard framework of Paretian welfare theory. Second, it also permits to study the interplay of two kinds of technological change, the introduction of an abatement technology (gradual change) and a new less polluting energy technology (structural change), as two competing abatement strategies. The major result is that, in addition to that induced by the emission externality, a further distortion arises due to the split of the social and

1.3 Main Contribution

3

private rates of time preference, the extent of which positively depends on the time lag in capital accumulation. To implement the socially optimal path, environmental policy thus needs to be complemented by technology policy, for which the payment of a Pigou investment subsidy is proposed. The model is formulated in continuous time. The actors’ intertemporal optimisation problems are solved using time-lagged optimal control theory. The applied analysis substantiates, differentiates, and extends the findings of the theoretical part. The aim is to quantify and to study the relevance of the welfare and policy implications of the split social and private time preferences derived in the theoretical part, at one particular, relevant case. In Germany, Europe’s largest economy, by 2020 40 GWe or about one third of the net installed generation capacity of the electricity industry are to be replaced as a part of usual reinvestment cycles, to which by about 2022 another 20 GWe add due to the political decision to phase out nuclear energy. Moreover, the country is subject to the EU emission trading scheme introduced in 2005, and disposes over a long experience with technology policy notably subsidising renewable energies, which further provides a valuable empirical background. The analytical focus changes to the partial-equilibrium perspective of a single cost-minimising utility. Its threefold investment-related trade-off under environmental policy is studied, taking into account one renewed and one new aspect: the deployment of new nuclear power stations and the new introduction of carbon-capture-and-storage (CCS) technologies for complete emission abatement. The analysis proceeds in two steps. First, its choice among three new generation technologies (coal, gas, nuclear) is investigated, then its choice of the optimal moment of transition from an established polluting to a new less polluting technology. For the second step the investment and replacement conditions analogous to those derived in the theoretical part are projected on a temporal scale. Each of the two decisions is investigated under seven scenarios. Apart from the no-policy benchmark, the cases of environmental and technology policy are analysed, first separately, then combined, for the two cases of, first, the absence and, second, the availability of an end-of-pipe abatement technology. The crucial unit of the applied analysis constitute the technology-specific unit costs of electricity. As financial model for their determination the conventional levelised-cost-of-electricity (LCOE) methodology is used. For the analysis it is slightly extended over the standard case (e.g., Bejan et al. 1996) by the explicit introduction of emission and abatement costs. The technical and economic parameters as well as, similarly, the sensitivity ranges of the policy parameters have been derived from scientific and public studies. The mostly threeor four-dimensional data at the basis of the analysis in chapters 6 and 7 are selfgenerated based on the financial model specified in section 5.2, using MS Excel.

1.3 Main Contribution The focus of the present study is on the environmental economics of technological change in the energy sector. Its main contribution is, more generally, to the

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1 Introduction

theory of environmental policy, in the realm of the literature on induced technological change and the environment.1 From the viewpoint of Paretian welfare theory, the usual normative analytical basis of environmental economics, this literature generally deals with two interacting sets of markets failures. First, there are the market failures associated with environmental pollution, as traditionally considered in environmental economics. They are usually connected with negative externalities in the sense that the polluter imposes pollution costs on others while reaping the benefits from polluting. In addition, since the 1980s, market failures associated with the innovation and diffusion of new technologies have increasingly come into the focus of environmental-economic research. They generally relate to positive externalities in the sense that the innovating firm typically by-creates benefits for others while incurring all the costs. Under free market conditions they imply underinvestment in new technologies as compared to the social optimum. Thus far, three categories of market failures of the latter kind may be distinguished from the literature (e.g., Jaffe et al. 2005): knowledge spillovers or spillovers of value or consumer surplus as related to the public-good nature of new knowledge, dynamic increasing returns in the adoption and diffusion of new technology as generated, e.g., by learning by doing, learning by using, or network externalities, and asymmetric information about prospective R&D success. As far as connected with an emission externality all of these market failures also constitute reasons to combine environmental and technology policies. Time preferences are treated in this literature only when dynamic analyses are performed. For such analyses, in general, either top-down or bottom-up approaches are used. Top-down approaches study induced technological change by applying one representative aggregated production technology, which becomes more efficient and/or less polluting by technological change (e.g., Bovenberg and Smulders 1995, 1996, Goulder and Mathai 2000, Nordhaus 2002, Newell et al. 1999, Tahvonen and Salo 2001). In bottom-up approaches, induced technological change also allows for structural change between competing technologies (e.g., Buonanno et al. 2003, Gerlagh and Lise 2005, Gerlagh and van der Zwaan 2006, Goulder and Schneider 1999, Van der Zwaan et al. 2002). They all assume, however, a unique rate of time preference. Moreover, while modeling technological change endogenously as a gradual improvement resulting either from R&D investments or learning effects, none of these studies considers time-lagged dynamics or the interplay of gradual and structural technological change. At the same time, distorted time preferences have long been an issue in the economic discounting debate. There they have especially been treated with respect to energy and environmental matters, however, without ever studying systematically their implications for private investments (section 2.1). Only Endres et al. (2007) have recently analysed in a simple model the robustness of the effect of diverging social and private discount rates on induced investments in improved abatement technology under different liability rules, but without reflecting on policy implications of the split discount rates. 1

Cf., e.g., Jaffe et al. (2002, 2005) for most encompassing surveys of this literature, K¨ohler et al. (2006) for a review especially of the applied literature.

1.4 Outline

5

The present study is, to the best of my knowledge, the first one to analyse the welfare-theoretic implications of distorted time preferences for technological change in general, and notably both in the presence of an environmental externality and of a time-to-build feature in capital accumulation. Moreover, also the explicit focus on the interplay of two kinds of technological change, gradual and structural, from an environmental-economic angle is uncommon in the literature. On theoretical level, the study thus contains four main novel contributions (chapters 2–4). First, it provides a new reason for a welfare-enhancing intervention of technology policy based on the split of social and private rates of time preference. Second, it shows, as a complementary result, that a policy intervention correcting the consequences of distorted time preferences is only justified, if the market failure underlying the distortion cannot directly or differently be remedied. Third, it shows that the time lag in the accumulation of a desired capital good affects only (positively) the magnitude of the distortion induced by the split of social and private time-preference rates. Fourth, it provides an additional reason for why in the transition to a low-carbon energy industry environmental policy should be complemented by technology policy. By implication the sole enactment of environmental policy favors both gradual change and stimulates structural change, however, the latter in general not sufficiently as compared to the social optimum. The analysis of the threefold trade-off of the investing utility under environmental policy in the applied part (chapters 5–7) substantiates these contributions, notably in three ways. First, the welfare implications of the split are quantified for the unit costs of electricity of different new generation technologies. Second, the impact of the split on the static technology ranking as well as the optimal moments of transition from an established to the new (reference) power plants is studied alone and against the background of varying environmental-policy levels. Third, the effect of the availability of an end-of-pipe abatement technology on technology choice and replacement times is investigated for the cases of environmental policy alone as well as the additional implementation of the social discounting level.2

1.4 Outline The study is organised in a theoretical and an applied part, each with three chapters. Chapter 2 introduces to the theoretical issue of this study and describes its relationship and contribution to the two strands of literature from which it departs. More particularly, section 2.1 discusses the crucial assumption of the split of social and private time preferences as treated in the economic discounting debate thus far, states open issues, and justifies the treatment of the assumption in the following model analysis. Section 2.2 motivates the taking up of the modeling framework of time-lagged capital theory and shows how it is further developed in the present study. Section 2.3 explains the analytical structure of the model in the subsequent 2 The contribution of the applied analysis as exceeding previous studies is described in subsection 5.1.3.

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1 Introduction

chapter. In chapter 3 a theoretical model is developed to study the transition from an established polluting to a new clean energy technology, taking account of the four conditions, (i)–(iv), of section 1.1. The model economy is introduced and social and individual preferences are specified in section 3.1. In sections 3.2 and 3.3 from the model necessary and sufficient conditions both for investment in the new and for replacement of the established technology are derived for the cases of the social optimum and of an unregulated competitive market economy, respectively. It is shown that in this setting, in addition to that induced by the emission externality, a further distortion arises due to the split of the social and private time-preference rates. Section 3.4 shows how the two distortions can be corrected via environmental and technology regulation. Chapter 4 summarises the results of chapter 3, discusses them with respect to model assumptions and policy implications, and states conclusions to the theoretical part. Chapter 5 sets out the foundations of the applied analysis. Section 5.1 introduces the analytical setting and specifics of the applied investigation. Section 5.2 specifies the financial model to calculate the unit costs of electricity of the different generation technologies. Section 5.3 describes the technologies referred to and specifies the technical and economic parameters. Section 5.4 identifies and discusses the policy parameters. Chapter 6 studies, based on the technical, economic and financing assumptions set out in the preceding chapter, the single and combined influence of environmental and technology policies on a hypothetic utility’s choice of a new electric generation technology, first for the case of the absence of a CO2 abatement technology (section 6.2). Section 6.3 analyses how results change if a CO2 abatement technology is available. Section 6.4 summarises and discusses the results. Chapter 7 studies, based on the assumptions of chapter 5, the single and combined influence of environmental and technology policies on the utility’s choice of the optimal moment of transition from its established to the new power plants. Again the two cases of the absence (section 7.3) and the availability of a CO2 abatement technology (section 7.4) are distinguished. Section 7.5 summarises and discusses the results. Chapter 8, finally, puts the results of the two parts in perspective, considers general policy conclusions, and states issues for further research.

Chapter 2

Foundations of the Theoretical Analysis

In this part of the study a theoretical model is developed to study the transition from an established polluting to a new clean energy technology. The model encompasses two distinctive features. First, the social rate of time preference is assumed to stay below the private. Second, the creation of new productive capital is supposed to exhibit a time-to-build property. This chapter introduces to the theoretical issue of this study and describes its relationship and contribution to the two respective strands of literature. Section 2.1 discusses the crucial assumption of the split of social and private time-preference rates as treated in the economic discounting debate thus far, states open issues and finally justifies the treatment of the assumption in the subsequent model analysis. Section 2.2 motivates the taking up of the modeling framework of time-lagged capital theory and shows how it is further developed in this study. Section 2.3 explains the analytical structure of the model developed in chapter 3.

2.1 Social versus Private Time Preferences The assumption of the social rate of time preference staying below the private builds on a long-standing debate in economics on discounting in general and the correct determination and relationship of social and private rates of time preference in particular. While already in the 1960s and 1970s wide unanimity could be reached on the relationship of the crucial rates in the first-best case on the one hand, referring to the basic discounted utility model, as well as on the empirical validity of positive discounting in general on the other,1 the ‘dark jungles of the second best’ (Baumol 1968) with respect to discounting have been remaining contentious. In more recent 1

Early authors, such as, e.g., Fisher (1930), Pigou (1952) and Ramsey (1928), still being hesitant on ethical grounds, positive discounting is today recognised especially as an expression of revealed dynamic preferences and used as a standard assumption in economic models (Arrow and Kurz 1970, Caplin and Leahy 2004). Moreover, there are, of course, well recognised exceptions where the discount rate is zero or negative (e.g., Dasgupta 2001). C. Heinzel, Distorted Time Preferences and Structural Change in the Energy Industry, Sustainability and Innovation, DOI 10.1007/978-3-7908-2183-3 2, © Physica-Verlag Heidelberg 2009

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years the debate has even gained in complexity due to new empirical objections and the rise of problems with particular long-run effects, such as, e.g., anthropogenic climate change. A complementary debate in finance discusses why the rates of return on private securities are so high (equity premium puzzle) and those on state securities so low (risk-free rate puzzle). This section introduces to the state of the economic discounting debate (subsection 2.1.1) and states three reasons for the social and private time-preference rates to diverge particularly relevant for investments in the energy sector (subsection 2.1.2). Subsection 2.1.3 summarises the findings from the literature survey and describes the treatment of the assumption in the model below as well as the contribution of the analysis.

2.1.1 The Economic Discounting Debate: First-best Benchmark, Second-best Cases, and Some More Recent Issues This subsection, first, introduces basic concepts and restates, as a benchmark for the further discussion, the first-best case referring to Ramsey’s (1928) basic model. Then some of the major general reasons for social and private rates of time preference to differ in terms of second-best arguments referring to the standard framework as well as policy implications that have been considered are introduced. Finally empirical objections put forward against the discounted-utility model with constant discount rate and empirical support for the split of time-preference rates, as well as theoretical implications are outlined and their importance for the present analysis is discussed.2

2.1.1.1 Equal Social and Private Rates of Time Preference in the First-best World In general, the determination and relationship of social and private rates of time preference may be described with reference to a certain configuration of eight basic concepts:3 1. 2. 3. 4.

the private rate of pure time preference, ρ p the private rate of time preference, δ p the (private) consumption rate of interest, CRI the private rate of return to investment, or marginal productivity of capital, i p

2 As regards the first-best case the account is based on Groom et al. (2005), Lind (1982) and Barro and Sala-i-Martin (2004: ch. 2). More complete accounts of the general debate and its current state can be found, e.g., in Lind et al. (1982), Portney and Weyant (1999), Frederick et al. (2002) and Groom et al. (2005). 3 The following list could be further enlarged, e.g., by the private and social marginal rates of intertemporal substitution in consumption and the opportunity cost of public investment.

2.1 Social versus Private Time Preferences

5. 6. 7. 8.

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the market interest rate, i the social rate of return to investment, is the social rate of time preference, δ the social rate of pure time preference, ρ

Note that the rates of pure time preference and of time preference are distinguished by the numeraire referred to. The rate of pure time preference represents the intertemporal weights placed on utility, the rate of time preference those on consumption. The rate of pure time preference is also called utility discount rate. In the following the relationship between these rates in the first-best world is explained departing from the Ramsey growth model. The Ramsey model determines, for units of consumption as the numeraire, the social discount rate endogenously from the optimal saving, consumption and production decisions over time of an infinitely lived representative agent. For simplicity, the following brief exposition abstracts from depreciation, population growth and technological changes. In the Ramsey model social welfare is represented by the intertemporal sum of the utility of a representative agent as follows:4 W (c(t)) =

∞ 0

U(c(t)) exp[−ρ t] dt .

(2.1)

Capital k(t) is supposed to generate output f (k(t)), which can be devoted to consumption or investment subject to the following equation of motion of the capital stock,5 dk(t) = f (k(t)) − c(t) . (2.2) dt Maximising welfare (2.1) subject to equation (2.2) yields the Euler equation: U (c(t)) f (k(t)) + U (c(t))

dc(t) − ρ U (c(t)) = 0 . dt

(2.3)

Substituting, in equation (2.3), the social rate of return to investment r(t) for the social marginal productivity of capital f (k(t)), and introducing the (per capita) consumption growth rate g(t) =

dc(t) dt

c(t) as well as the elasticity of U (t) consumption θ (t) = − U (t) c(t), yields, when simplified, the

is = ρ + θ g = δ .

the marginal utility of familiar Ramsey rule: (2.4)

The Ramsey rule (2.4) shows that in the centralised economy on the optimal path the social planner will choose consumption and savings such that the social rate of time preference equals the social rate of return to investment, δ = is . Note that, The instantaneous utility function U is assumed to be twice differentiable with U > 0, U ≤ 0, and to satisfy Inada conditions, limc→0 U = ∞, limc→∞ U = 0. 5 Instantaneous output f is assumed to be twice differentiable, with f > 0, f ≤ 0, and to satisfy Inada conditions, limk→0 f = ∞, limk→∞ f = 0. 4

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by definition, the sum of the social rate of pure time preference ρ and the desire to smooth growing wealth over time θ g is equal to the social rate of time preference δ .6 The private rates become relevant when the decentralised economy is considered. Therefore, assume a representative consumer, a representative firm and a public sector to interact on perfectly competitive markets for consumer and capital goods as well as financial capital under conditions of full rationality, complete certainty and in the absence of transaction costs and further externalities or distortions. Then the (private) consumption rate of interest, CRI, i.e. the rate at which consumers are willing to exchange consumption now to consumption in the future (equivalent to the private marginal rate of intertemporal substitution in consumption), thus coincides with the private rate of time preference, δ p . The latter derives as δ p = ρ p + θ g. Moreover, in particular in the case of a representative consumer or of n identical individuals, as arising from aggregation over the individual(s), the social rate of time preference, δ , and the social rate of time pure preference, ρ , equal the respective private rates, δ p and ρ p . Furthermore, the private consumption rate of interest, CRI, or private rate of time preference, δ p , is equal to the market rate of interest, i, for, inequality would offer the possibility of arbitrage between the purchase of consumption goods and saving. Similarly, the firms’ marginal rate of return to (private) investment, i p , equals the market rate of interest, i, for, inequality would offer the possibility of arbitrage between investment in capital goods and investment on the financial market. Their equality to the market interest rate i implies furthermore that the four rates coincide, CRI = δ p = i = i p . Due to the absence of distortions, also the social rate of return to investment, is , equals the private rate of return to investment, i p , such that rates (2)–(7) coincide. Note that public investments can only be carried out at the expense of resources (i.e., related to an equal opportunity cost) in the private sector such that their financing necessarily crowds out either private consumption, private investment, or a mixture of the two. Therefore, as an outcome of the Ramsey model, both is , i, and δ represent appropriate candidates for social discount rates to evaluate public investment projects, as long as costs and benefits are measured in consumption equivalents. The CRI is often used to measure δ , using observed rates of return on savings. The social utility discount rate, ρ , is the appropriate discount rate, if costs and benefits are measured in utility. Thus, in general, in the first-best world in a decentralised economy with growth all rates (1)-(8) coincide apart from ρ and ρ p . If there is no growth (i.e., dc(t) dt = g(t) = 0 ∀t), also the identical social and private rates of pure time preference, ρ = ρ p , are equal to the other rates.

θ (t) is a measure of the curvature of the utility function and equivalent to the coefficient of relative risk aversion. It represents preferences for smoothing consumption over time.

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2.1 Social versus Private Time Preferences

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2.1.1.2 Second-best Issues and Policy Implications as Considered Thus Far In the literature a multitude of reasons has been discussed for the social and private time-preference rates to differ (e.g., Baumol 1968, Lind 1982, Luckert and Adamowicz 1993, Stiglitz 1982, Tirole 1981). Particular attention has been paid to distortionary taxation, distortionary public investment and policies, imperfect competition, externalities in production, imperfect information, as well as intergenerational distributional concerns (i.e. altruism).7 Especially with respect to the first four of these categories of reasons the existence of distortions in the real world is well established. For these four cases also the means to their avoidance or remedying are clear, at least theoretically. Distortionary taxation and distortionary public investment and policies are just to be avoided, imperfect competition necessitates an appropriate market regulation, production externalities are to be internalised. The respective measures are thus not necessarily directed directly to a correction of the rates of return or discount rates in question. With respect to the issue of the present study, the broad debate which has been led in economics reveals, however, two lacunae. First, while a large part of the debate has been focusing on the public sector and the correct determination of the social discount rate to value public investment projects using cost-benefit analysis, it has not reflected, from a private-sector perspective, on the welfare-theoretic implications for private investment projects (e.g., to wit, Arrow and Kurz 1970, Lind et al. 1982, Arrow et al. 1995, Portney and Weyant 1999, Weitzman 2001, Groom et al. 2005). Second, abstracting from the four mentioned categories of reasons there remains a series of reasons which are particularly relevant in the present context for which there is, thus far, no optimal policy treatment as well established as for the first four cases. Three examples for such further reasons will be considered in subsection 2.1.2. Among the exceptions, which have alluded welfare-theoretic implications for private investment projects, has been especially Hirshleifer (1966). In a discussion of the appropriate relationship of public and private discount rates he alluded the possibility of a subsidy for equilibrating different risk-pooling abilities between the public and private sectors and within the private sector. He concluded that such a subsidy is only justified if some kind of market imperfection hinders an efficient pooling of risks. His position has been supported by Baumol (1968). Reexamining Hirshleifer’s discussion, Arrow and Lind (1970) have pointed out that Hirshleifer assumes identical costs of risk-bearing in the private and public sectors. They show that the costs of risk-bearing are negligible when risks are publicly borne. They underline that, therefore, the case that a public investment with a lower expected return than a given private investment is superior to the private alternative need not 7

The case of distortionary taxation is particularly impressive, as, e.g., already Baumol’s (1968) classic example showed: For corporation taxes of 0.5, income taxes of 0.25, and the social rate of time preference δ amounting to 0.06, firms, when investing, must pay dividends to shareholders such that they obtain a return of 0.06. Thus, shareholders must earn a pre-tax profit of 0.08 (for 0.08 ∗ (1 − 0.25) = 0.06), while firms must earn 0.16 (for 0.16 ∗ (1 − 0.5) = 0.08). As a consequence, i p = 0.16, whereas δ = 0.06.

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be a cause for concern. They are critical with direct subsidies to encourage more private investment, as they will not alter costs of risk-bearing but may encourage investments which are inefficient when the risk-bearing costs are taken into account. To achieve the desired result, they rather recommend policies which complete the system of markets for insurances relevant for private investments. More recently, Grant and Quiggin (2003) have taken up the issue of the debate between Hirshleifer and Arrow–Lind in the context of the modern equity-premium debate.8 They show that in the presence of financial-market imperfections the ability of superior risk-spreading via the taxation system may offset differences in technical efficiency between public and private projects. They discuss two approaches to stay with the advantages of risk-spreading without incurring the cost of undertaking projects with lower expected returns. First, they consider, similar to Arrow and Lind (1970), the possibility of a government offer of insurance against losses associated with cyclical fluctuations. They recognise that, while a voluntary public insurance would face the same adverse-selection problems as a privately provided insurance, a compulsory public insurance with the necessary degree of regulation and oversight to mitigate moral hazard problems could overcome the latter problems. At the same time the required regulation and oversight would, however, amount to a partial or complete public ownership of the project. In conclusion they find it more useful to consider a policy of public holdings of equity in private enterprises. Second, they consider the design of a set of payments to and from individuals that could mimic the risk-spreading benefits of a given public investment project without incurring any efficiency losses. For their single-period multi-state model a tax-financed unemployment benefit paid only in the recession state would have the appropriate properties. They point out that such a policy raises, however, difficulties of its own, notably if the labor supply response is taken into account. With respect to environmental liability law, Endres et al. (2007) have recently analysed in a simple two-period partial-equilibrium model the robustness of the effect of diverging social and private discount rates on the abatement level in the two periods and the investment into abatement-technology improvements, and thus induced innovation, under different liability rules. They stay, however, with a welfare comparison and do neither reflect on the causes nor on policy implications of the split of discount rates.

2.1.1.3 Empirical Objections, Experimental Support, and Their Importance for the Present Study While the traditional literature on project evaluation has usually been assuming agents to discount the future exponentially at one constant rate (e.g., Arrow and Kurz 1970, Lind et al. 1982), in the last decades the empirical foundations of the discounted-utility model have increasingly been investigated and questioned. Objections have been raised, e.g., with respect to the constancy of the discount rate 8

Grant and Quiggin’s (2003) basic model is detailed in subsection 2.1.2.2.

2.1 Social versus Private Time Preferences

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over time, its unicity in different cases of intertemporal choices, and the axiom of intertemporal independence (Frederick et al. 2002). Among the anomalies observed the variability of the discount rate over time, in terms of hyperbolic discounting, has attracted the most attention (e.g., Loewenstein and Prelec 1992, Laibson 1997, Harris and Laibson 2001, Groom et al. 2005, Winkler 2006). In the following it is first dealt with hyperbolic discounting and its theoretical implications. Then a number of experimental studies is considered which have directly investigated the relationship of social and private time-preference rates. Finally the importance of this research for the present study is discussed. Hyperbolic discounting means that agents apply higher discount rates to nearterm returns than to returns in the distant future. Thus, from the present perspective, t0 , a certain project evaluated at a discount rate D0 in t0 is discounted at some rate D1 < D0 in t1 > t0 . Discounting at a declining discount rate implies in general a time-inconsistent behavior, in the sense that the same project, the investment in which was found optimal in t0 for t1 > t0 , is not judged so anymore in t1 for that moment (Heal 1998, Winkler 2006).9 Cropper and Laibson (1999) analyse the implications of hyperbolic preferences for private investment choices and public policy. Striving for time-consistent plans for a consumer with hyperbolic preferences, they formalise the agent’s behavior as a game played by the consumer’s different temporal selves. In the case of a rational, finite-lived consumer, the game has a unique subgame perfect equilibrium which may be characterised by an Euler equation similar to that of the Ramsey model (Arrow 1999). The consumption plan of the hyperbolic consumer characterising this equilibrium is thus observationally equivalent to the consumption path of a consumer who discounts the future exponentially. Along the optimal path the consumption rate of interest should always equal the rate of return on capital, CRI = i p . The equilibrium of this game is, however, not Pareto efficient. For, consumers would be better off at any time, if each of them saved more. In absence of a commitment mechanism this will not occur (Phelps and Pollak 1968). Thus, government can induce Pareto improvement by subsidising the private rate of return on capital, or, equivalently, by lowering the required rate of return on investment. Note that this result arises irrespective of whether the government anticipates its own hyperbolic behavior or not. Rather, its optimal intervention brings the economy back to a path equivalent to one of exponential discounting. There exists furthermore a number of experimental studies which have directly investigated the relationship of social and private rates of time preference. Thus, e.g., Pope and Perry (1989) conducted an experiment on management strategies for soil-erosion control. They show that a sample of business and natural-science students would apply a significantly higher discount rate, if a depletable natural resource was, hypothetically, under their own control, than they would prefer, if it was publicly managed. Similarly, Luckert and Adamowicz (1993) find in an experimental setting that students of a first year physiology course, abstracting from risk and inflation, recommend to use a lower discount rate, if a renewable natural resource, 9 By contrast, in the case of exponential discounting with a constant discount rate, if at some time t0 < t2 investment in a project in t2 has been found optimal, it will still be found optimal, when the project is reevaluated, at any other time t1 > t0 , implying time-consistent behavior.

16

2 Foundations of the Theoretical Analysis

such as a forest, is publicly managed than if it is under private control. Lazaro et al. (2001) find that law students reveal higher rates of time preference when evaluating both future health benefits and monetary gains at an individual level than at a social level. While Pope and Perry (1989) do not reflect on theoretical reasons for their findings, the two latter papers refer for theoretical support to the so-called shizophrenic behavior approach as described, e.g., by Sen (1961, 1967) and Marglin (1963). According to this approach, individuals tend to apply higher rates of time preference in individual than in social decision contexts depending on whether they feel to act as an economic agent or as a social citizen, respectively.10 As regards the relationship of social and private time-preference rates, both (private) hyperbolic discounting and the experimental studies lead to the clear result of a private rate exceeding the social. Hyperbolic discounting can constitute a further reason for government intervention. However, it is neither specially linked to the energy sector, nor would its consideration change the analytical results of this study. Therefore, it will not be further considered in the model analysis in chapter 3. The schizophrenic behavior approach, as it does not explain the social rate as a result of aggregation of private rates, questions, in effect, the individualistic foundations of Paretian welfare theory, on which the basic argument of this study relies. Therefore, this approach will not be further considered here either.

2.1.2 Three Reasons Particularly Relevant for the Present Analysis This subsection considers three more recent arguments for the social rate of time preference to stay below the private, which are, first, particularly relevant in the case of structural change in the energy industry under conditions of anthropogenic climate change and liberalised markets, and, second, abstract from the standard cases of distortionary taxation, distortionary public investment, imperfect competition, and production externalities. They both indicate the current heterogeneity of approaches and the complexity of aspects that matter. The first is environmentspecific and focusses on the welfare and growth implications of the long-run environmental impact related to energy generation in a world of certainty. It goes back to Weitzman (1994). The second specially relates to private investment financing and refers to differing risk-premium claims on the financial market by individuals and the government, respectively. Based on a well-known observation in the finance literature, the long-standing theoretical economic argument has only recently particularly been substantiated by Grant and Quiggin (2003). The third relates to long-run uncertainty. It explains a declining social discount rate as an outcome of uncertainty over the growth rate in the long run and goes back to Gollier (2002a). In contrast to the first, the second and the third reason do not necessarily relate to environmental considerations. 10

More recently, implicitly supporting this approach, the terms homo oeconomicus for an individual maximising private utility, and homo politicus for an individual who seeks to maximise social welfare have been introduced into the literature (e.g., Faber et al. 1997, 2002, Nyborg 2000).

2.1 Social versus Private Time Preferences

17

2.1.2.1 The “Environmental” Discount Rate According to Weitzman (1994) Weitzman (1994) develops a rationale for how environmental externalities influence the social discount rate, both immediately and over time. The focus of his argument is on ‘environmental spending’, Ψ . By environmental spending he means that GDP fraction which is spent on environmental improvement. Ψ constitutes a social cost external to the production process. To state his argument he departs from the stylised fact that in a world of environmental transition environmental spending increasingly grows important. His two theses are (1) that enduring environmental spending makes the social discount rate stay below the (undistorted) private discount rate, and (2) that the increasing environmental spending over time implies an intertemporally declining social discount rate. His reasoning is as follows. Weitzman departs from a closed model economy in which (homogeneous) national income, Y , is either spent for consumption, C, gross investment, I, or environmental spending, Ψ : Y (t) = f (k(t)) = C(t) + I(t) + Ψ (t) ,

(2.5)

where f is the production technology, k the aggregate capital stock. He defines the relation between environmental spending, Ψ , and environmental damage, Θ , both expressed as a proportion of income, as:

Θ Ψ =Γ( ) , Y Y

(2.6)

where Γ is a twice continuously differentiable function with constant returns to ∂Γ ∂ 2Γ scale and ΓΨ ≡ ∂Ψ < 0 and ΓΨΨ ≡ ∂Ψ 2 > 0. Increased investment at time t by a marginal reduction in consumption, holding environmental spending constant, the following equation derives for the private rate of return on capital, i p :

∂Y = f (k) = i p . ∂k

(2.7)

In order to prove his first thesis Weitzman claims environmental damage to be maintained at some initial level, Θ . Given equation (2.6) this can only be achieved by a Ψ marginal increase in environmental expenditure, Ψ = ddY , diverted from each unit ∂Y of incremental output, ∂ k . Hence, the social rate of return to investment derives as the rate of return in terms of output minus the rate of increase in expenditure required to maintain environmental standards: is =

∂Y ∂Y −Ψ = i p [1 − Ψ ] . ∂k ∂k

(2.8)

Taking the total derivative of equation (2.6) with Θ = Θ with respect to Y , solving for Ψ , and inserting in equation (2.8) yields:

18

2 Foundations of the Theoretical Analysis

1 is = i p 1 − Z 1 + , Λ

(2.9)

where Z ≡ ΨY is the proportion of national income spent on environmental improvement, Λ ≡ −Z ΓΓΨ the elasticity of environmental improvement (i.e. reducing Θ ) with respect to environmental expenditure or the ease with which environmental damage can be reduced. This analysis has two implications for the social discount rate. First, according to equation (2.9), for all Z, Λ > 0 the social rate of discount is lower than the private, is < i p . Second, as is negatively depends on Z, for rising Z over time the socially efficient discount rate will decline. Thus, according to Weitzman’s analysis, the existence of consumption externalities reduces the level of the social rate of return below the private when society must divide the marginal return from investment between consumption and environmental protection. Moreover, the socially efficient discount rate will decline over time if the proportion of income spent on environmental goods, Z, increases, which holds if the elasticity of environmental improvement declines over time, or, similarly, if, with positive growth, environmental resources are luxury goods, as he maintains, too. Weitzman’s analysis has been criticised on a number of counts, notably for his reduced-form analytical set up without explicit modeling of preferences, environmental goods and externalities (Groom et al. 2005). While the assumption that some arbitrary environmental standard, Θ , must be maintained captures these effects generally, the substraction of environmental expenditures from the private rate of return in equation (2.8) remains rather ad hoc. Arrow et al. (1995) question moreover the interpretation of the derived is as a proper discount rate for its lack of an explicit conversion of the environmental benefits into equivalents of produced consumption. However, despite the apparent further research need, it may be retained for the present analysis that, under fairly general conditions as those from which Weitzman (1994) departs, (negative) environmental externalities may induce the social rate of return to stay below the private. Moreover, it will decrease over time if the proportion of income spent on environmental goods, Z, increases. Anthropogenic climate change may be seen as a case in point for Weitzman’s stylised fact of the positive and increasing environmental spending.

2.1.2.2 Diverging Social and Private Risk-premia on the Financial Market as Explained by Grant and Quiggin (2003) In the finance literature, it is a well known empirical fact that there exists a (negative) spread between government and private security rates of any maturity. Thus, both the rates of return on equity capital (e.g., stocks) and on debt capital (e.g., corporate bonds with maturities of 10 years and more) exceed the rates of return on state securities with respective maturities. The issue has been discussed in a broad literature in both economics and finance particularly following the statement of the so-called equity premium puzzle and the risk-free rate puzzle (Mehra and Prescott

2.1 Social versus Private Time Preferences

19

1985, Weil 1989). They state that standard theory, assuming complete asset markets and costless trading, can neither fully explain the observed high spread between the rates of return on government bills and private stocks, nor, why the government rates, usually dubbed ‘risk-free’, are so low as compared to historical data.11 The discussions on the analytical puzzles add to an earlier literature in economics on uncertainty and financial-market distortions, with contributions by authors such as Sen (1961), Samuelson (1964), Hirshleifer (1966), Baumol (1968), Arrow and Lind (1970), and Stiglitz (1982), newly reflected, in part, e.g., by Hanley (1992) and Grant and Quiggin (2003). It has, apart from distortionary taxation, particularly been referring to differing risk-pooling and risk-spreading capacities at the individual and social levels. The more recent literature has moreover considered, e.g., idiosyncratic and uninsurable income risks, agent heterogeneity, borrowing constraints, and transaction costs. To date, however, none of the puzzles has been fully solved Kocherlakota 1996, Mehra and Prescott 2003. In the following a theoretical argument provided by Grant and Quiggin (2003) is introduced. It substantiates the earlier arguments concerning risk pooling and spreading in the context of the debate on the equity premium puzzle. Grant and Quiggin formalise a statement by Mankiw (1986). Mankiw argued in an atemporal model with two dates that financial markets will not spread risks perfectly, if individuals, who are, ex ante, homogeneously exposed to risk, are, ex post, heterogeneously affected by catastrophes. Grant and Quiggin consider a framework where problems of adverse selection prevent individuals from insuring against systematic risk in labour income, modelled as the return to human capital. To state their argument, they study the formation of equilibrium asset prices in a model with two dates, t = 0, 1, using the state-claim approach. They assume a continuum of firms J uniformly distributed over the interval [0, 1], and a continuum of individuals I uniformly distributed over the rectangle [0, 2] × [0, 1]. Individuals are assumed as risk-averse expected-utility maximisers with concave von Neumann-Morgenstern utility indices, ui . Each individual is supposed to be endowed with human capital of quality hi and to be employed by firm j. More particularly, Grant and Quiggin define for each i ∈ [0, 2] the set of individuals who have human capital of quality hi as Hi ≡ {(i , j) : i = i} and assume that every individual (i, j) ∈ Hi has the same preference relation over contingent consumption. There are two types of firms, ‘risky’ and ‘safe’, depending on whether they will shut down in recession or not. The share ι ∈ [0, 1] of firms is assumed as risky, the remainder as safe. The type of a firm is supposed to be uncertain for anyone in the economy until uncertainty is resolved in t = 1. The model is normalised so that in the boom event both aggregate income and the return to human capital equal 1.Thus, in aggregate, the total endowment of

11

Thus, for U.S. data from 1889 to 1978 (2000), the average annual stock return amounted to 6.98 (7.9)%, while that on T-bills were at 0.8 (1.0)%, giving rise to an equity premium of 6.18 (6.9) percentage points. By contrast, the Mehra and Prescott (1985) model predicted a stock return of 14.1, a risk-free rate of 12.7%, and, thus, in particular an average equity premium of 1.4 percentage points. Qualitatively equivalent findings hold also for France, Germany, Japan, and the U.K. which together account for more than 85% of capitalised global equity value (Mehra and Prescott 2003).

20

2 Foundations of the Theoretical Analysis

human capital for the economy is h. Further crucial model parameters are the riskiness of returns to physical (i.e., non-human) capital relative to the returns to human capital, ν , and the probability of recession, π . In the model three states of the world arise. To the two global states, ‘boom’ (B) and ‘recession’ (R), add, for the case of recession, the two individual states of ‘job’ ( j) and ‘job loss’ (n j): (Bi) boom, occurring with probability 1 − π , (Ri j ) recession without job loss, occurring with probability π (1 − ι ), (Rin j ) recession with job loss, occurring with probability πι . νι ) In the boom state, any firm generates revenue equivalent to h + (1−h)(1− units 1−ι of the single consumption good, if it is safe, and h + (1 − h)ν , if it is risky, with ν > 0 by assumption. In both cases the wage paid to employee i by firm l is hi. The ι) payout to non-employees is (1−h)(1− in the case of a safe firm, and (1 − h)ν in the 1−νι case of a risky firm. In the recession state, safe firms generate the same income as in the boom state, paying the same amount to their employees and non-employee claimants. However, the risky firms vanish and seize to generate income. With respect to the financial market the model contains two types of securities, bonds and equity shares. The bond is assumed to be risk-free, in zero net supply, and to pay one unit of consumption in t = 1 in every state of the world. Equity is the total sum of the firms’ state-contingent non-wage or non-human capital payments. Equity supply is assumed to be fixed at one share. In the boom state, equity pays (1 − h), in the recession state (1 − h)(1 − νι ) units of the single consumption good. Each individual is supposed to be endowed with i units of equity and zero units of bonds. Moreover, the authors assume that trade in securities takes place before individuals have information about the index of the firm that employs them. No trade is possible after this information has become known. For their analysis, Grant and Quiggin then consider two kinds of personal insurance contracts, with a positive payout in state Ri1 and a negative payout in the other two states. In both cases, the insurance contracts must be entered into before individuals have information about the index of the firm which employs them. However, in the first case, the insurance contracts may not be renegotiated subsequently. As a result, idiosyncratic risk is fully pooled, i.e., for each i ∈ [0, 2] every individual in the set Hi will pool the returns to the individual’s human capital and, thus, receive the (deterministic) return (1 − ι )hi in the global recession event. In the second case, individuals are free to withdraw from the contracts after receiving private information about the index of their firm. Then, as a result of adverse selection, only individuals who find themselves employed by a risky firm will adhere to insurance contracts. Thus, in this case no pooling of idiosyncratic risk takes place. To derive the equity risk premium for the two cases, the authors first find, relying on standard theory, that for any securities market equilibrium and any individual i there exists a supporting vector (pBi ,pRi j ,pRin j ) of state-contingent claim prices, where each price ratio equates the marginal rate of substitution between the respective state-contingent consumption claims. Moreover, for ui strictly concave, the supporting price vector for individual i is unique. If the price b of a bond with payoff

2.1 Social versus Private Time Preferences

21

(1,1,1) is normalised to 1, the supporting state-contingent claims price vector may, thus, be derived as the solution of the following system of equations: pBi + pRi j + pRin j = 1 , pRi j π (1 − ι )u(yRi j ) , = pBi (1 − π )u(yBi ) pRin j πι u (yRin j ) , = pBi (1 − π )u(yBi )

(2.10)

with (yBi ,yRi j ,yRin j ) being the income vector of individual i. Since the boom state is the same for all individuals, and the set of securities spans the global boom and recession states, there exists a unique pB in equilibrium, satisfying for all i pB =

(1 − π )u(y

(1 − π )u(yBi ) , Bi ) + π (1 − ι )u (yRi j ) + πι u (yRin j )

(2.11)

which implies, from the normalisation b = 1, that for all i pRi j + pRin j = 1 − pB .

(2.12)

With b = 1, moreover, the price of a unit of equity may be expressed as pe = (1 − h)pB + (1 − h)(1 − νι )(1 − pB)

(2.13)

= (1 − h)[1 − νι (1 − pB)] . Since the expected return to a bond is 1 and that to a unit of equity is (1−h)(1−νιπ ), the risk premium for equity, q, expressed in proportional terms, is then given by q=

νι [(1 − π ) − pB] . 1 − νι (1 − pB)

(2.14)

In order to characterise the equilibrium price for a claim on a unit of income in the boom state, pB (and, hence, pe and q), first, for the case of full pooling of risk among each class Hi of individuals, second, for the case with no pooling of idiosyncratic risk, they consider the following portfolio budget constraint for individual i in t = 0: pe ηi + bi ≤ pe i ,

(2.15)

where ηi is the individual’s holding of equity, bi the individual’s holding of bonds. In the first case, where all individuals are able to pool their idiosyncratic risky returns to their human capital in the recession state, the common return vector of individuals i to human capital is [hi, (1 − ι hi)]. Given the portfolio (ηi , bi ), this gives rise to the income vector

22

2 Foundations of the Theoretical Analysis p yBi = hi + ηi(1 − h) + bi , p yRi j = (1 − ι )hi + ηi(1 − h)(1 − νι ) + bi , p yRin j

(2.16)

= (1 − ι )hi + ηi(1 − h)(1 − νι ) + bi .

Inserting the income vector (2.16) in equation (2.11) for the price of a claim to consumption in the boom state gives: (1 − π )ui[hi + ηi (1 − h) + bi] . (1 − π )ui[hi + ηi(1 − h) + bi] + π ui[(1 − ι )hi + ηi(1 − h)(1 − νι ) + bi] (2.17) In the second case, without risk pooling, the income vector is p

pB =

ynp Bi = hi + ηi (1 − h) + bi , np yRi j = hi + ηi(1 − h)(1 − νι ) + bi , ynp Rin j

(2.18)

= ηi (1 − h)(1 − νι ) + bi .

Hence, the price of a claim to consumption in the boom state has to satisfy for all individuals i (1 − π )ui[hi + ηi (1 − h) + bi] , (2.19) pnp B = E[u (y)] where E[u (y)] = (1 − π )u[hi + ηi(1 − h) + bi] + π (1 − ι )u[hi + ηi (1 − h)(1 − νι ) + bi] + πι u [ηi (1 − h)(1 − νι ) + bi] . Assuming prudent behavior in the sense of Kimball (1990), i.e. marginal utility, ui , strictly convex for all i, they show that, for given choices of (ηi , bi ), the price of a claim to consumption in the boom state in the case without risk pooling must exceed p that of the case with risk pooling, pnp B > pB , which, according to equation (2.13), np this also holds for the equity prices, pe > pep , and, thus, by equation (2.14), for the p equity premia, qnp e > qe . That is, the absence of the capacity to pool idiosyncratic risk leads to an enhanced risk premium for equity. Grant and Quiggin derive their result in an atemporal model with two dates. Further distortions absent, they show that an equity (risk) premium arises as a result of a market failure stemming from adverse selection, when an insurance contract against idiosyncratic income risk may be renegotiated after uncertainty is resolved. When risk-averse individuals can, thus, not fully spread the risk associated with recession, they are less willing to hold equity than they would be in a world of perfect financial markets. The static model Grant and Quiggin (2003) analyse does not permit to consider the possibility of smoothing consumption over time through borrowing, lending, or asset liquidation. One objection raised by Kocherlakota (1996) in this respect against Grant and Quiggin’s predecessor model by Mankiw (1986) is that difficulties

2.1 Social versus Private Time Preferences

23

associated with the absence of insurance markets could be overcome by intertemporal consumption-smoothing. However, Kocherlakota’s argument is based on the assumption that individuals can borrow and lend freely at the bond rate. Thus, Grant and Quiggin maintain that, since governments can borrow and lend freely at the bond rate in their model, a dynamic analogue of it, where individuals face idiosyncratic human capital risks that are correlated with systemic risks to equity that unfold through time, would yield results similar to those derived in the static context. The importance of Grant and Quiggin’s argument in the context of the present analysis is obvious. In liberalised markets, (private) utilities rely upon the private financial market to finance investments in new technologies. Any negative distortion of it, as induced, e.g., by uninsurable risks, tends to hamper private investment. Grant and Quiggin’s suggestions to increase social efficiency have briefly been considered in subsection 2.1.1.2. The treatment of the distortions in the conditions of structural technological change in the energy sector proposed in section 3.4 is generally in vein with their second suggestion.

2.1.2.3 Declining Social Discount Rate in View of an Uncertain Future According to Gollier (2002a) Gollier (2002a) studies the effect of uncertain growth in the long run on the social rate of time preference, δ , considering particularly the importance of risk preferences in this context. His motivation is that financial markets hardly provide an optimal guideline for investing in technologies that prevent long-lasting risks to occur, as liquid financial instruments with such maturities do not exist.12 Instrumental to his model is the concept of prudence, as formalised by Kimball (1990). An agent is prudent if his willingness to save increases in the face of an increase in his future income risk or, technically, if the third derivative of his utility function is positive. Gollier shows that prudence leads, first, to a social discount rate that is smaller than in the case of certain growth, and, second, moreover to one that declines over time.13 In order to state his argument, Gollier departs from the framework of a ‘tree economy’ (Lucas 1978) in which each individual is endowed with some productive capital, a ‘tree’, generating a number of ‘fruits’ in each period. There is no possibility to plant new trees. The number of fruits, i.e. the income or, equivalently, consumption, is assumed to grow in period t at the uncertain and exogenous rate gt , the gt being independently and identically distributed over time for all t. For simplicity, he concentrates on a two-period model with three dates, t = 0, 1, 2. He defines c = c0 as consumption in t = 0 and ct = ct−1 (1 + gt ) as consumption at dates t = 1, 2. Seen 12 Time horizons, e.g., of government bonds generally do not exceed 40 years, whereas relevant time horizons associated with global climate change extend, at least, over some 100 years. 13 With respect to the shape of the socially efficient discount rate, Weitzman (1998) derived a similar result studying the effect of uncertainty of the social rate of return to capital, is , on the social discount rate, assuming risk neutral agents. His analysis omits, however, the explicit treatment of risk preferences. See Groom et al. (2005: 460–465) for a discussion.

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from t = 0, the ct for t = 1, 2 are uncertain. In order to describe the effect of uncertain growth on the short-term behaviour of the discount rate, he first considers only the first period. To disentangle the attitudes towards time and risk, Gollier assumes for the social planner Kreps–Porteus–Selden preferences (Kreps and Porteus 1978, Selden 1979). He represents them by defining the certainty equivalent consumption m in t = 1, as usual under expected utility theory: v(m) = Ev( c1 ) ,

(2.20)

and intertemporal social welfare as: u(c) + (1 + ρ )−1u(m) ,

(2.21)

where the utility functions v and u are assumed to be increasing and weakly concave in their argument, and ρ is the social rate of pure preference. For u ≡ v, from this representation the intertemporal time-separable expected utility model derives, with the classical objective function, v(c) + (1 + ρ )−1Ev( c1 ) .

(2.22)

In this economy the only possibility is to invest in some prevention effort to improve future individual crops. To evaluate the effect of the uncertain growth on the socially optimal discount rate, Gollier considers when society should invest in a marginal project which costs a small x (Δ c = −x) in t = 0 and brings a sure benefit (1 + r)x in period t = 1. This sure benefit increases the certainty equivalent consumption in t = 1 by

∂ m c1 ) Ev ( (1 + r) . = ∂ x x=0 v (m)

(2.23)

The social welfare function (2.21) is increased by this investment if: −u (c) + (1 + ρ )−1 u (m)

∂ m ≥ 0 ∂ x x=0

(2.24)

or, equivalently, r ≥

u (c) v (m) − 1 = δ1 , −1 (1 + ρ ) u (m) Ev ( c1 )

(2.25)

where δ1 is the social rate of time preference in period 1, here equivalent to socially efficient discount rate, corresponding to the equilibrium risk-free rate in this exchange economy. Gollier now compares δ1 and δ1c , the socially optimal discount rate in an economy with a sure consumption level equal to E c1 in t = 1. As without uncertainty risk aversion does not matter, the certainty equivalent in such an economy is then m = E c1 , such that

2.1 Social versus Private Time Preferences

δ1c =

u (c) −1 . (1 + ρ )−1 u (E c1 )

25

(2.26)

From conditions (2.25) and (2.26) for time-separable expected utility preferences with u ≡ v follows: δ1 ≤ δ1c ⇔ Ev ( c1 ) ≥ v (E c1 ) . (2.27) As the right-hand side constitutes Jenson’s inequality, equivalence (2.27) holds for any c and any distribution of c1 , if and only if the marginal utility of consumption, v , is convex. Thus, uncertainty in growth will reduce the discount rate, or, equivalently, precautionary saving will occur, if and only if individuals behave in a prudent way (v > 0). In order to describe the effect of uncertain growth on the long-term behaviour of the discount rate, Gollier extends the analysis to the second period, with (1+ g1 )(1+ g2 ) − 1 being the growth rate over the two periods. While with u ≡ v, according to condition (2.25) the socially optimal (gross) rate to discount costs and benefits occurring at date t = 1 is 1 + δ1 =

u (c) , (1 + ρ )−1E[u (c(1 + g1))]

(2.28)

the socially optimal discount rate per period for a cash flow occurring at t = 2 derives as: u (c)

. (1 + δ2)2 = (2.29) (1 + ρ )−2E u (c(1 + g1)(1 + g2)) Gollier notes that δ2 is not equal to δ1 , except in the case of the isoelastic utility function, with v (c) = cφ for some constant relative risk aversion φ > 0, as can easily be seen departing from conditions (2.28) and (2.29), which yield for v (c) = cφ with φ > 0: (1 + δ1)2 = [(1 + ρ )−1E(1 + g1)−φ ]−2

= (1 + ρ )2 [E(1 + g1)−φ E(1 + g2)−φ ]−1 = (1 + ρ )2 [E((1 + g1)(1 + g2))−φ ]−1 = (1 + δ 2)2 ,

(2.30)

implying that δ 2 = δ1 . Thus, for constant relative risk aversion the wealth effect of a longer time horizon just compensates the precautionary effect. Using conditions (2.29) and (2.30), Gollier then shows that for the consumption growth rate nonnegative almost surely and a three times differentiable utility function v, the following equivalence holds,

δ2 ≤ δ1 ⇔ v (c)E v [c(1 + g1)(1 + g2)] ≥ E v [c(1 + g1)]v [c(1 + g2)] , (2.31) if there is, in addition to the former assumptions, decreasing relative risk aversion.14 Thus, in the case of an almost surely positive growth rate per period, prudent Gollier (2002a: 158) provides the following proof: Let function h: R2+ → R, h(x1 , x2 ) ≡ v (cx1 , x2 ), be log supermodular, i.e. for all (x1 , x2 ), (x1 , x2 ) ∈ R2+ :

14

26

2 Foundations of the Theoretical Analysis

behavior and decreasing relative risk aversion are sufficient, first, for the socially efficient discount rate to stay below that in the case of certain growth, and, second, for the long-term discount rate to be smaller than the short-term one. The latter result also extends on indeterminate, and thus in particular infinite, time horizons (Gollier 2002a,b). That is, with increasing time horizon, the socially efficient discount rate declines. Gollier (2002a) provides a theoretically most rigorous rationale for declining discount rates. His analysis implies potentially testable propositions derived from expected utility theory. The formal economic foundation of the determination of long-term discount rates avoids ad-hoc adjustments of the discount rate. The complexity of the analysis depends on the assumptions concerning the probability distribution of growth and the intertemporal relationships. For convenience, although unrealistic, Gollier (2002a) assumes that the growth shocks are i.i.d. He, thus, avoids the complications associated with the analysis of serially correlated shocks. At the same time, to determine the trajectory of the social discount rate based on his analysis knowledge about the aversion to consumption fluctuations over time, the pure time-preference rate, and the degree of relative risk aversion is necessary. In addition, the probability distribution of growth has to be characterised in some way. Thus, an actual empirical application of his approach would be associated with high informational requirements. The importance of Gollier’s study for the present analysis coincides with its motivation. Gollier’s aim is to determine the socially optimal discount rate for public investment projects that entail costs and benefits in the very long run, thus, the time horizons of which extend far beyond the longest maturity of any security available. His focus is on the effect of uncertain (consumption) growth. While he does not treat a specific source of uncertainty, it is clear that anthropogenic climate change may constitute an important cause. Prudent behavior, which is crucial for his argument, occurs as a rational strategy in the face of uncertainty. The factual inability of financial markets to reflect, and, in particular, to insure against, such long-term risks

h[min(x1 , x1 ), min(x2 , x2 )] h[max(x1 , x1 ), max(x2 , x2 )] ≥ h(x1 , x2 ) h(x1 , x2 ) . For x1 = x2 = 1 and all x1 , x2 > 1, the log supermodularity of h implies: h(1, 1) h(x1 , x2 ) ≥ h(1, x2 ) h(x1 , 1) , which is, for all g1 = x1 − 1 and g2 = x2 − 1 with g1 , g2 > 0, equivalent to v (c) v [c(1 + g1 )(1 + g2 )] ≥ v [c(1 + g1 )] v [c(1 + g2 )] . Given an almost surely positive growth rate per period, the log supermodularity of h is sufficient to guarantee that the latter condition holds almost everywhere. Taking the expectation of this inequality directly yields inequality (2.31), which implies in turn that δ2 < δ1 . For a three times differentiable utility function v, the log supermodularity of h means, furthermore, that the cross derivative of log h is positive, which is equivalent to require that relative risk aversion is decreasing.

2.1 Social versus Private Time Preferences

27

constitutes another case for welfare-enhancing government intervention. Therefore, Gollier’s analysis implies another second-best case relevant for the present analysis.

2.1.3 Summary and Treatment of the Assumption in the Model This subsection summarises the findings from the analysis of the discounting literature, states open issues, and then describes the treatment of the assumption in the model below and the contribution of the analysis.

2.1.3.1 Summary of the Findings from the Analysis of Discounting Literature In this section, as a benchmark for the further discussion, first, the first-best case was restated with reference to Ramsey’s (1928) basic model. It establishes the equality of the above mentioned rates (2)–(7), including, in the case of the absence of growth, rates (1) and (8), and thus of the social and private rates of (pure) time preference. Then deviations from first-best conditions were considered. It was shown that there exists in economics a series of well recognised reasons for the social and private rates of time preference to differ in real world. They include distortionary taxation, distortionary public investment, imperfect competition, and production externalities. They generally imply the social rate to stay below the private. Moreover it was shown that (private) hyperbolic discounting may lead to the same conclusion of a socially efficient rate of time preference staying in general below the private, and that also experimental evidence supports this divergence. In addition, the corresponding (negative) spread between government and private security rates of any maturity is a well established fact in finance. Economists have thus been advancing over Baumol’s (1968) ‘dark jungles’ insofar as there is now wide unanimity that and how in general social and private rates of time preference differ. Economists also widely agree about optimal policy treatments for the four mentioned, well established causes for the split of time-preference rates, at least in theory. Thus, while the welfare-theoretic consequences of diverging time-preference rates for private investments have never systematically been addressed, in this respect these four causes do not constitute an issue. In subsection 2.1.2, however, three reasons were introduced, which are clearly relevant for investments in the energy sector but also clearly go beyond the four standard cases. As put forward by Weitzman (1994), Grant and Quiggin (2003) and Gollier (2002a), they relate, respectively, to increasing environmental externalities over time as well as adverse-selection problems or uninsurable long-run risks as inducing financial-market distortions. The arguments were set out in detail in order, first, to illustrate the current heterogeneity of approaches to state causes for the split discount rates, and, second, to further detail to some extent the complexity of the aspects that matter.

28

2 Foundations of the Theoretical Analysis

Among the three contributions only Grant and Quiggin (2003) consider possibilities of internalisation with respect to the second-best case they deal with. The two approaches they discuss – insurance provision and (redistributive) subsidies (subsection 2.1.1) – stand for two major policy options. Their considerations point, however, at the same time to significant transaction-cost, incentive, and feasibility issues which may be generally related to the implementation of such policies. Weitzman (1994) and Gollier (2002a) do not reflect on second-best implications. Given that the discount-rate distortion considered by Weitzman arises only due to environmental externalities, only the case of incomplete environmental policies, as possibly occuring in practice, would let it persist as a second-best issue. In this case a direct correction of the discount rate might occur as a useful complementary second-best policy. The reduced-form set-up of his model does, however, not allow for a respective extension of the analysis. To cope with distortions from uninsurable long-run risks as pointed out by Gollier also the two policy approaches considered by Grant and Quiggin constitute possible general options. Taking into account in addition the three contributions considered in subsection 2.1.2, six further points can be retained with respect to second-best issues relating to the split social and private time-preference rates.15 First, neither the causes of the split nor policy implications associated with it or the welfare and policy implications as directly induced by it have, thus far, been subject to a systematic analysis. Second, to explain the causes of the split at present no unique or encompassing framework is available. Rather a multitude of different models prevails. Third, the variety of models and explanations does not only show the particular complexity of relevant aspects to be taken into account, but indicates in particular that the split is in general induced by several causes. Fourth, the split in itself does not constitute a market failure, but may be – though not necessarily, e.g., in the case of distortionary policies – induced by an underlying one. It is, however, in general the sign of the existence of a welfare-decreasing distortion in the economy. Fifth, there exists a number of reasons, such as transaction costs or incentive issues, for which the split in itself, rather than an underlying market failure directly, may be the point of reference for a welfare-enhancing policy intervention. Finally, there is a number of cases of market failure which are clearly relevant for investments in the energy industry under the condition of anthropogenic climate change and for which no optimal policy treatment is established.

2.1.3.2 Treatment of the Assumption in the Model The present study is interested in the welfare-theoretic implications of the split of social and private time-preference rates for the conditions of structural technological change in the energy sector. In line with this focus the subsequent model analysis just departs, like Arrow and Kurz (1970: 116), from differing time preferences of 15 Note that, though necessarily incomplete, the analysis of the literature has been including the major surveys as well as a number of key contributions in detail. The following statements are consistent with the whole of the literature consulted.

2.2 Time-Lagged Capital Theory

29

the representative consumer and the society, assuming in particular the private rate of time preference to exceed the social (section 3.1). In view of the multitude of different reasons relevant for the split and the to a good part still open state of discussion with respect to causes, an endogenous explanation of the split is avoided. Thus, e.g., the public sector (apart from the regulator), financial markets, eventual imperfections of the commodity markets, production externalities, and uncertainty remain exogenous to the analysis. Moreover, the specification of the environmental externality is such that it does not influence the private time preferences. This proceeding allows for the most general analysis of the welfare and policy implications of this assumption. In the light of the above literature analysis the claim of generality needs, however, a qualification in two respects. First, the welfare implications of the split, whatever they are, occur always, irrespective of the particular causes of the split. Second, a policy intervention aiming at the correction of the consequences of distorted timepreference rates is only justified, if and only if the split is induced by an underlying market failure which cannot directly or differently be remedied. Thus, also for the most general study of policy implications of the split, the analysis is to be restricted, on welfare-theoretic grounds, to only the respective subset of all causes. Accordingly, the investigation below provides a general clarification with respect, first, to the welfare implications of the split for private investments irrespective of its causes, and, second, to its policy implications for a certain class of causes. However, it does not shed further light on particular causes of the split, their implications for the determination of the social discount rate or policy implications directly related to the causes.

2.2 Time-Lagged Capital Theory Structural change is usually defined as a change in the relative composition of an economy’s capital stocks. In this study, as applied to the energy sector, it is assumed to be characterised by a shift in the relative use of different energy technologies over time. It thus usually occurs, e.g., when an old, established energy technology is partially or fully replaced by a new one. In the energy industry this kind of technological change is particularly marked by two features. First, power plants are particularly long-lived and cost-intensive capital goods. That is, as compared to other private investment projects, their construction necessitates a particularly large reallocation of resources from other opportunities in the economy, which, of course, will only be made if it seems economically profitable. Therefore, the current conditions of investment and replacement are instrumental to determine whether and when structural change will occur. Second, the construction period of a new power plant is often particularly long as compared to other investment projects. Economically speaking, there is a substantial time lag – to be designated by σ in the following – between the costs of investment and the benefits of production of new capital goods.

30

2 Foundations of the Theoretical Analysis

The kind of economic modeling that exactly captures these two features is timelagged capital theory. In chapter 3 it is used to analyse the transition from an established polluting to a new clean energy technology. This section briefly highlights the historical evolution of time-lagged capital theory and introduces the basic model of the particular strand which is taken up in this study (subsection 2.2.1). Subsection 2.2.2 describes the contributions made to its further development in this study.

2.2.1 Its Evolution and the Basic Neo-Austrian Three-process Model The idea of time-lagged capital accumulation goes back to the Austrian school of economics, especially to the work of von B¨ohm-Bawerk ([1889]1921).16 It was revived by the neo-Austrian capital theory in the 1970s. Von Weizs¨acker (1971), Hicks (1973), and Faber (1979) stand for three major approaches in this vein. With Kydland and Prescott (1982) the time-to-build feature became, moreover, prominent in the modern macroeconomics real business cycle literature. The modeling framework used in the following analysis stands in the tradition of the third of the three strands of neo-Austrian capital theory.17 This approach is basically characterised by its basic three-process model. It studies the conditions of innovation of a new production technique, T2 , which is only to be produced, into a system with an already existing technique, T1 (Faber and Proops 1991, Winkler 2005). A technique is defined as the minimal combination of production processes necessary to produce the consumption good from non-produced inputs. The two techniques are assumed to produce a homogeneous consumption good c(t) = c1 (t)+ c2 (t). Labor is the only primary input. It is usually supposed to be given in a fixed amount l¯ at all times t. Thus, while T1 produces c1 (t) from labor l1 (t) alone, T2 comprises an additional capital good production process in order to generate c2 (t) from labor l2 (t) and capital k(t).18 However, capital good production is assumed to be time-lagged by one period, such that the equation of motion of the capital stock is k(t) =

16

l3 (t − 1) + (1 − γ )k(t − 1) , λ3

(2.32)

Austrian economists were particularly interested in the issues of time and change in the economy. Schumpeter (1934, 1939), e.g., particularly dealt with structural technological change as an aspect of evolutionary change in the economic process. 17 Further important contributions to this strand include, e.g., Bernholz et al. (1978), Faber (1986), Faber and Proops (1991, 1998), Faber et al. (1995, 1999), Stephan (1995), and Winkler (2003, 2005). See Winkler (2003: ch. 2) for a survey of the development of capital theory in general and its neo-Austrian variant in particular. 18 By convention, all three production processes have usually been assumed to be linearlimitational. In equilibrium, labor is efficiently allocated to the three processes, such that l¯ = l1 (t) + l2 (t) + l3 (t), where l3 (t) is the amount of labor used in the capital good process.

2.2 Time-Lagged Capital Theory

31

where λ3 is labor coefficient of capital good production, γ the deterioration rate of capital. Both are assumed to be constant and exogenously given. Crucial concepts for the statement of the necessary and sufficient investment conditions are those of the roundaboutness and superiority of techniques. A technique (T2 in the present case) is said to be more roundabout than another technique (T1 in the present case), if and only if it needs more time to produce the same amount of c(t) as the other technique (T1 in the present case). A technique is called superior to another one, if and only if for a given endowment of non-produced inputs the maximal producible sum of consumption goods within the given time horizon τ is larger for that technique than for the other one. Suppose a representative consumer who maximises her aggregate utility from consumption over time with a positive rate of time preference ρ > 0. Then, obviously, superiority of T2 over T1 is a necessary condition for the innovation of T2 to be optimal. For sufficiency, T2 has to yield a higher intertemporal utility to the representative consumer within the given time horizon τ than T1 . This is satisfied for a representative consumer with rate of time preference ρ > 0 and given positive time horizon τ , if her instantaneous utility function U(c(t)) is concave, i.e. Uc > 0, Ucc < 0. Initially formulated for finite time horizons the modeling framework was extended to infinite time horizons by Stephan (1983, 1985, 1995). More recently Winkler (2003, 2005, 2008) provided a series of further refinements and extensions. He proved that the necessary and sufficient conditions for innovation of the new technique can be derived from the first-order conditions of the respective intertemporal optimisation problem. He systematically analysed the effect from joint production of the consumption or the capital good and a flow or stock pollutant, respectively, on the necessary and sufficient conditions for innovation. Moreover, he considered, as means of pollution treatment, the cases of complete abatement and the imposition of an emission standard as well as, separately, the negative valuation of environmental degradation by emissions entering into the utility function in addition to consumption. In no case he considers market interactions. He formulated and solved the model in continuous time using optimal-control techniques and calculated optimal paths of the model variables by use of numerical methods. Finally, he considered a version of the model with the consumption-good sector modeled by a Cobb-Douglas function in which two new clean energy technologies compete for their introduction in a system with an established polluting energy technology. While the analysis in this framework has usually been carried out for a centralised economy, Stephan (1995) has discussed prices and price systems in finiteand infinite-horizon models of the neo-Austrian kind in discrete time. He proves, however, only the existence and Pareto optimality of a general equilibrium in an economy with markets only for non-durable goods. The modeling framework has, thus far, not yet been used for the explicit analysis of market failures in a decentralised economy with a complete market system. Nor have in this framework ever the effects from diverging social and private rates of time preference or the interplay between different kinds of technological change been analysed.

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2 Foundations of the Theoretical Analysis

2.2.2 New Extensions The model set up in the next chapter takes up (a slightly modified version of) the basic three-process model with infinite time horizon and adds, in a new combination, different elements developed in a general way by Winkler (2003, 2005). As compared to the basic neo-Austrian three-process model the consumption-good sector is substituted for an energy sector. For convenience, utility is assumed to directly derive from energy consumption. The model is formulated in continuous time. It takes into account joint production of energy and emissions. The latter are supposed to be negatively valued by the consumer. In addition to that, for the analysis aimed at in the present study the modeling framework is methodically further extended in three new ways: 1. By introducing a complete market system, it is now opened to the explicit analysis of market failures, and their remedying, in the standard framework of Paretian welfare economics. 2. The specification of an abatement function allows to analyse the interplay of two kinds of technological change, gradual, i.e. the (gradual) refinement of a technology by enactment of an end-of-pipe abatement technology, and structural.19 3. In addition to the social, private time preferences are considered which may differ from the social. On the level of modeling these three elements systematically extend the former framework of this kind of time-lagged capital theory. All of them are essential for the analysis in chapter 3, the results of which are particularly driven by the emission externality, the split of social and private rates of time preference and the timelagged structure of capital accumulation.

2.3 Analytical Structure of the Model in Chapter 3 The model developed in chapter 3 to study the conditions of structural change in the energy industry under the conditions (i)–(iv) as specified in section 1.1 is an intertemporal general equilibrium model with infinite time horizon formulated in continuous time. The infinite time horizon has been chosen in order to analytically concentrate on the effects related to the (constant) rate of time preference as the only other remaining time-related parameter. The agents – the regulator in the cases of the centralised and the regulated decentralised economy, the representative Ramsey consumer and two representative firms in the cases of the unregulated and regulated decentralised economy – are supposed to maximise their intertemporal welfare or their profits, respectively, under certain constraints subject to the standard

19 The term gradual has only been adopted in this study in order to terminologically distinguish this kind of technological change from the notion of structural technological change.

2.4 Conclusion

33

assumptions of full rationality and complete certainty.20 On the production side a vertically integrated time-lagged production system is assumed composed of an energy and an investment sector. From the model necessary and sufficient conditions for investment in the new technology and for partial and full replacement of the established technology are derived, both at the social optimum and in the unregulated market equilibrium. To derive these conditions the stationary states occurring in the optimal development of the economy are exploited. Two stationary states, both at the social optimum and in the unregulated competitive market equilibrium, arise as a consequence of the linear or linear-limitational functions assumed in the production sectors, which provide the respective corner solutions.21 At the social optimum, in addition, a third stationary state occurs associated with an interior equilibrium. The method used to solve the agents’ intertemporal optimisation problems is time-lagged optimal control theory. In general, optimal control theory provides the optimal paths of the control variables (i.e., those variables the actor can influence) which maximise a goal functional (here, the intertemporal welfare function of the regulator or the representative consumer, respectively) subject to a given set of stock variables and their dynamics and a set of further restrictions. The understanding of the solutions requires some familiarity with optimal control theory and the theory of ordinary differential equations.22 At places requiring a particular knowledge, e.g., with respect to the time-lagged nature of the problem analysed, respective references are indicated. All results presented have been derived analytically, i.e. without use of numerical methods. In particular, the question under study did not require the consideration of the optimal paths of variables out of the stationary states. However, in general, as soon as the investigation had been extended to the explicit analysis of such optimal paths the use of numerical methods would have been necessary.

2.4 Conclusion In this chapter the literature behind the two distinctive features in the following model analysis was considered and the relationship and contribution of this study to it was described, first with respect to the crucial assumption of the split of social and private time-preference rates, then with respect to time-lagged capital theory. At the same time it was introduced to the theoretical issue of this study. Finally the analytical structure of the model at the basis of the analysis in the following chapter was explained. In the next chapter the theoretical model of structural technological change in the energy sector is introduced and analysed. 20

The assumptions of exponential (e.g., versus hyperbolic) discounting and certainty, and their relationship to the subsequent analysis have been discussed in section 2.1. 21 The rationale for these specific functional forms as well as further assumptions concerning the energy industry and their analytical implications are discussed in section 4.2. 22 Useful general treatments of optimal control theory can be found, e.g., in Chiang 1992, Feichtinger and Hartl 1986,Gandolfo 1996 and Kamien and Schwartz (1991).

Chapter 3

A Theoretical Model of Structural Change in the Energy Industry

In this chapter, a theoretical model is developed to study the transition from an established polluting to a new clean energy technology, if (i) the social rate of time preference stays below the private, (ii) the creation of new productive capital is time-lagged, (iii) emissions are negatively valued, and (iv) an end-of-pipe abatement technology is available. Section 3.1 introduces the model economy and specifies social and individual preferences. In sections 3.2 and 3.3, from the model necessary and sufficient conditions both for investment in the new and for replacement of the established technology are derived for the cases of the social optimum and an unregulated competitive market economy, respectively. It is shown that, in addition to that induced by the emission externality, a further distortion arises due to the split of the social and private rates of time preference, the extent of which positively depends on the time lag in capital accumulation. Section 3.4 shows how the two distortions can be corrected via environmental and technology regulation.1

3.1 Model Consider an economy with a production system composed of two vertically integrated sectors, the energy sector and the investment sector. Labor constitutes the only primary input. By assumption, it is fixed to unity at all times t. The energy sector comprises two technologies, an established and a new one. The established technology is assumed to be fully set up at the beginning of the planning horizon. As a consequence, capital is not explicitly considered for the established technology, but the costs of employing and maintaining the capital stock are included into the labor costs, which are normalised to 1. The established technology generates one unit of energy x for every unit of labor l1 employed. In addition, each unit of energy produced gives rise to one unit of an unwanted and harmful joint output j: 1

The chapter is mainly based on Heinzel and Winkler (2006).

C. Heinzel, Distorted Time Preferences and Structural Change in the Energy Industry, Sustainability and Innovation, DOI 10.1007/978-3-7908-2183-3 3, © Physica-Verlag Heidelberg 2009

35

36

3 A Theoretical Model of Structural Change in the Energy Industry

x1 (t) = l1 (t) , j(t) = x1 (t) = l1 (t) .

(3.1) (3.2)

The joint output can be (partially) disarmed by abatement. Let a denote the abatement effort per unit of output (or joint product, respectively). The function G denotes the fraction of the joint output j which is disarmed by abatement. G is assumed to be concave and twice continuously differentiable, satisfying: G(0) = 0 ,

G > 0 ,

G < 0 ,

lim G(a) = 1 .

a→∞

(3.3)

Moreover, the Inada conditions are imposed: lim G (a) = ∞ ,

a→0

lim G (a) = 0 .

a→∞

(3.4)

They ensure that the abatement effort a along the optimal path is strictly positive and finite as long as l1 is positive. As a consequence, net emissions e equal the amount of joint output j minus abatement: (3.5) e(t) = x1 (t) 1 − G(a(t)) . The new technology employs λ units of labor together with κ units of the capital good k to produce one unit of energy:

l2 (t) k(t) x2 (t) = min , . (3.6) λ κ Assuming an efficient labor allocation among the three production processes in the two sectors, i.e. 1 = (1 + a(t)) l1 (t) + l2 (t) + i(t) ∀t, an initial capital stock of k(0) = 0, and intertemporal welfare as defined in equations (3.9) and (3.10) below, full employment of the capital stock can be shown to be efficient (Winkler 2005), and equation (3.6) yields x2 (t) = l2λ(t) = k(t) κ . In contrast to the established technology, the new one does not produce any unwanted joint output.2 Energy is supposed to be homogeneous. Thus, total energy production x equals: x(t) = x1 (t) + x2(t) .

(3.7)

The investment sector employs one unit of labor to produce one unit of the capital good. It is assumed that it takes a positive time span σ to turn the investment i into productive capital k, which, in turn, deteriorates at the constant and exogenously given rate γ . Therefore, the equation of motion for the capital stock k reads: dk(t) = i(t − σ ) − γ k(t) . dt 2

(3.8)

The non-pollution assumption of the new technology is without loss of generality as compared to the case of positive but less pollution, because the optimality condition only depends on the difference of the pollution factors.

3.1 Model

37

Due to the time lag σ , the equation of motion for the capital stock (3.8) constitutes a retarded differential-difference equation, such that variations of the capital stock k do not only depend on parameters evaluated at time t, but also on parameters evaluated at the earlier time t − σ . To close the model, consider a representative consumer who derives instantaneous utility from energy consumption and disutility from net emissions.3 Like Arrow and Kurz (1970: 116), the representative consumer’s private time preferences are, however, assumed to differ from the social.4 More particularly, the representative consumer is supposed to apply different intratemporal weights between utility derived from consumption and disutility derived from net emissions, and different intertemporal weights, i.e. rates of time preference, between welfare today compared to welfare tomorrow, as the social planner maximising social welfare. For the sake of simplicity, instantaneous welfare is assumed to be additively separable in energy consumption x and net emissions e. As a consequence, the representative consumer (privately) maximises Wp =

∞

U(x(t)) − α D(e(t)) exp[−ρ pt] dt ,

0

(3.9)

while, at the same time, the social planner maximises W=

∞ 0

U(x(t)) − D(e(t)) exp[−ρ t] dt ,

(3.10)

where U and D are twice differentiable functions with U > 0, U < 0, and limx→0 U = ∞ and D (0) ≥ 0, D > 0 for any positive amount of emissions e, and D > 0. Without loss of generality, it is assumed in the following that the weighting factor α = 1, as it has no effect on the outcome of the analysis. This holds because net emissions e constitute an externality in the unregulated market solution, which is not taken into account by the market mechanism, and, thus, the market outcome is independent of the individual valuation of the disutility derived from net emissions. However, as regards intertemporal valuation, the private rate of time preference ρ p is assumed to exceed the social rate of time preference ρ , i.e. ρ p > ρ .

3

Obviously, CO2 is a stock and not a flow pollutant. However, assuming the negative externality on utility to be caused by the emissions and not the global stock simplifies the further calculations without impacting on the qualitative results (for further discussion, see subsection 4.2.5). 4 This assumption as well as its motivation in the context of the present analysis have been discussed in detail in section 2.1.

38

3 A Theoretical Model of Structural Change in the Energy Industry

3.2 Social Optimum Now the optimal plan for the development of the model economy as outlined in section 3.1 is derived. Social welfare is assumed to be given by equation (3.10). Thus, the social planner solves the following maximisation problem: max W =

a(t),i(t)

∞ 0

U(x(t)) − D(e(t)) exp[−ρ t] dt ,

(3.11a)

subject to 1 − λκ k(t) − i(t) 1 + k(t) , 1 + a(t) κ 1 − λ k(t) − i(t) κ e(t) = 1 − G(a(t)) , 1 + a(t) x(t) =

dk(t) = i(t − σ ) − γ k(t) , dt i(t) ≥ 0 , l1 (t) ≥ 0 , k(0) = 0 , i(t) = 0 ,

(3.11b) (3.11c) (3.11d) (3.11e) (3.11f) (3.11g)

t ∈ [−σ , 0) .

(3.11h)

For the dynamics of the model economy it is important that, due to the linearity of the production techniques, two corner solutions can occur along the optimal development path. Either, it can be optimal to only use the established technology at all times, which corresponds to i(t) = 0 ∀t. Or, if investment in the new technology is optimal (i.e. i(t) > 0 ∀t), it may eventually be optimal for the new technology to fully replace the established one and thus l1 (t) = 0 ∀t ≥ t . As a consequence, these two corner solutions have to be checked explicitly, apart from the inner solution, in order to characterise the complete dynamics of the model economy.

3.2.1 Necessary and Sufficient Conditions for Social Optimum The optimisation problem (3.11) is solved by applying the generalised maximum principle derived in El-Hodiri et al. (1972) for time-lagged optimal control problems. One obtains the following present-value Hamiltonian H :

3.2 Social Optimum

39

H = U(x(t)) − D(e(t)) exp[−ρ t] 1 − λκ k(t) − i(t) 1 + k(t) − x(t) + qx (t) 1 + a(t) κ 1 − λ k(t) − i(t) κ + qe (t) 1 − G(a(t)) − e(t) 1 + a(t)

(3.12)

+ qk (t + σ )i(t) − qk (t)γ k(t) + qi (t)i(t) + ql1 (t)

1 − λκ k(t) − i(t) , 1 + a(t)

where qk denotes the costate variable or shadow price of the capital stock k, and qx , qe , qi and ql1 denote the Kuhn-Tucker parameters for the (in)equality conditions (3.11b), (3.11c), (3.11e) and (3.11f). Assuming the Hamiltonian H to be continuously differentiable with respect to the control variables a and i, the following necessary conditions hold for an optimal solution: qx (t) = U (x(t)) exp[−ρ t] , qe (t) = qx (t)l1 (t) = 1 + a(t) qx (t) = 1 + a(t) dqk (t) = dt

(3.13a)

−D (e(t)) exp[−ρ t] , (3.13b)

ql (t)l1 (t) 1 − G(a(t)) −qe (t)l1 (t) G (a(t)) + , (3.13c) + 1 1 + a(t) 1 + a(t)

ql (t) 1 − G(a(t)) −qe (t) , (3.13d) + qk (t + σ ) + qi(t) − 1 1 + a(t) 1 + a(t) ql1 (t)λ λ (1−G(a(t)) 1+a(t) − λ qe (t) − qx (t) + qk (t)γ + , κ (1+a(t)) κ (1+a(t)) κ (1+a(t))

qi (t) ≥ 0 ,

qi (t) i(t) = 0 ,

(3.13e) (3.13f)

ql1 (t) ≥ 0 ,

ql1 (t)l1 (t) = 0 .

(3.13g)

As the maximised Hamiltonian is concave (cf. appendix A.1), the necessary conditions (3.13a)–(3.13g) are also sufficient if, in addition, the following transversality condition holds: (3.13h) lim qk (t)k(t) = 0 . t→∞

Due to the strict concavity of the maximised Hamiltonian, the optimal solution is also unique. Conditions (3.13a) and (3.13b) state that along the optimal path the shadow price of energy equals the marginal utility of energy and the shadow price of net emissions equals the marginal disutility of net emissions. From condition (3.13g) we know that ql1 l1 = 0 holds at all times t. Hence, the last term in condition (3.13c) equals 0 and, as long as l1 (t) > 0, inserting conditions (3.13a) and (3.13b) leads to:

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3 A Theoretical Model of Structural Change in the Energy Industry

U (x(t)) = D (e(t)) G (a(t)) (1 + a(t)) + 1 − G(a(t)) .

(3.14)

This condition expresses that along the optimal path (and as long as condition (3.11f) is not binding) the utility (in current values) of an additional marginal unit of energy equals the disutility (in current values) of the emissions induced by that marginal unit of energy. Along the optimal path this equation determines the optimal value of the abatement effort a per unit of output x1 . In the case that inequality (3.11f) is binding, and thus l1 equals 0, condition (3.13c) reduces to the truism 0 = 0. It is obvious, however, that in the case where the established technique is not used at all, the optimal abatement effort a = 0 as no emissions have to be abated. As noted above, the optimal system dynamics of the optimisation problem (3.11) splits into three cases, an interior solution and two corner solutions. In appendix (A.2) the system of functional differential equations for the system dynamics are derived and each case is shown to exhibit a (different) stationary state. In particular, the stationary state of the interior solution represents a saddle point, i.e. for all sets of initial conditions there exists a unique optimal path which converges towards the stationary state. First, the case of an interior solution, i.e. both qi (t) = ql1 (t) = 0, is considered. Together with transversality condition (3.13h) and inserting conditions (3.13a) and (3.13b) condition (3.13e) can be unambiguously solved: ∞ U (x(s))(1+a(s)−λ ) + D (e(s))λ 1−G(a(s)) (3.15) qk (t) = κ (1+a(s)) t × exp[−γ (s − t) − ρ s)]ds . Thus, along the optimal path the shadow price for the capital stock equals the net present value of all future welfare gains of one additional marginal unit of the capital good. As capital goods are long lived, they contribute over the whole time horizon increasingly less though due to deterioration. The fraction under the integral equals the marginal instantaneous welfare gain of an additional unit of capital, which comprises two components. The first is the direct welfare gain due to the energy produced. It is positive if the new technology needs less labor input per unit of output than the established one, i.e. λ < 1 + a. The second term is always positive and denotes the welfare gain due to emissions abated by switching from the established to the new production technique. Inserting conditions (3.13a) and (3.13b) in equation (3.13d) yields: U (x(t)) − D (e(t)) 1 − G(a(t)) exp[−ρ t] = qk (t + σ ) (3.16) 1 + a(t) The equation states that along the optimal path the present value of the welfare loss by investing in one marginal unit of new capital, which is given by the present value welfare gain of the alternative use of one marginal unit of labor in the established production technique (left-hand side), equals the net present value of the sum of all future welfare gains by using the new capital good in production. As the investment

3.2 Social Optimum

41

needs the time span σ to become productive capital, the sum of all future welfare gains of an investment at time t is given by the shadow price of capital at time t + σ , qk (t + σ ). Note that equation (3.16) implies that pk is always positive along the optimal path and, thus, the second term of the fraction in equation (3.15) outweighs the first.

3.2.2 Conditions for Investment and Replacement So far, however, it is not clear to which of the three possible stationary states the system will tend. In the following, conditions for the exogenous parameters are derived identifying which of the three possible cases for the system dynamics applies. In fact, these conditions determine whether there is any investment in the new technology, and if so, whether the established technology is eventually fully replaced by the new one. It is started with the investment condition. In order to derive a condition which identifies whether investment is optimal, the economy is assumed to stay in the no investment corner solution, and a condition is derived for which the corner solution violates the necessary and sufficient condition for an optimal solution. The following proposition states the result. Proposition 3.1 (Investment condition in the social optimum). Given the optimisation problem (3.11), the new technology is innovated, i.e. i(0)>0, if and only if the following condition holds: 1 + a0 +

1 − G(a0) > λ + κ (γ + ρ ) exp[ρσ ] , G (a0 )

(3.17)

where a0 is determined by the unique solution of the implicit equation: D

U (1 − a0) = G (a0 )(1 + a0) + 1 − G(a0) . (1 − a0)(1 − G(a0))

(3.18)

Proof. Assume that it is optimal not to invest at all times t. As a consequence, the economy will remain in the no investment corner solution where no capital is accumulated. Hence, i(t) = 0, qi (t) ≥ 0 ∀t and inequality (3.11e) is binding. All energy is solely produced by the established production technique which implies that x0 = x01 = 1 − a0 , x02 = 0, l10 > 0 and inequality (3.11f) is not binding (i.e. ql1 = 0). The optimal abatement effort a0 is determined by equation (3.14) by inserting x0 = 1 − a0 and e0 = x0 (1 − G(a0 )) which yields equation (3.18). Due to the assumed curvature properties of U, D and G, there exists a unique solution for a0 . In the corner solution i(t) = 0, we derive the shadow price of capital q0k (t) by inserting equation (3.14) in equation (3.15) and solving the integral: exp[−ρ t] . q0k (t) = D (e0 ) (1 + a0 − λ )G (a0 ) + 1 − G(a0) κ (γ + ρ )

(3.19)

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3 A Theoretical Model of Structural Change in the Energy Industry

Equating conditions (3.13c) and (3.13d), and inserting (3.13b) and q0k (t + σ ) yields the following necessary and sufficient condition for the corner solution to be optimal: D (e0 )G (a0 ) exp[−ρ t] − qi(t) = exp[−ρ (t + σ )] . D (e0 ) (1 + a0 − λ )G (a0 ) + 1 − G(a0) κ (γ + ρ )

(3.20)

Taking into account that qi (t) ≥ 0, dividing by D (e0 )G (a0 ) and rearranging terms yields: 1 − G(a0) 1 + a0 + ≤ λ + κ (γ + ρ ) exp[ρσ ] . (3.21) G (a0 ) Note that condition (3.21) is independent of t. This implies that it is optimal not to invest at all times t, if it is optimal not to invest at time t = 0. Thus, if condition (3.21) holds, the optimal solution of the optimisation problem (3.11) is to remain in the no investment corner solution forever. This, in turn, implies that it is optimal to invest in the new technology, if and only if condition (3.21) does not hold, which is exactly what condition (3.17) states. Condition (3.17) for investment in the new technology has an intuitive economic interpretation. In the corner solution without investment the left-hand side corresponds to the unit costs of energy production of the established technology UCT01 , the right-hand side to the unit costs of energy production of the new technology UCT02 . Thus, condition (3.17) states that, for the new technology to be innovated, its unit costs of production have to be below those of the established technology, i.e. UCT02 < UCT01 . The unit costs of production of the first technology are composed of three components, the ‘pure’ labor costs per unit of energy production, the labor costs for abatement per unit and the social costs of unit emissions in terms of labor. The unit costs of production of the non-polluting new technology comprise apart from the ‘pure’ labor costs per unit the costs for building up and maintaining the necessary capital good in terms of labor per unit of output. Obviously, the capital costs per unit of output depend positively on the capital intensity, κ , the dynamic characteristics γ and σ of the capital-good production, as well as on the time-preference rate ρ . In particular, the longer the time lag σ and the higher the time-preference rate ρ the higher are the unit costs of energy of the new technology.5 Despite the infinite time horizon and the linearity of the two production techniques, full replacement of the established technology by the new technology in the long run is not guaranteed, if condition (3.17) holds. In the following, we deduce conditions for which complete or partial replacement occur in the long run.

5

In general the unit costs of energy during transition periods are not constant, as consumption and emission levels change over time. Thus, they are not necessarily given by UCT01 and UCT02 .

3.2 Social Optimum

43

Formally, the case of full replacement of the established by the new production technique is given by the full replacement corner solution l1 (t) = 0. The line of argument to derive a condition for full replacement is similar to the inference of Proposition 3.1. Assuming the economy to be in a long-run stationary state in which the new technology is fully developed and all labor is used up to employ and maintain the capital stock it is investigated under which conditions such a full replacement stationary state is consistent with the necessary and sufficient conditions for an optimal solution as given by equations (3.13a)–(3.13h). The following proposition states the result. Proposition 3.2 (Full replacement condition in the social optimum). Given the optimisation problem (3.11) and assuming U (x∞ ) − D (0) = 0, full replacement of the established technology by the new one in the long-run stationary state is consistent with the necessary and sufficient conditions for a social optimum, if and only if the following condition holds: 1+

D (0)

U (x∞ ) − D (0)

where x∞ is given by x∞ =

≥ λ + κ (γ + ρ ) exp[ρσ ] ,

(3.22)

1 λ +κγ .

Proof. Assume that it is optimal in the long-run stationary state to use the total labor endowment to employ and maintain the capital stock for the new technology, i.e. 1 ∞ ∞ x∞ 2 = λ +κγ . Then, all output is solely produced by the new technology, i.e. x = x2 , ∞ ∞ x1 = l1 = 0. In addition, no emissions are produced and have to be abated and, thus, e∞ = 0 and a∞ = 0. Inserting conditions (3.13a) and (3.13b) into equation (3.13e) yields:6 −

U (x∞ )(1 − λ ) + D(0)λ − q∞ dq∞ l1 λ k (t) = exp[−ρ t] − qk(t)γ . dt κ

(3.23)

Together with the transversality condition (3.13h), equation (3.23) can be solved to yield:

exp[−ρ t] ∞ U (x )(1 − λ ) + D(0)λ − q∞ (3.24) q∞ k (t) = l1 λ . κ (γ + ρ ) By inserting conditions (3.13a), (3.13b) and q∞ k (t + σ ) into equation (3.13d), and ≥ 0, we derive condition (3.22). taking into account that q∞ l1

Note that ql1 (t) is constant in current values in the stationary state and, thus, ql1 (t) = q∞ l1 exp[−ρ t] with some constant q∞ l1 ≥ 0 in present values.

6

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3 A Theoretical Model of Structural Change in the Energy Industry

The economic interpretation of the full replacement condition (3.22) is analogous to the case of the investment condition (3.17). Full replacement can only take place, if the costs per unit of output of the new technology in the full replacement stationary state UCT∞2 (right-hand side) are smaller than or equal to the costs of the established technology UCT∞1 (left-hand side). As there are no emissions, there are no labor costs for abatement effort in the full replacement stationary state. Thus, the unit costs of the established technology only consist of the ‘pure’ labor costs plus the social costs, which stem from emissions. In the common case that the first marginal unit of emissions does not induce any environmental damage, i. e. D (0) = 0 (holding, for example, if the disutility function D is a power function with an exponent greater than 1), the unit costs of the established technology reduce to the ‘pure’ labor costs of production. Note that condition (3.22) is not well defined, if limx→x∞ U (x) = D (0) holds. However, also in this special case full replacement will occur if, in addition, condition (3.17) holds because the welfare gain of an additional unit of labor assigned to the old technology vanishes while the shadow price of capital, which is the net present value of all future welfare gains of an additional unit of capital, remains positive. The unit costs of the new technology are identical in both situations as they do not depend on the level of emissions and its implied disutility.7 For full replacement to occur conditions (3.17) and (3.22) must hold at the same time. Thus, a straightforward corollary from Propositions 3.1 and 3.2 is that partial replacement of the established by the new technology (i.e. the long-run stationary state is an interior solution) takes place, if condition (3.17) holds but condition (3.22) is violated. Corollary 3.1 (Partial replacement condition in the social optimum). Given the optimisation problem (3.11) and that U (x∞ ) − D (0) = 0 partial replacement of the established technology by the new one is optimal in the long-run stationary state, i.e. the long-run stationary state is an interior solution, if and only if the following condition holds: 1 + a0 + where x∞ = (3.18).

1 − G(a0) D (0) > , λ + κ ( γ + ρ ) exp[ ρσ ] > 1 + G (a0 ) U (x∞ ) − D (0) 1 λ +κγ

(3.25)

and a0 is given by the unique solution of the implicit equation

In sum, investment is never optimal if the labor costs per unit of output of the new technology, UCT2 = UCT02 = UCT∞2 , are higher than the labor costs per unit of output of the established technology in the no investment corner solution, UCT01 . If investment is optimal, i.e. UCT2 < UCT01 , then full replacement in the long-run stationary state is optimal if, in addition, UCT2 ≤ UCT∞1 holds. Otherwise, i.e. if UCT∞1 < UCT2 < UCT01 , the new technology will partially replace the established technology in the optimal long-run stationary state. 7

In fact, the unit costs of the new technology are the same among all possible stationary states.

3.3 Unregulated Competitive Market Equilibrium

45

3.3 Unregulated Competitive Market Equilibrium In this section, the allocation of the model economy is assumed to determined by an unregulated market regime. Competitive markets for labor, capital and energy are assumed, in which one representative household and two representative firms interact. All markets are supposed to be cleared at all times and thus supply equals demand. As emissions are free, though negatively valued by the household, the firms do not account for them in their market decisions. Moreover, as explained in section 3.1, a representative consumer is considered who exhibits different preferences in an individual as compared to a social decision context. More precisely, in the market regime the representative consumer’s preferences are assumed to be given by equation (3.9) (with α = 1), which differs from equation (3.10) by a higher rate of time preference ρ p . In analogy to the analysis of the social optimum, the conditions for investment in the new technology, and for replacement of the established technology in the longrun stationary state are derived. It is studed how the emission externality and the varied time preferences affect these conditions.

3.3.1 The Household’s Market Decisions The household is assumed to own the two firms and the total labor endowment 1 in the economy. In line with the standard literature on capital accumulation and growth (e.g. Barro and Sala-i-Martin 2004: chap. 2), it is assumed in addition that capital is owned by the household. Thus, the household chooses between selling labor to the firms at the market price of labor w or to invest labor in the accumulation of capital k, which the household rents to the firms at the market price of capital r. In addition, the household buys energy x at the market price of energy p. As the household cannot incur debts, the following budget constraint has to hold at all times t: (3.26) p(t)x(t) = w(t) 1 − i(t) + r(t)k(t) + π1(t) + π2(t) , where π1 and π2 denote the profits of firm 1 and 2. In addition, capital can be accumulated according to equation (3.8). The household is assumed to maximise its intertemporal welfare (3.9), i.e. the household solves the following maximisation problem: max i

subject to

∞ 0

U(x(t)) − D(e(t)) exp[−ρ pt] dt ,

(3.27a)

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3 A Theoretical Model of Structural Change in the Energy Industry

p(t)x(t) = dk(t) = dt i(t) ≥ k(0) =

w(t) 1 − i(t) + r(t)k(t) + π1(t) + π2(t) ,

(3.27b)

i(t − σ ) − γ k(t) ,

(3.27c)

0, 0,

(3.27d) (3.27e)

i(t) = ξ (t) = 0,

t ∈ [−σ , 0) .

Thus, the present value Hamiltonian H H reads:

H H = U(x(t)) − D(e(t)) exp[−ρ pt]

+ qb (t) w(t) 1 − i(t) + r(t)k(t) − p(t)x(t) + qk (t + σ )i(t) − qk (t)γ k(t) + qi (t)i(t) ,

(3.27f)

(3.28a) (3.28b) (3.28c) (3.28d)

where qk denotes the costate variable or shadow price of the capital stock k, and qb and qi denote the Kuhn-Tucker parameters for the (in)equality conditions (3.27b) and (3.27d). The strict concavity of the Hamiltonian H H can be shown following a similar line of argument as in appendix A.1. Assuming that the Hamiltonian H H is continuously differentiable with respect to the control variable i the following necessary conditions hold for an optimal solution: qb (t)p(t) = U (x(t)) exp[−ρ pt] , qb (t)w(t) = qk (t + σ ) + qi(t) , dqk (t) = qb (t)r(t) − qk (t)γ , − dt qi (t) ≥ 0 , qi (t)i(t) = 0 .

(3.29a) (3.29b) (3.29c) (3.29d)

Due to the concavity of the Hamiltonian, the necessary conditions (3.29a)–(3.29d) are also sufficient if in addition a transversality condition analogous to condition (3.13h) holds. Moreover, the strict concavity of the Hamiltonian ensures a unique solution. Then, together with condition (3.29a) condition (3.29c) can be unambiguously solved: qk (t) = exp[γ t]

∞

t

qb (s)r(s) exp[−γ s]ds .

(3.30)

3.3.2 The Firms’ Market Decisions The firms are assumed to maximise their profits in the competitive market equilibrium taking prices as given. Firm 1 produces energy according to the first production technology described by equations (3.1) and (3.11c). Thus, the profit π1 at time t is given by:

3.3 Unregulated Competitive Market Equilibrium

π1 (t) = p(t)l1 (t) − w(t) 1 + a(t) l1 (t) .

47

(3.31)

Firm 1 chooses l1 and a such as to maximise the net present value of all future profits which is equivalent to maximise the profit π1 at all times t. As the negative externality of emissions is not accounted for in the unregulated market economy, abatement effort a is a pure cost to the firm. As a consequence, a necessary condition for profit maximisation for firm 1 is: a(t) = 0 .

(3.32)

As π1 is linear in l1 , π1 is non negative for any l1 > 0 as long as output prices exceed input prices. The labor demand of firm 1 is given by the following correspondence: ⎧ , if p(t) > w(t) ⎪ ⎨= ∞ l1 (t) ∈ [0, ∞) , if p(t) = w(t) . (3.33) ⎪ ⎩ =0 , if p(t) < w(t) Firm 2 produces energy according to the second production technology described by equation (3.6). Thus, the profits π2 at time t equal:

π2 (t) =

1 λ p(t)k(t) − w(t)k(t) − r(t)k(t) , κ κ

(3.34)

which is a linear function of k. As a consequence, profits π2 are non negative for any k > 0 as long as the value of outputs exceeds the value of inputs. Analogously to firm 1, firm 2 demands as much capital as possible together with λκ k units of labor, if the value of the output exceeds the value of the inputs. Thus, the demand of firm 2 is given by the following correspondence: ⎧ λ ⎪ ⎨ = ∞ ∧ l2 (t) = κ k(t) = ∞ , if p(t) > λ w(t) + κ r(t) k(t) ∈ [0, ∞) ∧ l2 (t) = λκ k(t) , if p(t) = λ w(t) + κ r(t) . (3.35) ⎪ ⎩ = 0 ∧ l2 (t) = 0 , if p(t) < λ w(t) + κ r(t)

3.3.3 Necessary and Sufficient Condition for Unregulated Market Equilibrium In the market equilibrium supply equals demand on all markets. As in the social optimum, the market solution may exhibit two corner solutions. This is either the case, if the household does not invest in capital at all times, or if the total labor endowment is used to employ and maintain the capital stock. In the former case, firm 2 is unable to operate, while in the latter case firm 1 is driven out of the market. First, the interior market equilibrium, where both firms operate, is analysed. The demand correspondences (3.33) and (3.35) of firm 1 and firm 2 imply that for any positive and finite amount of l1 , l2 and k the following conditions hold:

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3 A Theoretical Model of Structural Change in the Energy Industry

w(t) = 1, p(t)

r(t) 1 = p(t) κ

w(t) 1−λ . 1+λ = p(t) κ

(3.36)

Solving equation (3.29a) for qb and taking into account conditions (3.36), the shadow price of capital qk derives as qk (t) =

1−λ exp[γ t] κ

∞ t

U (x(s)) exp[−(γ + ρ p)s] ds ,

(3.37)

and the following necessary and sufficient condition for an interior market equilibrium as: U (x(t)) exp[−ρ pt] = qk (t + σ ) . (3.38) Analogously to the corresponding condition (3.16) in the social optimum, equation (3.38) states that along the optimal path the present value of the household’s welfare loss by investing in one marginal unit of new capital, given by the present value welfare gain of the alternative use of one marginal unit of labor in the established production technique (left-hand side), equals the net present value of the sum of all future welfare gains by using the new capital good in production. As investment needs the time span σ to become productive capital, the sum of all future welfare gains of an investment at time t is given by the shadow price of capital at time t + σ , qk (t + σ ). Both costs and benefits of investment are smaller in the market equilibrium compared to the social optimum. However, in order to decide how the market failures influence the conditions of investment and replacement they have to be checked explicitly.

3.3.4 Conditions for Investment and Replacement In order to derive an investment condition similar to condition (3.17) in the social optimum, the economy is again assumed to stay in the no investment corner solution. Given the stationary state with no investment in capital at all times, a condition on the exogenous parameters is derived for which the corner solution violates the necessary and sufficient condition (3.38) for an unregulated market solution. The following proposition states this condition. Proposition 3.3 (Investment in the competitive market regime). Given the optimisation problem (3.27) of the representative household and the profit functions (3.31) and (3.34) of firm 1 and firm 2, the new technology is innovated, i.e. i(0) > 0, if and only if the following condition holds: 1 > λ + κ (γ + ρ p) exp[ρ p σ ] .

(3.39)

Proof. Assume that it is optimal not to invest at all times t. As a consequence, the economy will remain in the no investment corner solution where no capital is

3.3 Unregulated Competitive Market Equilibrium

49

accumulated. Hence, i(t) = 0, qi (t) ≥ 0 ∀t and inequality (3.29d) is binding. All energy is solely produced by the established production technique (i.e. x0 = x01 = 1, x02 = 0). From the demand correspondences (3.33) and (3.35) we know that r(t) 1 w(t) w(t) 1−λ = 1, ≥ . (3.40) 1−λ = p(t) p(t) κ p(t) κ Solving equation (3.29a) for qb and inserting it, together with conditions (3.40), in equation (3.30) yields the following inequality for the shadow price of capital: q0k (t) ≥

1−λ U (1) exp[−ρ pt] . κ (γ + ρ p)

(3.41)

Inserting qb (t) and q0k (t + σ ) into equation (3.29b) and taking into account that qi (t) ≥ 0 yields the following necessary and sufficient condition for the corner solution to be a market equilibrium: U (1) exp[−ρ pt] ≥

1−λ U (1) exp[−ρ p (t + σ )] . κ (γ + ρ p)

(3.42)

Dividing by U (1) exp[−ρ pt] and rearranging terms yields that it is optimal to invest in the new technology, if and only if condition (3.39) holds. Condition (3.39) displays the unit costs of energy production of the established and the new technology, respectively, in the competitive market equilibrium. Again, the new technology has to necessarily display lower unit costs of production than the established technology in order to be innovated. As the social costs of pollution are not accounted for in the unregulated market regime, firm 1 has no incentive to abate. The unit costs of energy of the established technology reduce to the ‘pure’ costs of production and are thus lower than socially optimal. The unit costs of energy of the new technology display the same composition as in the social optimum. As they now depend on ρ p > ρ , they exceed the socially optimal unit costs of energy of the new technology. Thus, for the technology to be innovated in the unregulated market regime, the unit costs of energy of the new technology, which are higher than in the social optimum, still have to be smaller than the units costs of energy of the established technology, which are lower than in the social optimum. As there is no abatement, investment in the new technology according to condition (3.39) always implies the full replacement of the initially established technology in the long run and thus excludes partial replacement. The following proposition states these results. Proposition 3.4 (Full replacement in the competitive market regime). Given the optimisation problem (3.27) of the representative household, the profit functions (3.31) and (3.34) of firm 1 and firm 2, full replacement of the established

50

3 A Theoretical Model of Structural Change in the Energy Industry

technology by the new one in the long-run stationary state is consistent with the necessary and sufficient conditions for a competitive market equilibrium, if and only if the following condition holds: 1 ≥ λ + κ (γ + ρ p) exp[ρ p σ ] .

(3.43)

In particular, this implies that partial replacement of the established technology by the new one cannot occur in the unregulated market regime. Proof. Assume that it is optimal in the long-run stationary state to use the total labor endowment to employ and maintain the capital stock for the new technology, i.e. l1∞ = 0, l2∞ = λ +λκγ . Then, all output is solely produced by the new technology,

1 ∞ ∞ i.e. x∞ = x∞ 2 = λ +κγ , x1 = l1 = 0. From the demand correspondences (3.33) and (3.35) we know that

w(t) ≥ 1, p(t)

r(t) 1 = p(t) κ

w(t) 1−λ . p(t)

(3.44)

Solving equation (3.29a) for qb and inserting it, together with conditions (3.44), into equation (3.30) yields for the shadow price of capital: q∞ k (t) =

1 − λ w∞ ∞ U (x ) exp[−ρ pt] , κ (γ + ρ p )

(3.45)

where w∞ = p(t) evaluated at the full replacement stationary state, and is thus a constant. Inserting qb (t) and q∞ k (t + σ ) into equation (3.29b), we derive the following condition: w(t)

w∞U (x∞ ) exp[−ρ pt] =

1 − λ w∞ ∞ U (x ) exp[−ρ p (t + σ )] . κ (γ + ρ p)

(3.46)

∞

) exp[−ρ p (t + σ )], taking into account that w∞ ≥ 1 and rearrangDividing by κU(γ (x +ρ p ) ing terms yields condition (3.43).

At first sight it might be puzzling that condition (3.39) is a strict inequality while condition (3.43) also allows for the equality sign to hold. The interpretation is, however, straightforward. Condition (3.43) states the requirements for a full replacement stationary state to be consistent with the necessary and sufficient conditions for a market equilibrium. However, from the strict inequality (3.39) we know that starting with a vanishing capital stock k(0) = 0 there is no investment at all times, if the equality sign in (3.43) holds. Nevertheless, in the hypothetical situation that the economy would already start with the full replacement capital stock k∞ = λ +κκγ

3.4 Competitive Market Equilibrium with Emission Tax and Investment Subsidy

51

and that, in addition, condition (3.43) holds with equality, the economy would stay in the full replacement market equilibrium forever. In sum, in the unregulated market economy the new technology has to exhibit lower costs per unit of output than the ‘pure’ labor costs of the established technology to be innovated. This holds as the social costs of emissions which are an inevitable joint output of the old production technique are not accounted for in the market equilibrium. Moreover, the unit costs of the new technology are higher in the unregulated market equilibrium as compared to the social optimum. This difference is caused by the costs of waiting until the new capital good becomes productive, which increase because of the higher rate of time preference ρ p of individual actors as compared to the social rate of time preference ρ . Thus, in a mutually reinforcing way the two market failures imply that the new technology might not be innovated in the competitive market equilibrium, although innovation would be socially optimal.

3.4 Competitive Market Equilibrium with Emission Tax and Investment Subsidy This section considers the implementation of the social optimum. In general, to implement the social optimum, corresponding to the two distortions arising in the model, two independent instruments are needed. Therefore, the introduction of an emission tax τe to internalise the external effect from emissions, and of an investment subsidy τi to internalise the second market failure associated with the individuals’ higher time preference is studied. The emission tax is assumed to be a tax per unit of emissions, directly collected from firm 1, the investment subsidy to be a subsidy per unit of investment, paid directly to the household. Note that, as explained in subsection 2.1.3, while the analysis in the former sections was valid irrespective of the causes of the split of the time preferences, the analysis in this section only refers to that subset of causes which cannot directly or differently be remedied.

3.4.1 The Household’s and Firms’ Market Decisions under Regulation The emission tax and the investment subsidy alter the profit function of firm 1 and the household’s maximisation problem, respectively. Thus, the corresponding decisions in a regulated market regime have to be reconsidered. Given a per unit tax τe per unit of emissions, the profit function of firm 1 alters as follows: π1 (t) = p(t)l1 (t) − w(t)(1 + a(t))l1(t) − τe (t) 1 − G(a(t)) l1 (t) . (3.47)

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3 A Theoretical Model of Structural Change in the Energy Industry

Firm 1 chooses both labor l1 and abatement effort a such as to maximise the net present value of all future profits, which is equivalent to maximising the profit π1 at all times t. A necessary condition for profit maximisation is

∂ π1 (t) = − l1 (t)w(t) + τe (t)G (a(t))l1 (t) = 0 , ∂ a(t)

(3.48)

which is an implicit equation for the unique optimal abatement effort a (t) as long as l1 (t) > 0. However, if l1 (t) = 0, the optimal abatement effort a (t) = 0 as in this case there are no emissions which have to be abated. Again, the profit function π1 (t) is linear in the labor demand l1 (t). Thus, the demand for l1 (t) is given by the following correspondence: ⎧ , if p(t) > w(t) 1 + a(t) + τe (t) 1 − G(a(t)) ⎪ ⎨= ∞ (3.49) l1 (t) ∈ [0, ∞) , if p(t) = w(t) 1 + a(t) + τe (t) 1 − G(a(t)) , ⎪ ⎩ = 0 , if p(t) < w(t) 1 + a(t) + τe (t) 1 − G(a(t)) where the optimal abatement effort a is given by the solution of the implicit equation τe (t)G (a(t)) = w(t) if l1 (t) > 0, and a(t) = 0 if l1 (t) = 0. With the investment subsidy τi (t) paid per unit of investment i, the household’s budget constraint equals:8 p(t)x(t) = w(t) 1 − i(t) − τi (t)i(t) + r(t)k(t) + π1(t) + π2(t) . (3.50) Thus, the necessary and sufficient condition (3.29b) is replaced by: qb (t) w(t) + τi (t) = qk (t + σ ) + qi(t) .

(3.51)

Neither the emission tax τe nor the innovation subsidy τi directly affect firm 2. As a consequence, the decision criteria of firm 2 remain unaltered.

3.4.2 Necessary and Sufficient Condition for Regulated Market Equilibrium Given the adjusted equations (3.47) and (3.51), which replace equations (3.33) and (3.29b) of section 3.3 in the case that an emission tax τe and an investment subsidy τi are enacted, it is now analyed how the interior market equilibrium changes. Conditions (3.48), (3.49) and (3.35) imply the following conditions for an interior market equilibrium where both firms operate (i.e. l1 (t) > 0, i(t) > 0):

8

For the sake of consistency, a positive τe (τi ) denotes a tax and a negative τe (τi ) denotes a subsidy.

3.4 Competitive Market Equilibrium with Emission Tax and Investment Subsidy

τe (t) G (a(t))(1 + a(t)) + 1 − G(a(t)) , p(t) e (t) 1 − τp(t) 1 − G(a(t)) w(t) = , p(t) 1 + a(t) τe (t) 1 + a(t) − λ + λ p(t) 1 − G(a(t)) r(t) = . p(t) κ (1 + a(t)) 1=

53

(3.52) (3.53) (3.54)

Solving equation (3.29a) for qb and taking into account conditions (3.54) we achieve for the shadow price of capital qk : τe (s) exp[γ t] ∞ 1 + a(s) − λ + λ p(s) 1 − G(a(s)) qk (t) = κ 1 + a(s) t × U (x(s)) exp[−(γ + ρ p)s] ds .

(3.55)

Inserting qb and equation (3.53) into equation (3.51) yields e (t) 1 − τp(t) 1 − G(a(t)) 1 + a(t)

U (x(t)) exp[−ρ pt] =

qk (t + σ ) −

(3.56)

τi (t) U (x(t)) exp[−ρ pt] . p(t)

which together with equation (3.52) determines the interior market equilibrium for a given emission tax τe and investment subsidy τi . Note that equations (3.52) and (3.56) determine the market equilibrium only in terms of relative prices. Thus, one price can freely be chosen as a numeraire. Choosing the price of energy p as numeraire, now the optimal emission tax and the optimal investment subsidy are calculated. Comparing equation (3.52) with the corresponding condition (3.14) in the social optimum the following condition is achieved for the optimal emission tax τeopt : D (e(t)) τe (t)opt = . p(t) U (x(t))

(3.57)

For condition (3.56) and the corresponding condition (3.16) in the social optimum to coincide the investment subsidy τiopt has to be set to: exp[−γ (t+σ )] τi (t)opt =− (3.58) p(t) κ U (x(t)) ∞ U (x(s))(1 + a(s) − λ ) + D(e(s))λ 1 − G(a(s)) × 1 + a(s) t+σ × exp[−γ s] exp[−ρ (s − t)] − exp[−ρ p (s − t)] ds .

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3 A Theoretical Model of Structural Change in the Energy Industry

Hence, if the two instruments are set in such a way that the market equilibrium is identical to the social optimum, τeopt is always positive (i.e. emissions are taxed) and τiopt is always negative (i.e. investment is subsidised). In the following, it is considered how the conditions for investment and replacement, i.e. the two corner solutions, change compared to the unregulated market economy when an emission tax τe is raised from firm 1 and an investment subsidy τi is paid to the household. It is shown that setting τe and τi as defined in equations (3.57) and (3.58) also implements the social optimum in case of the corner solutions.

3.4.3 Conditions for Investment and Replacement Again, first the case that the economy stays in the no investment corner solution is considered. A condition for positive investment to be a market equilibrium in the regulated market regime with emission tax τe and investment subsidy τi is derived. The following proposition states this condition. Proposition 3.5 (Investment in the regulated market regime). Given the optimisation problem (3.27) of the household with the adjusted budget constraint (3.50), the profit functions (3.47) and (3.34) of firm 1 and firm 2, and the e (t) i (t) and the investment subsidy τp(t) in units of the numeraire p, the emission tax τp(t) new technology is innovated in the market equilibrium, i.e. i(0) > 0, if and only if the following condition holds:

1 − G(a0) τi0 0 > λ + 1 + 0 0 κ (γ + ρ p) exp[ρ p σ ] , 1+a + (3.59) G (a0 ) τe G (a ) e (t) i (t) , τi0 = τp(t) evaluated at the no investment stationary state and a0 is where τe0 = τp(t) determined by the unique solution of the implicit equation: (3.60) 1 = τe0 G (a0 )(1 + a0) + 1 − G(a0) .

Condition (3.59) for the market equilibrium is identical to the corresponding condition for the social optimum (3.17), if τe0 and τi0 are set as follows: D (e0 ) > 0, U (x0 )

D (e0 ) (1+a0 −λ )G (a0 )+1−G(a0 ) 0 τi = κ U (x0 ) exp[−ρ p σ ] exp[−ρσ ] × − < 0, γ + ρp γ +ρ

τe0 =

where x0 = 1 − a0 and e0 = (1 − a0)(1 − G(a0)).

(3.61) (3.62)

3.4 Competitive Market Equilibrium with Emission Tax and Investment Subsidy

55

Proof. The proof is analogous to the proof of Proposition 3.3. Assume that it is optimal not to invest at all times t. As a consequence, the economy will remain in the no investment corner solution where no capital is accumulated. Hence, i(t) = 0, qi (t) ≥ 0 ∀t and the inequality (3.29d) is binding. All energy is solely produced by the established production technique (i.e. x0 = x01 = 1 − a0 , x02 = 0). We know from conditions (3.48), (3.49) and (3.35): 1 = τe0 G (a0 )(1 + a0) + 1 − G(a0) , (3.63a) w(t) = τe0 G (a0 ) , p(t)

τe0 (1 + a0 − λ )G (a0 ) + 1 − G(a0) r(t) ≥ . p(t) κ

(3.63b) (3.63c)

Equation (3.63a) determines the profit maximising abatement effort a0 of firm 1. Solving equation (3.29a) for qb and inserting, together with conditions (3.63c), in equation (3.29c) yields the following inequality for the shadow price of capital: q0k (t) ≥

τe0 (1 + a0 − λ )G (a0 ) + 1 − G(a0) U (x0 ) exp[−ρ pt] . κ (γ + ρ p)

(3.64)

Inserting equation (3.63b), qb and q0k into equation (3.51) and taking into account that qi (t) ≥ 0 we derive:

τe0 G (a0 )U (x0 ) ≥ (3.65)

τe0 (1 + a0 − λ )G (a0 ) + 1 − G(a0) U (x0 ) exp[−ρ pσ ] − τi0U (x0 ) . κ (γ + ρ p) Dividing by τe0 G (a0 )U (x0 ) and rearranging terms yields that the no investment corner solution is a market equilibrium, iff:

λ + 1+

τi0 1 − G(a0) . κ (γ + ρ p) exp[ρ p σ ] ≥ 1 + a0 + 0 0 τe G (a ) G (a0 )

(3.66)

That, in turn, implies that in the regulated market equilibrium there is investment in the new technology, if and only if condition (3.59) holds. 0) By setting τe0 = UD (e , condition (3.63a) which determines the profit maximis(x0 ) ing abatement effort a0 becomes identical to equation (3.18) which determines the socially optimal abatement level. Furthermore, inserting τe0 and τi0 from equations (3.61) and (3.62) into condition (3.59) yields (after some tedious calculations) the investment condition in the social optimum (3.17).

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3 A Theoretical Model of Structural Change in the Energy Industry

Condition (3.59) displays the unit costs of energy production of the established and of the new technology, respectively, in the no investment market equilibrium when an emission tax τe is imposed and an innovation subsidy τi is paid. Imposing the emission tax τe enforces the incorporation of the socail costs of emissions into the unit costs of production of the established technology. By setting τe0 equal to the ratio between marginal damage from environmental degradation and marginal benefit from consumption the unit costs of production of the established technology are raised to their socially optimal level and thus the external effect from the emissions is internalised. However, it is obvious from condition (3.59) that an emission tax does not suffice for the market equilibrium to resemble the socially optimal outcome. In addition, an investment subsidy has to be paid, lowering the unit costs of energy production for the new technology to their level at the social optimum. Note that conditions (3.61) and (3.62) are identical to the corresponding conditions (3.57) and (3.58) for an interior market equilibrium evaluated at the no investment corner solution. Now, the conditions are derived for which full replacement of the established by the new technology is a market equilibrium in the long run, given that the state imposes an emission tax τe and pays an investment subsidy τi . Proposition 3.6 (Full replacement in the regulated market regime). Given the optimisation problem (3.27) of the household with the adjusted budget constraint (3.50), the profit functions (3.47) and (3.34) of firm 1 and firm 2, the e (t) i (t) and the investment subsidy τp(t) , full replacement of the established emission tax τp(t) technology by the new one in the long-run stationary state is consistent with the necessary and sufficient conditions for a regulated market equilibrium, if and only if the following condition holds:

τ∞ τ∞ 1 + e ∞ ≥ λ + 1 + i ∞ κ (γ + ρ p) exp[ρ p σ ] , (3.67) 1 − τe 1 − τe e (t) i (t) , τi∞ = τp(t) evaluated at the long-run stationary state. where τe∞ = τp(t) Condition (3.67) for the market equilibrium is identical to the corresponding condition for the social optimum (3.22), if τe∞ and τi∞ are set as follows:

D (0) ≥ 0, U (x∞ ) U (x∞ )(1 − λ ) + D(0)λ τi∞ = κ U (x∞ ) exp[−ρ p σ ] exp[−ρσ ] × − < 0, γ + ρp γ +ρ

τe∞ =

where x∞ =

(3.68) (3.69)

1 λ +κγ .

Proof. Assume that using the total labor endowment to employ and maintain the capital stock for the new technology in the long-run stationary state is a market

3.4 Competitive Market Equilibrium with Emission Tax and Investment Subsidy

57

equilibrium, i.e. l1∞ = 0, i∞ > 0 and q∞ i = 0. Then, all output is solely produced by 1 ∞ ∞ = the new technology, i.e.x∞ = x∞ 2 λ +κγ and x1 = l1 = 0. In addition, no emissions ∞ are produced and have to be abated and, thus, e = 0 and a∞ = 0. For this case, we know from the demand correspondences (3.49) and (3.35) of firm 1 and firm 2: w(t) τe (t) ≤ 1− , p(t) p(t) 1 r(t) w(t) = 1−λ . p(t) κ p(t)

(3.70a) (3.70b)

Solving equation (3.29a) for qb and inserting it, together with condition (3.70b), in equation (3.29c), yields for the the shadow price of capital: q∞ k (t) =

1 − λ w∞ ∞ U (x ) exp[−ρ pt] , κ (γ + ρ p)

(3.71)

where w∞ = w(t) p(t) evaluated at the full replacement stationary state and thus is a constant. Inserting qb , qk and inequality (3.70a) into equation (3.51), and taking into account that qi (t) = 0, we derive the following condition: (1 − τe∞ )(λ + κ (γ + ρ p) exp[ρ p σ ]) ≤ 1 − τi∞κ (γ + ρ p) exp[ρ p σ ] .

(3.72)

Dividing by (1 − τe∞) and rearranging terms yields condition (3.67). Furthermore, inserting τe∞ and τi∞ from equations (3.68) and (3.69) into condition (3.67) yields (after some tedious calculations) the full replacement condition in the social optimum (3.22). Note that, although in the case of full replacement the external effect from the emissions vanishes, the emission tax has to be raised as long as D (0) > 0 for the market equilibrium to resemble the social optimum. If D (0) = 0, then the optimal tax in the full replacement stationary state is given by τe∞ = 0. However, the optimal investment subsidy τi∞ has to be non-zero in any case. As in the case of the social optimum, conditions (3.59) and (3.67) have to hold simultaneously for full replacement to occur in the regulated market regime in the long run. Moreover, if the emission tax τe and the investment subsidy τi are such that condition (3.59) is always fulfilled but condition (3.67) is always violated, the economy exhibits a market equilibrium where both technologies are used, i.e. there is a partial replacement of the established by the new technique.

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3 A Theoretical Model of Structural Change in the Energy Industry

3.5 Conclusion In this chapter a theoretical model of structural change in the energy industry was developed and analysed. The aim was to study the welfare-theoretic implications of a social rate of time preference staying below the private and a time-to-build feature in capital accumulation for the conditions of structural technological change in the energy sector in a situation, where emissions are negatively valued and an end-ofpipe abatement technology is available. The next chapter summarises the results of the model analysis. They are discussed with respect to model assumptions and policy conclusions.

Chapter 4

Summary of Results, Discussion of Assumptions, and Policy Implications

This chapter summarises the results of the previous analysis (section 4.1), and discusses them with respect to model assumptions (section 4.2) and policy implications (section 4.3). Section 4.4 provides conclusions to the theoretical part.

4.1 Summary of Results In chapter 3 a theoretical model was developed to study the effect from the social rate of time preference staying below the private and a time-to-build feature in capital accumulation on the conditions of structural change between an established polluting and a new clean energy technology, when emissions are negatively valued and an end-of-pipe abatement technology is available. From the model necessary and sufficient conditions were derived for investment in the new clean, and for replacement of the established polluting energy technology for the situations of the social optimum and an unregulated competitive market economy. It was shown that two distortions arise in the unregulated market economy, one induced by the emissions, the other one stemming from the split of social and private time-preference rates. Moreover, it was shown how the two distortions can be corrected by environmental and technology policies. The following six points summarise the findings of the model analysis in detail.

4.1.1 Too Low Unit Costs of Energy of Established Technology as Compared to Social Optimum Due to Pollution With respect to the emission externality the model analysis takes up the environmental economic standard feature. In an unregulated competitive market economy there is no incentive to abate. The social costs of emissions, which arise due to the household’s negative valuation of the environmental degradation caused by emissions, are C. Heinzel, Distorted Time Preferences and Structural Change in the Energy Industry, Sustainability and Innovation, DOI 10.1007/978-3-7908-2183-3 4, © Physica-Verlag Heidelberg 2009

59

60

4 Summary of Results, Discussion of Assumptions, and Policy Implications UCT1 45⬚

1+a0+

full replacement

1−G(a0) G′(a0)

partial replacement

no investment

t e0 te 1

UCT2

0 Unregulated markets: Social optimum:

ti

1 1+

D′(0) U ′(x )−D′(0)

Fig. 4.1 Full replacement, partial replacement, and no investment in the unregulated market equilibrium and the social optimum.

not taken into account by the polluting firm. As a consequence, in the unregulated market economy the unit costs of the established technology, UCT1 , equal its ‘pure’ labor costs per output unit of 1 both in the condition for investment in the new technology and in that for full replacement of the established technology (conditions (3.39), (3.43), left-hand sides). They thus stay in both cases below their socially op0) (0) timal level of 1 + a0 + 1−G(a and 1 + U (xD ∞ )−D (0) , respectively (conditions (3.17), G (a0 ) (3.22), left-hand sides). Hence, pollution leads both in the case of the investment condition and in that of the full-replacement condition to unit costs of energy of the established technology which are too low as compared to the social optimum.

4.1.2 Too High Unit Costs of Energy of New Technology as Compared to Social Optimum Because Private Time-Preference Rate Higher Than Socially Optimal In addition to the standard setting it was assumed that (i) the social rate of time preference stays below the private and (ii) the creation of new productive capital exhibits a time lag σ . These two elements have direct implications for the unit costs of energy of the new technology, UCT2 , which are composed of the labor costs per output unit, λ , and the capital costs per output unit. First, it was shown that the

4.1 Summary of Results

61

capital costs per output unit positively depend on the rate of time preference in any case. Thus, as implied by the assumption of the social time-preference rate to be below the private, the UCT2 in the unregulated market equilibrium exceed their socially optimal level, both in the case of the investment condition (conditions (3.39), (3.17), right-hand sides) and of the full-replacement condition (conditions (3.43), (3.22), right-hand sides). This results arises irrespective of the cause of the split of time-preference rates. A corollary is that the higher the difference between private and social rate of time preference, ρ p − ρ , the higher the excess of the UCT2 in the unregulated market equilibrium over their socially optimal level, thus, the distortion of UCT2 .

4.1.3 Time Lag of Capital Accumulation Reinforces Distortion from Split of Social and Private Time-Preference Rates In any case the capital costs per unit of output of the new technology also positively depend on the time lag σ in the accumulation of the specific capital good of the new energy technology (equation (3.8)). The time lag is not necessary for the second distortion to occur. However, it amplifies the distortion imposed by the diverging time-preference rates, as can easily be seen from the term ρ p exp[ρ p σ ] in the unit costs of the new technology. That is, this distortion gains the more importance the higher σ .

4.1.4 Distortions Imply in Mutually Reinforcing Way Less Favorable Circumstances for Innovation and Replacement The basic, intuitive, result of Propositions 3.1 to 3.4 is that the new technology is innovated, and (at least partially) replaces the old one, if and only if the unit costs of energy of the new technology stay below those of the established.1 In the unregulated competitive market economy pollution leads to UCT1 which are too low, and the private rate of time preference exceeding the social to UCT2 which are too high as compared to the social optimum, the latter effect being reinforced by the time lag σ . Thus, both for investment in the new technology and replacement of the established to be (individually) optimal, in the unregulated market regime, as compared to the social optimum, higher UCT2 have to stay below lower UCT1 . This implies that the two distortions create in a mutually reinforcing way less favorable circumstances for the innovation of the new and the replacement of the old technology as compared to social optimum. 1

While in the unregulated market equilibrium the fulfillment of the investment condition always implies full replacement in the long run, at the social optimum also partial replacement may occur (Corollary 3.1). The case of partial replacement derives, however, only as a technical artefact.

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4 Summary of Results, Discussion of Assumptions, and Policy Implications

4.1.5 Social Optimum May Be Implemented by Setting Appropriate Emission Tax and Investment Subsidy While the analysis in the former sections was valid irrespective of the causes of the split of time preferences, the implementation of the socially optimal path was explicitly considered only for the case that the split arises due to causes which cannot directly or differently be remedied.2 It was shown for this case that the two distortions of the investment and replacement conditions, from the emission externality and induced by the split of time-preference rates, may be corrected by setting an emission tax and an investment subsidy, respectively (Propositions 3.5 and 3.6). Figure 4.1 illustrates graphically for this case the conditions of investment and full and partial replacement in the unregulated competitive market regime and the social optimum, as well as the effects of the application of the two policy instruments. It shows that the levy of the emission tax τe has a double effect. First, τe0 raises the unit costs of energy of the established technology in the investment condition 0) to its socially optimal level of 1 + a0 + 1−G(a . Thereby it creates, in particular, G (a0 ) the possibility of an interior solution with both technologies operating in the longrun stationary state. Second, τe∞ moves the point until which full replacement takes (0) place to 1 + U (xD ∞ )−D (0) . However, the social optimum can in general only be implemented if, in addition, an investment subsidy τi is paid, which reduces the unit costs of the new technology to their socially optimal level.

4.1.6 Environmental Policy Alone Biased Towards Gradual Change, Technology Policy Alone Independant of Environmental Effect A corollary of the necessary application of the two instruments, corresponding to the two underlying market failures, to achieve the social optimum is that the imposition of only one of them in general leads to a bias in the optimal control of technological change. For the sake of clarity of results in the model only the established technology was assumed to be polluting and only the new technology to rely, in addition to the labor input, on a capital input, which only has to be produced. Environmental policy thus directly affects only the UCT1 , correcting them to their (higher) socially optimal level. It does not correct the UCT2 to their (lower) socially optimal level. Hence, the standard environmental policy of solely imposing an emission tax tends to be biased towards gradual technological change and may not sufficiently account for structural technological change as compared to the social optimum.3 It is to be noted that if the new technology was also polluting, optimal 2 As discussed in subsection 2.1.3, the occurrence of the second distortion always necessitates an additional policy intervention, however, not necessarily in the way considered here. 3 The introduction of an emission permit trading scheme would yield the equivalent result.

4.2 Discussion of Model Assumptions

63

environmental policy would in general also raise the unit costs of energy of the new technology and thus directly hamper structural technological change. This would not affect the necessary level of an optimal technology policy. Due to the additional necessary input of capital which only has to be produced, the UCT2 depend, in contrast to the UCT1 , also on the actor’s time preferences, viz their time-preference rate, and are, thus, affected by any split of the social and private rates. Accordingly, in effect, technology policy, of the kind described above, only corrects the UCT2 to their (lower) socially optimal level but does not affect the UCT1 . While in the given setting, with a polluting established and a clean new technology, technology policy has a positive environmental (side-)effect, its application is generally independant from the environmental effect possibly implied. This implies in turn that, given the negative valuation of emissions, environmental policy constitutes a necessary complement of technology policy to control the direction of the technological transition process.

4.2 Discussion of Model Assumptions The discussion of the results of the model analysis with respect to model assumptions in this section takes up, continues and complements the discussion of the assumption of the split of social and private time-preference rates as well as different technological assumptions in sections 2.1 and 2.3, respectively.

4.2.1 Social Rate of Time Preference Below Private The crucial assumption for the model results to hold is that social and private rates of time preference differ, more particularly that the social stays below the private in a way relevant for the technological transition in the energy industry. In subsection 2.1.2 three reasons particularly relevant in this context were introduced. It was pointed to rising environmental externalities and imperfections of financial markets due to adverse-selection problems and uninsurable long-run risks. As discussed in subsection 2.1.3, notably in view of the multitude of different relevant reasons for the split of social and private time-preference rates, in chapter 3 an endogenous explanation of the split of time-preference rates was omitted. It rather concentrated on the effect of this assumption on the necessary and sufficient conditions for investment and replacement in the energy industry.

4.2.2 Time Lag in Capital Accumulation The other distinctive feature of the model, the assumption that the accumulation of the specific capital good for the new technology exhibits a substantial time lag

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4 Summary of Results, Discussion of Assumptions, and Policy Implications

σ , was introduced in section 2.2. As stated in subsection 4.1.3, the time lag is not necessary for the second distortion to occur. But it amplifies the distortion imposed by the diverging time-preference rates. The considerable length of the time to build in energy plant construction – ranging, e.g., from two years for gas cogeneration plants up to five to seven years for the construction of a nuclear power plant (section 5.3) – underlines the particular importance this distortion may have in the context of the technological transition of energy systems.

4.2.3 Focus on Linear-limitational, General Energy Technologies By modeling the energy producing technologies as linear and linear-limitational functions, respectively, very specific forms of technology for the production of energy were assumed. The rationale for this specific functional form is to account for rigidities in energy production due to technical and thermodynamic constraints. Moreover, from a more technical point of view, as noted in subsection 2.3, it is the linearity of the production functions which gives rise to the corner solutions, which were exploited to derive conditions for investment, and partial and full replacement. In addition, for the sake of generality, it was referred to general energy technologies and abstracted from different specifics that relate to particular types of technology. Accordingly, the finiteness of conventional energy sources was assumed to be non-binding over time. The technologies were supposed to exhibit constant returns to scale over a possibly infinite lifetime. And fuel inputs were not explicitly considered but, as far as relevant in terms of costs, subsumed under the single non-producible input of labor. Given these simplifications the established polluting technology may thus stand for a conventional fossil-fuelled, e.g., coal-fired, power plant. The new clean technology can be seen to represent either renewable energies, new carbon-neutral fossil-fuelled technologies, or nuclear power. Carbon neutrality of fossil-fuelled technologies could be achieved, at the cost of somewhat increased unit costs of labor, using carbon-capture-and-storage (CCS) technologies (section 5.3). While long construction and lifetimes are more important in the case of conventional technologies, free fuel, unlimited over time, is realistic for renewable energies.

4.2.4 Labor Only Primary Input, Energy Homogeneous Output As the focus was on the substitution effects between (the established and the new) energy production technologies, the above analysis abstracted from substitution possibilities between different factors within the individual energy technologies. In line with the aim of modeling general energy technologies it was therefore sufficient to

4.3 Policy Implications

65

restrict the analysis to labor as the only primary input.4 Moreover, as the opposite assumption would not have supplied further insights, the considered economy was assumed to be non-growing, i.e., labor was assumed to be available in fixed amount of 1 at any time t (section 3.1). For the sake of clarity of results, as traditionally common in the literature, energy was assumed as a homogeneous output. This simplification also corresponds to the analytical focus on production structures.

4.2.5 Emissions as Flow Pollutant In the model a flow pollutant is considered, whereas the accumulation of greenhouse gases in the atmosphere causing the rise of global mean temperature is a stock-pollutant problem. This simplification does not qualitatively affect the results. Rather, for a stock pollutant the split of time-preference rates would imply an underestimation of the future damages from emissions today by the individual households compared to the social planner. As a consequence the unit costs of production of the established technology would be further underestimated in the unregulated market economy.

4.2.6 Abstraction from Peculiarities of Economics of Power Systems For the sake of tractability the model abstracted from a series of peculiarities of the economics of electric power systems. Thus, the energy industry is subject to oscillatory demand fluctuations on different time-scales (e.g., day/night-time or summer/ winter). Different energy technologies exhibit different turn-on/turn-off costs and rigidities. Therefore a mix of energy technologies is in general preferable over ‘energy monocultures’. In contrast to the assumption of a perfectly competitive market, and to the ideal of liberalised energy markets, the energy industry is, in part, still confronted with oligopolistic market structures. As is well known from the industrial organisation literature, unregulated oligopolistic market regimes lead in general market failures in the sense that the market outcome is not socially optimal. These additional market failures were not considered explicitly in order to concentrate on the distortions imposed by emissions and split time-preference rates.

4.3 Policy Implications Although the analysis in chapter 3 has been carried out in a stylised theoretical framework, there are direct policy implications to be drawn which are relevant for the regulation of the energy industry sustaining a socially optimal transition towards 4

A more comprehensive set of input factors is considered in the applied part of this study.

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a cleaner energy system. They are summarised in this section in five points, building, especially, on the model results as stated in section 4.1.

4.3.1 New Reason for Technology Policy First, the analysis in chapter 3 provides an additional reason for policies that subsidise the introduction of new (energy) technologies, based on the split of social and private time-preference rates, given that their divergence occurs for reasons that cannot directly or differently be remedied. It was shown that the extent of the distortion to be internalised, in particular, positively depends on the height of the difference between private and social time-preference rates and the length of the time lag in capital accumulation.

4.3.2 No Support of Subsidies for Specific Technologies Second, the analysis in chapter 3 gives no support for a, in general distortionary, subsidising of only particular technologies, such as renewable energies. Rather, the rationale developed above applies, independantly of the particular type, to any kind of technology, as long as the split of social and private time-preference rates affects its financing in a relevant way. However, the optimal levels of the investment subsidy will vary across different technologies due to differing specific parameter values, such as in the present analysis for the particular labor intensity (λ ), capital intensity (κ ), rate of capital depreciation (γ ), and time lag in construction (σ ) (expressions (3.62), (3.69)).

4.3.3 Necessary Completion of Environmental by Technology Policy Third, the analysis implies that for the transition towards a low-emission energy industry the imposition of an environmental tax alone is in general not sufficient to achieve the social optimum. Rather, environmental policy should be complemented by technology policy. As a general result this is not new, for, it is well known that the process of technological transformation is accompanied by different kinds of (potential) market failures, which provide reasons for state interventions of technology policy (section 1.3). However, from the model this result was derived without taking into consideration the established cases of spillovers of knowledge or consumer value, dynamic increasing returns from learning by using, learning by doing or network externalities, or asymmetric information. In the model it is rather the split of the social and private rates of time preference which leads to the additional distortion.

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4.3.4 Environmental Policy Alone Favors Gradual Change Fourth, more particularly, the analysis suggests that the standard environmental policy of solely imposing an emission tax, or equivalently a permit trading scheme, favors gradual technological change and may not sufficiently account for structural technological change as compared to the social optimum. This result derives from the formulae of the unit costs of production for the established and the new technology. For, while environmental policy, inducing gradual change, always imposes an additional cost to the polluting technology, it does not correct the unit costs of production of the new technology to its (lower) socially optimal level.

4.3.5 Substantiation of Win-win Hypothesis of Environmental Regulation Finally, in the environmental economics literature there has been a broad and often critical discussion of Porter and van der Linde’s (1995) claim that a “well-designed” environmental regulation may exhibit a double dividend in the sense of achieving, by higher environmental standards, taxes, etc., both less pollution and a higher competitiveness through a simultaneously induced increase in resource productivity. The present analysis substantiates this claim with respect to what constitutes a “welldesigned” environmental regulation. As obvious from the formulae of the unit costs of production for the established and the new technology, gradual change always induces additional costs to the existing technology, and thus raises its unit costs of production as compared to the new technology. At the same time, the new technology always exhibits either higher, equal or lower unit costs of production as compared to the established technology. It is the latter case, in which the new technology is introduced, which offers a double dividend in the sense of the Porter hypothesis (no emissions, lower unit costs). A complementary optimal technology policy further facilitates the structural change.

4.4 Conclusions to Theoretical Part Corresponding to the first part of the task deriving from the research question as stated in section 1.1, in this part of the study first the theoretical status of the split of social and private rates of time preference was clarified (section 2.1). It was argued that (a) the split in itself does not constitute a market failure, but occurs as an effect of some underlying distortion. (b) It is generally induced by several different causes at the same time. (c) It may, notably due to transaction costs or incentive issues, constitute itself the direct point of reference for a welfare-enhancing policy intervention. (d) There is number of cases of market failure (especially financial-market

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distortions, e.g., due to adverse-selection problems or uninsurable long-run risks), which are clearly relevant for investments in the energy industry, and may fall in the latter category. Then, the welfare-theoretic implications of diverging social and private time preferences and the time-to-build feature in capital accumulation for the conditions of investment and replacement in the energy industry were analysed. Therefore, a dynamic general equilibrium model of time-lagged capital theory was developed. The ratio of the unit costs of energy of the two technologies derived as the decisive criterion whether investment in the new and partial or full replacement of the established technology occur. It was shown that the split of time-preference rates induces, in addition to that from the standard emission externality, a further distortion, the extent of which positively depends on the time lag in capital accumulation. Both distortions create in a mutually reinforcing way less favorable circumstances for the introduction of the new and the replacement of the established energy technology as compared to the social optimum. As this result holds irrespective of the causes of the split of time-preference rates, the split generally constitutes a case for an additional welfare-enhancing policy intervention. The time lag in capital accumulation matters for the distortion and a corresponding policy intervention only in magnitude. It was finally shown for the case that the consequences of the distorted time preferences cannot otherwise directly or differently be remedied, that the implementation of the social optimum requires, apart from environmental policy, the additional enactment of technology policy, e.g., via payment of an investment subsidy. Of course, the analysis in this part only provides a theoretical indication. The next part substantiates, differentiates, and extends the findings of this part by applying the present analytical setting to the concrete circumstances of structural and gradual change as expected for the German electricity industry around 2015.

Chapter 5

Foundations of the Applied Analysis

The analytical situation studied in the theoretical part is applied in this second part to the concrete circumstances of structural and gradual technological change as expected for the German electricity industry around 2015. The primary aim is to quantify, and to study the relevance of, the welfare and policy implications of the split social and private time preferences derived above theoretically, at one particular, relevant case. Therefore, the economics of conventional energy technologies is, for this case, newly discussed, taking into account one renewed and one new aspect: the deployment of new nuclear power stations and the new introduction of carboncapture-and-storage (CCS) technologies for (quasi-)complete emission abatement. The explorative analysis focuses on two investment-related decisions of a single cost-minimising utility, its choice (i) among three new generation technologies, and (ii) of the optimal moment of transition from an established polluting to a new less polluting technology. Each decision is studied under seven scenarios. In this chapter the analytical setting and specifics of the applied investigation are introduced (section 5.1). Moreover, the chapter sets out the financial model to calculate the unit costs of electricity of the different generation technologies (section 5.2), describes the technologies referred to and specifies the technical and economic parameters (section 5.3), and introduces the policy parameters (section 5.4). Table B.1 in appendix B.1 summarises the assumptions for the technical, financing, and cost parameters.

5.1 Analytical Setting and Specifics of the Applied Investigation This section introduces the analytical setting of the applied investigation (subsection 5.1.1), and explains the focus on the particular cases of Germany around 2015 and conventional generation technologies (subsection 5.1.2). Subsection 5.1.3 highlights previous studies and describes the contribution and the data sources of the present analysis. Subsection 5.1.4 explains its relationship to the theoretical part. C. Heinzel, Distorted Time Preferences and Structural Change in the Energy Industry, Sustainability and Innovation, DOI 10.1007/978-3-7908-2183-3 5, © Physica-Verlag Heidelberg 2009

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5.1.1 Analytical Setting The focus of the analysis changes in this part, for analytical tractability, to the partial-equilibrium perspective of a single cost-minimising utility. The utility is supposed to run a polluting coal-fired power plant commissioned in 1990. Moreover, it is assumed to dispose over three new specific types of generation technologies, a new coal-fired, a gas-fired, and a nuclear power plant, available for commercial operation by 2015. In contrast to the theoretical part, in general also the new technologies may be polluting. For end-of-pipe emission abatement, a carbon-captureand-storage (CCS) technology may be enacted. In accord with the ideal of, in particular, liberalised energy markets, conditions of perfect competition are assumed for all markets such that the utility acts as a price taker. Electricity is supposed to be homogeneous.1 The construction of a new power plant constitutes a small private investment project and does, thus uncorrelated with GDP, not affect the social rate of return, is . Due to rising unit costs of production over time, the economic life of the power plants is finite. The analysis is carried out in discrete time. The two kinds of distortions considered above, one stemming from the (negatively valued) CO2 emissions, the other one related to the split of social and private rates of time preference, induce environmental and technology policies, respectively. However, in view of the state of research concerning the causes of the split, the term technology policy stands now for the policy mix necessary to correct all of the resulting distortions (subsection 5.4.2). In this setting the utility decides (i) which of the three new technologies will be the most profitable, and (ii) when to introduce it, given the ongoing production with its established polluting plant with rising unit costs of production over time. Both decisions are studied under seven scenarios. Apart from the no-policy benchmark, the cases of environmental and technology policy are analysed, first separately, then combined, for the two cases of, first, the absence and, second, the availability of an end-of-pipe CO2 abatement technology. The technology-specific unit costs of electricity constitute the crucial unit of analysis. As financial model for their calculation the conventional levelised-costof-electricity (LCOE) methodology is used, the standard methodology to calculate electric generation costs of particular generation technologies in national and international comparisons. In accord with the applied perspective a more differentiated set of cost categories is considered comprising, apart from capital-investment costs, fuel, operation and maintenance (O&M) and decommissioning costs. In the case of environmental policy, moreover, emission costs and abatement costs eventually add as a further categories. Technology policy affects the calculations as a reduction of the imputed interest rate. The length of the construction period, σ , which ranges depending on the specific technology between 2 and 7 years, enters implicitly into the calculation of the capital-investment costs.

1

Note that the analysis focuses on costs and does not explicitly account for the output market.

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5.1.2 Focus on Germany Around 2015 and Conventional Generation Technologies The cases of Germany around 2015 and conventional technologies seem particularly well-suited for the application of the theoretical reasoning of part one for a number of reasons. First, related to politically secunded efforts to reduce emissions, the liberalisation of energy markets since 1998, and in view of upcoming major reinvestment cycles,2 in recent years the development of the German energy sector has been subject to an intense research such that a well-elaborated empirical background and accessible data for the analysis aimed at are available. Second, as Germany, as an EU Member State, has since 2005 been subject to the EU emission trading scheme for this country for the first time empirical CO2 price data are now being generated. Third, as since the beginning of the 1990s an active national technology policy, supporting especially renewable energy sources by feed-in tariffs, has been conducted, the country disposes over an even longer experience with an ecological technology policy.3 This provides empirical data to compare with it the rationale and findings of the present analysis. Conventional energy sources, including especially lignite, hard coal, natural gas, and nuclear energy, have been contributing until the present the major shares to gross installed capacity, with 74.6 (92.1)% in 2005 (1991), and gross electricity supply, with 84.8 (93.8)% in 2006 (1991) (Table 5.1) and will along with an only slightly Table 5.1 Shares of gross installed capacity by end of 1991/2005 and gross electricity generation in 1991/2006 in Germany (percent), totals absolute (GWe, TWh) (BMWi 2007b)

Lignite Hard coal Gas Oil Nuclear Water Wind Other Total (abs.)

Capacity 1991 2005 23.6 16.6 27.2 22.2 14.3 15.6 8.3 4.1 18.8 16.1 6.9 13.9 0.0 7.7 1.0 3.8 125.9 132.5

Generation 1991 2006 29.3 23.9 27.7 21.4 6.7 11.6 2.7 1.7 27.3 26.3 3.6 4.4 0.0 4.8 2.6 6.0 540.2 635.8

decreasing power demand still play the major role in upcoming reinvestment cycles (EWI and Prognos 2005: ch. 9). This is in spite of the 2002 decision to phase out nuclear energy by about 2022, notably because, despite high subsidising, renewable energy sources will continue to be only partly marketable and their expansion 2 In Germany, by 2020 40 GWe or about one third of the net installed capacity of the electricity industry are to be replaced as a part of usual reinvestment cycles. To this by about 2022 another 20 GWe add due to the political decision to phase out nuclear energy (IEA and NEA 2005: 119). 3 Cf. subsection 6.2.2 for details on this kind of technology policy.

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immediately necessitates an increase of conventional back-up capacities. In addition, a renewed research need on these technologies is given with respect to nuclear power and CCS abatement. Contrary to the respective international discussion, recent scientific and public studies for Germany have been paying only few attention to nuclear power as a renewed option in the German generation mix. The potential impact of the new CCS abatement option on the economics of energy technologies continues only to be to be studied.4 Due to their long construction times – denoted above by the time lag σ – conventional generation technologies fit furthermore well to the analytical model of chapter 3. For the same reason, these technologies are likely to be particularly affected by interest-rate distortions. The upcoming CCS technologies, as an end-ofpipe approach for the (quasi-)complete abatement of CO2 emissions from operation of fossil-fuelled plants, make for the first time the possibility of a (quasi-)clean energy technology – as generally postulated above for the new technology – no fiction also in the case of fossil fuels.

5.1.3 Previous Literature, Contribution, and Data Sources Major studies which have recently analysed the economics and prospects of new generation technologies for Germany include BEI (2004), Enquetekommission (2002), EWI and Prognos (2005), and IEA and NEA (2005). BEI (2004) studies investment options in the German energy industry under liberalised market conditions in 2003 and 2020 with a focus on fossil and renewable energy sources. Enquetekommission (2002) explores the general prospects of all relevant generation technologies in a business-as-usual benchmark and a number scenarios in which an 80% greenhouse-gas emission reduction goal by 2050 as compared to 1990 is implemented. EWI and Prognos (2005) projects the development of the energy markets, including that of technologies, installed capacity, and electricity generation, until 2030 with a particular focus on Germany. IEA and NEA (2005) provides in an international comparison among OECD countries including Germany detailed cost estimates for coal-fired, gas-fired, nuclear, and renewable-energy power stations to be built or approved by 2010. For their analyses BEI (2004) and IEA and NEA (2005) focus on the unit costs of electricity of different generation technologies. Enquetekommission (2002) conducts an explorative analysis of different hypothetic scenarios under the given reduction goal as framework condition. EWI and Prognos (2005) uses a simulation 4

Note that lignite, though the most important domestic energy carrier, has not been included in the analysis as its technology is expected to similarly develop as that of hard coal. Moreover, there is no actual market for lignite, for resource exploitation and plant operation are usually made by the same enterprise, often in the same place. Due to its persistently low and, in real terms, constant price, it is expected to continue to keep its share in the German generation mix in the period under consideration despite a cost-intensive rise in net thermal efficiency from 43 to 48% and its higher emission factor of 0.396 t CO2 /MWh (BEI 2004, EWI and Prognos 2005, Schiffer 2002).

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model of the actual generation capacities based on best available data. To derive technology-specific generation costs, all studies rely on the LCOE methodology. However, due to their different analytical approaches, slight variations in the financial models, and the high number of parameters included, the results of the different studies, including the present, can in general only be compared with qualifications. With regard to the prospects of particular technologies, neglecting nuclear power, the studies generally project for the mid-2010s, in the case without policies, the lowest unit costs of baseload electricity generation for lignite before hard coal, gas, and renewable energies. As regards nuclear power the indications differ. While IEA and NEA (2005) ranks it in its r = 0.1 scenario as third option close to hard coal and in its r = 0.05 scenario clearly as first option, Enquetekommission (2002) is more skeptical about its economic prospects, without indicating a clear ranking of generation costs.5 Mostly conducted before the introduction of the EU ETS, the studies consider the impact of environmental policy only for particular cases. BEI (2004: sec. 8.7) finds that gas becomes profitable over hard coal from CO2 prices of about 30–35 ¤/t for r = 0.08, IEA and NEA (2005: 123), for r = 0.05, for prices of about 30 ¤/t. EWI and Prognos (2005: ch. 9) projects the persistence of status-quo environmental and technology policies, notably with a linearly rising CO2 price from 5 to 15 ¤(2000)/t between 2010–2030. It forecasts the shares of gross installed capacity by 2030 in the case of lignite to remain constant at about 17%, for hard coal to decrease to below 10%, for gas to increase to about 34% and for renewable energies to rise to about 40%. Renewable energies would thus provide in 2030 with 26% for the third highest share of gross electricity behind gas and lignite, with about 33 and 29%, respectively.6 The CCS abatement option is discussed in these studies only for some cases. While the older ones, BEI (2004: sec. 6.4) and Enquetekommission (2002: 477), judge it not to be applicable before 2020/2025, EWI and Prognos (2005: 121– 125) estimates it to be available by 2015. Only IEA and NEA (2005: 119–123), though without commenting on its feasibility, includes in its technology comparison a hard coal-fired integrated-gasification-combined-cycle (IGCC) power plant with CO2 capture. It becomes profitable in the r = 0.05 scenario over the plant without CO2 capture from a CO2 price of 15 ¤/t and from 20 ¤/t over the pulverised-fuel power plant, the type usually considered in this study. The abatement unit costs implied, however, only cover the costs for CO2 capture, and not those for transportation and storage as actually arising in addition. For comparisons with the present analysis, its indications are therefore only of a limited value. Recently, WI et al. (2007) has provided an encompassing analysis of the CCS option for the German energy system until 2050. It notably supports the technical and economic indications for CCS in EWI and Prognos (2005). WI et al. (2007: 206) 5

The generation costs of nuclear power are discussed in subsection 5.3.3. In a variant of their study with higher oil prices, EWI and Prognos (2006) account for implied hard-coal and gas-price escalations by 10 and about 25%, projecting their shares of gross installed capacity in 2030 with 19 and 17%, respectively. With regard to unchanged fundamental data, the authors judge the variant, however, as less probable. This study sticks to their former report. 6

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shows for 2020 that the unit costs of electricity of a coal-fired power plant with CCS abatement immediately exceed those of a gas-fired power plant with CCS facility, irrespective of the CO2 price. This is because the capital-investment and operationand-maintenance costs rise in the case of the coal-fired plant relative to the plant without CCS facility, in absolute terms, clearly stronger than in the case of the gasfired plant. It finds CCS abatement in 2020 for a CO2 price of about 15 ¤/t by far not profitable. Further scientific studies differentiate the analyses of the mentioned studies, e.g., with respect to the effect of different regulatory measures on the electricity supply industry and supply security in Germany (Brunekreeft and Twelemann 2005) or the general influence of the choice of different policy instruments on CCS application (Gerlagh and van der Zwaan 2006). Schwarz (2005) shows that both environmental policy and the nuclear phase-out will significantly intensify modernisation activities on conventional power plants and thus enhance their lifetimes. However, these further studies do not consider investments in new nuclear power plants, or discuss the further particular issues which are in the focus of the present study. In addition to the discussions in Enquetekommission (2002), IEA and NEA (2005), as well as, e.g., EWI and EEFA (2005), there is on international level an ongoing, in part controversial, debate on the expected costs and economic prospects of nuclear power under liberalised market conditions (e.g., Epaulard and Gallon 2001, Gollier et al. 2005, Lescoeur and Penz 1999, MIT 2003, NEA 2003, Roques et al. 2006, Rothwell 2006, The University of Chicago 2004). In these discussions, notably, the LCOE methodology has been criticised for not sufficiently accounting for the increased uncertainty of power-plant investments after liberalisation (e.g., MIT 2003, IEA and NEA 2005). Instead, e.g., real-option approaches have been used. However, while these studies indicate an important direction for further research, thus far no alternative analytical scheme has been established. For this reason on the one hand and for the sake of comparability on the other, it seems appropriate in this study to stay with the conventional LCOE methodology. To this literature, the applied analysis in this part of the study contributes notably in five ways. First, obviously, while the importance of the discount rate has often been emphasised and results are sometimes considered for different levels of it, none of these studies has analysed the impact of correcting optimal technologypolicy interventions as induced by deviations from its socially optimal level. Second, considering the impact of interest-rate distortions against the background of, and in interplay with, varying CO2 -price levels, this study adds a detailed analysis of the impact of environmental policy on the ranking of generation technologies and the optimal moments of transition to different new technologies to this literature. Third, by taking into account nuclear power, notably in two different cost scenarios, clarification is added to the relative prospects of this technology in the future German generation mix. Fourth, treating both emission and abatement costs as separate cost categories in the financial model, the analysis supplements the previous studies by a systematic investigation of the necessary levels of abatement unit costs and CO2 prices for a new end-of-pipe abatement option to become relevant. Finally, the projection of the investment conditions for the new generation technologies on

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a temporal scale allows the present analysis to complement previous studies by an explicit consideration of the impact of different policy measures and the abatement option on the timing of structural change in the energy industry. The data for the determination of the parameters for the analysis in chapters 6 and 7 are mostly taken from the four mentioned major studies as well as, for the established coal-fired power plant, from Schneider (1998). For nuclear power it is, in addition, especially referred to the two recent major U.S. studies, MIT (2003) and The University of Chicago (2004). More detailed information on specific contents of the studies consulted, as far as relevant, as well as the data used are provided in section 5.3.

5.1.4 Relationship to Theoretical Part The analysis of the theoretical part both motivates and provides the theoretical rationale for the analysis in the applied part. As obvious from the description of the analytical setting in subsection 5.1.1, this second part takes up the analytical situation studied in the theoretical part with only minor adaptations for the sake of realism. The time horizons considered are now finite. The analysis is in discrete time. Also the established technology is assumed to deteriorate, such that its unit costs rise over time. Now both the established and the new technologies may be polluting and, accordingly, subject to end-of-pipe abatement. In contrast to the concave abatement function dependent on the abatement effort (section 3.1), for analytical tractability and in accord with the given data, an end-of-pipe technology for complete emission abatement with fixed abatement unit costs is considered. The formulae for the unit costs of energy are calculated in a more differentiated way using a particular financial model with a more encompassing set of cost categories, which notably also accounts for fuel as well as eventual emission and abatement costs. The analysis being centred on costs and, in particular, the quantification of above derived welfare and policy implications, both the demand side and distorted financial markets remain exogenous. The influence of varying levels of environmental and technology policies is studied by considering relevant sensitivity ranges. For the given modifications, in substance, all propositions of the theoretical part remain valid also in this analytical setting, with the only exception that – due to the deterioration also of the established technology, the (as assumed) monotonous behavior of the unit costs of electricity over time, and the finite time horizons – the corresponding conditions of investment and (full) replacement coincide (chapter 7). On this theoretical basis, the analysis substantiates, differentiates, and, to some extent, extends the findings of the theoretical part. Chapter 6 takes the enlarged unitcost formula of the new technology (as calculated based on the financial model of section 5.2) to quantify the distortion induced by the split of social and private discount rates, shown in Propositions 3.1 and 3.3 of chapter 3. At the same time, it indicates maximal levels of the Pigou investment subsidy for the case that the distortion is internalised according to Proposition 3.5. The former analysis is supplemented by

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an investigation of the separate and combined influence of environmental and technology policies on the choice among the three technologies considered for the construction of new generation capacity. Chapter 7 projects the conditions of investment and replacement as stated in the propositions of chapter 3, in analogy, on a temporal scale, allowing for the analysis of the impact of environmental and technology policies on the optimal moments of transition from the established to the new technologies. By considering the variation of technology choice and optimal moments of transition for the cases of both the absence and the availability of an end-of-pipe abatement technology, the analysis in chapters 6 and 7 differentiates the results of the theoretical part concerning the interplay of gradual and structural change.

5.2 Financial Model The financial model at the basis of the applied analysis is adapted from Bejan et al. (1996: ch. 7). Their treatment is oriented, in turn, towards the standards set out by EPRI (1991). It calculates the unit costs of electricity of generation technologies depar- ting from the capital costs (subsection 5.2.1) and different kinds of costs during operation (subsection 5.2.2) based on the levelised-cost methodology (subsection 5.2.3). The particular determination of the unit costs of electricity of the established power plant in this study is explained in subsection 5.2.4.

5.2.1 Capital Costs The capital costs of a power plant comprise its capital-investment and its decommissioning costs.7 The two types of cost occur before commissioning and after the end of the operating time of a power plant, respectively. They constitute one-time costs with respect to the operating life of a plant. The capital-investment costs, CC, consist of the power plant’s constructioninvestment costs and the imputed interest payment. The construction-investment costs, Ic , are made up by its fixed-cost, or overnight, investment costs and so-called other outlays. The overnight investment costs account for the undiscounted capital outlays before a plant’s commissioning. They are separated into direct and indirect costs. Direct fixed-capital investment costs are for all permanent equipment, materials, labor and other resources involved in the fabrication, erection and installation of the permanent facilities. Indirect fixed-capital investment costs account for those resources which do not become a permanent part of the facilities but are required for the orderly completion of the project, including supervisory engineering and support labor costs, contingencies, the owner’s costs of infrastructure and training incurred to get the plant running safely when built, and, eventually, first-of-a-kind 7

In accord with the empirical data available, major refurbishment, as a type of capital cost occuring during operation, is included in the O&M costs (subsection 5.2.2).

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(FOAK) or Nth -of-a-kind (NOAK) capital costs. Other outlays consist of the startup costs, working capital, costs of licensing, R&D, and the interest payments during design and construction. The specific (construction) investment costs of a technology, Isp , are usually indicated per unit of net installed capacity, ICnet . The constructioninvestment costs thus derive as Ic = Isp ICnet .

(5.1)

The construction-investment costs are included in the annual cost analysis via the cost-accounting depreciation. For convenience, straight-line depreciation is assumed. Thus, the annual amount of depreciation, D(t), derives as the Td th part of Ic , where Td is the cost-accounting term of depreciation, D(t) =

Ic . Td

(5.2)

Economically, Td coincides with the (expected) economic life of a plant. However, in accord with the applied literature, to account for the increased uncertainty under liberalised market conditions, in this study Td is assumed not to exceed the planning horizon, T , of a power-plant investment project, such that Td ≤ T . For all technologies, moreover a common cost-accounting term of depreciation of Td = 20 is assumed. This facilitates the calculations, but clearly constitutes a simplification.8 The annual imputed interest payment, IIP(t), refers to the salvage value of Ic in t. Payments and depreciation are assumed to be made at the end of a period. In the first year of operation, the interest is thus paid on the full construction-investment costs. The imputed interest payment in period t is determined as Ic (1 − t−1 Td )r , if t ≤ Td IIP(t) = , (5.3) 0 , if t > Td where r is the real imputed interest rate, which is assumed to be constant. The annual capital-investment costs of a power plant in period t of operation then amount to Ic 1 + (T − t + 1)r , if t ≤ Td d Td . (5.4) CC(t) = 0 , if t > Td A plant’s decommissioning costs, DC, derive as the product of the specific decommissioning costs of the technology, DCsp , and net installed capacity, ICnet , DC = DCsp ICnet .

(5.5)

8 The reduced depreciation term provides, to some extent, for less favorable unit costs of electricity, the more the higher the construction-investment costs of a technology. The appropriate treatment of Td in the calculation of generation costs constitutes a particular issue to be clarified with respect to the systematic consideration of the utilities’ varied risk exposure (subsections 5.1.3, 5.4.2, section 8.3).

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5.2.2 Costs During Operation Usually, two basic categories of costs incurred during a plant’s economic lifetime are distinguished, (i) operation and maintenance (O&M) and (ii) fuel costs.9 For the analysis of the impact of environmental policy, (iii) emission and (iv) abatement costs are added as two further categories. O&M costs, OMC, are composed of all costs for operation and maintenance of the plant, apart from fuel, emission, and abatement costs. In general, they divide into a fixed and a variable part. Fixed specific annual O&M costs, OMC f ix (t), comprise labor, maintenance and insurance costs per unit of net installed capacity, ICnet , in t. Variable specific O&M costs, OMCvar , consist of the costs for operating supplies other than fuel and emission costs, per amount of output produced in t, x(t). The latter derives as net installed capacity times hours of full-load operation, h f l (t), x(t) = ICnet h f l (t) .

(5.6)

The O&M costs in period t can thus be determined as OMC(t) = OMC f ix (t)ICnet + OMCvar x(t) .

(5.7)

Fuel costs, FC, include the costs related to fuel supply at the power plant, including commodity price and transportation.10 Instead of considering an eventual fuel-price escalation, the present study refers to the estimated (mean) fuel price, pfuel , during the remaining economic life of a power plant. The annual fuel costs are further determined by the annual fuel consumption, FCs(t), which derives as the amount of electricity generated in t, x(t), divided by the plant’s net thermal efficiency, ηnet , x(t) FCs(t) = . (5.8) ηnet The annual fuel costs are then calculated as the product of fuel consumption in t and mean fuel price (5.9) FC(t) = FCs(t)p f uel . Emission costs, EC, are calculated as the product of the annual amount of emissions generated, E(t), deriving as annual fuel consumption times technology specific emission factor, fem , E(t) = FCs(t) fem , (5.10) and the emission price, τe (t), which is assumed to be in real terms, EC(t) = τe (t)E(t) . 9

(5.11)

Though another kind of operating costs, fuel costs are usually separated from the remaining O&M costs because of their particular importance. 10 In the case of nuclear power, they include all costs related to the up-stream and down-stream steps of the fuel cycle as well as the costs of transportation between the steps.

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Abatement costs, AC, are calculated as the product of the annual amount of emissions generated, E(t), and specific abatement costs, ACsp (t), per mass unit of emission,11 AC(t) = ACsp (t)E(t) . (5.12)

5.2.3 Unit Costs of Electricity of the New Technologies The unit costs of electricity are determined in two steps departing from the present values at the date of commissioning of the different cost components occuring until the end of economic life and the decommissioning costs as an overnight cost occuring at the end of a plant’s life. First, the real levelised costs of electricity generation, RLC, over the planning horizon, T , are calculated. Second, they are divided by the mean annual amount of electricity generated, x. The real levelised costs, RLC, indicate the mean annual costs of electricity generation by a power plant in a particular year of operation during the planning horizon, T . In this study T is determined according to the co-termination approach (Bejan et al. 1996: 386f). According to it, for the technology comparison for all projects a common planning horizon is chosen, which may be of any meaningful length. Thus, T is assumed to equal the expected economic lifetime of the shortest lived alternative. In this case for any longer lived alternative the salvage value at the end of the planning horizon is added to the particular project’s net present value discounted with the discount rate of the last year of the planning horizon. In order to calculate the RLC, then, first, the present value of the costs incurred before decommissioning, PVbd (T ), is determined. It derives as the sum of the present values of capital investment, O&M, and fuel, as well as, eventually, emission and abatement costs, or CC(t) + OMC(t) + FC(t) + EC(t) + AC(t) . (1 + r)t t=1 T

PVbd (T ) = ∑

(5.13)

The corresponding part of the real levelised costs is calculated by multiplication r(1+r)T with the capital-recovery factor, (1+r) T −1 . As the decommissioning costs only occur after the end of economic lifetime of a plant, they are to be levelised using the uniform-series sinking fund factor, (1+r)rTd −1 .12 The real levelised costs thus 11 Despite the capital-cost component of the end-of-pipe abatement facility, in accord with the empirical data, in this study abatement costs are only considered as proportional to current emissions. 12 Bejan et al. (1996: 355–357) derive the two levelisation factors as follows: They can be derived 1 from the single-payment present-value, or discount, factor (1+r) n , or its reciprocal value, the singlepayment compound-amount factor. In order to calculate the ordinary annuity A of the known future sum F, the future value or amount of the annuity, accrued at the end of the period t, F is divided by (1+r)n −1 , the uniform-series compound amount factor, the reciprocal value of which is called the r uniform-series sinking fund factor. For N = Td , the uniform-series sinking fund factor constitutes the levelisation factor of DC.

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amount to RLC = PVbd (T )

r r(1 + r)T + DC . T (1 + r) − 1 (1 + r)Td − 1

(5.14)

Finally the unit costs of electricity of a particular reference power plant derive as UCel =

RLC . x

(5.15)

Note that the UCel in general vary for different years of commissioning, and are insofar time-dependant.

5.2.4 Unit Costs of Electricity of the Established Technology At the basis of the determination of the optimal moment of transition from the established to a new technology in chapter 7 is the schedule of the unit costs of electricity of the established technology, UCT1 (t), between t1 and tn , the first and the final year of analysis. t1 is the first year in which the new power plants could be commissioned, tn the moment of transition to the highest-cost alternative in the no-policy benchmark. By definition, for the end of the plant’s expected economic lifetime tend ∈ [t1 ,tn ] holds (section 7.1). In general, the UCT1 are determined as indicated above in this section. However, as the established power plant enters the analysis at some time t1 during its time of operation and for the analysis its unit costs in that period and the later years of operation are needed (rather than those of the full investment project at the time of commissioning), their determination is subject to some particularities. Due to the lack of reliable empirical data in the literature, for the present analytical purposes the UCT1 shape in the no-policy benchmark is calibrated with respect to the following stylised indications, ceteris paribus: (1) In t1 , the established plant is fully depreciated and financial reserves are built up for decommissioning, such that all capital costs are sunk. Over the whole of the plant’s time of operation, the net installed capacity, ICnet , the output, x, and, with ηnet , also the input, FCs(t), are fixed. The behavior of UCT1 (t), t ∈ [t1 ,tn ], is thus only determined by the development of p f uel , OMC f ix , and OMCvar . While the p f uel schedule is empirically given, for the OMCk , k ∈ { f ix, var}, only mean values over the plant’s expected economic lifetime are available in the literature. (2) In t1 , the OMCk , k ∈ { f ix, var}, meet their arithmetical mean over the plant’s expected economic lifetime, OMCk .

In order to derive the present value of the annuity, defined as the amount of money that would have to be invested at the beginning of the annuity term (present time) at an effective compound rate of return per period r, the uniform-series sinking fund factor is to be divided by the singlepayment compound amount factor, yielding the uniform-series present-value factor. For N = T , its reciprocal value, the capital-recovery factor, constitutes the levelisation factor of PVop (T ).

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(3) In tend , the UCT1 are equal to the UCT2 of the least-cost alternative among the new technologies, such that for t = tend the following equation holds: UCT1 (t) =

OMC f ix (t) ICnet + OMCvar (t) x + p f uel (t)FCs = UCT2 (t) . (5.16) x

(4) For any t ∈ {t1 ,t2 , ...,tn }, the OMCk (t), k ∈ { f ix, var}, are determined as OMCk (t) = OMC k such that

OMC (t ) t−1 tend −1 k end , OMC k

(5.17)

1 tend OMCk (t) = OMC k , TL t=t∑ com

where tcom is the plant’s year of commissioning, TL its expected economic lifetime. (5) In any specific year t ∈ {t1 ,t2 , ...,tend }, the UCT1 (t) are determined like UCel in equation (5.14), with T = tend − t + 1. The new planning horizon T = 1 in each further period t ∈ {tend + 1,tend + 2, ...,tn }, which comes to the same as to substitute in equation (5.14) for RLC the current costs, i.e. here OMC(t) + FC(t). In the case of environmental policy, the UCT1 are further determined by emission as well as eventual abatement costs.

5.3 Technical and Economic Parameters In this section the technologies, technical assumptions, and directly technologyspecific cost assumptions of the reference power plants for the analysis in chapters 6 and 7 are set out. In accord with the empirical data the plants are assumed to be built on new sites. All indications are net of taxes. Unless differently indicated, the technical account follows IEA and NEA (2005), where also more detailed information and further references can be found. The studies referred to for the cost assumptions are briefly described in the respective places.

5.3.1 Old and New Coal-fired Reference Power Plants The cost estimates for the coal-fired power plants refer to plants operating on the basis of combustion of pulverised coal in conventional boilers at baseload. Other generation technologies commonly used in OECD countries include fluidised-bed boilers and integrated gasification combined cycles (IGCC).

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5.3.1.1 Basic Technology and Plant Features Conventional pulverised-coal boilers burn finely ground coal particles in a boiler with water-cooled walls. Steam is raised in these walls and in a series of heat exchangers which cool the hot combustion gases. The steam is then passed through a condensing steam turbine which drives a generator. Fluidised-bed boilers burn coal in a “bed” or dense cloud of aerodynamically suspended particles. The airflow suspending the particles is sufficiently strong such that a portion of the particles is entrained out of the boiler and then recirculated to it via cyclones. As in conventional boilers, the heat released by combustion is captured within the boiler in water-cooled walls and then a series of heat exchangers which cool the combustion gases. Atmospheric fluidised beds operate at atmospheric pressure, whereas pressurised fluidised beds use a combustion chamber which is held at pressure. The latter allow to combine them with gas turbines which compress the combustion air and provide the expansion turbine for hot gases. Pressurised fluidised beds may also be used to gasify coal for power production. IGCC plants convert coal first to a combustible fuelgas, or synthetic natural gas, and then burn this fuel in a gas turbine combined cycle. The principal components of a IGCC plant are thus a coal gasification facility, typically including an oxygen-production and gas-cleaning facility, and a combined-cycle power plant (see description in subsection 5.3.2). The gasifier functions by only partially combusting the coal. This partial combustion provides enough energy to drive off volatile compounds and drive gasification reactions to create hydrogen, carbon monoxide, and methane gas. The basic configuration of steam generation followed by expansion in a steam turbine is used in all boiler steam-electric power plants. The pressure and temperature at which steam is generated constitute key design features. In the past, the majority of coal-fired boilers built in the OECD has been subcritical. In subcritical boilers, steam pressure is below the critical pressure of water, at about 220 bar. Supercritical boilers raise steam above the critical pressure of water. Using steam at supercritical pressure may increase the efficiency of steam power cycles, both in pulverised-coal and fluidised-bed boilers. The special steels capable of resisting higher temperatures and pressures while still resisting corrosion imply at the same time a higher cost of boiler, steam turbine and control valves. Other cycle improvements, such as double reheat, once-through steam heating, enhanced feedwater heating, and reduced piping pressure drops, also improving cycle efficiency, increase the expenses for equipment and materials. The increased costs are expected to be compensated by the enhanced efficiency and emission reduction under environmental policy. Net plant efficiency, which was in Germany for new power plants since the 1980s and in average until recently about 38%, was raised to 45-46% using supercritical steam cycles in the 2000s (BMWA 2003: 26, BEI 2004: ch. 6). By 2010-2020, steam conditions above 250 bar and 566°C, or advanced supercritical conditions, are projected to increase cycle efficiencies to about 51%. For the established coal-fired power station considered in this study, which is supposed to be commissioned in 1990, a net thermal efficiency of 45% is assumed.

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The new coal-fired power station, commissioned in 2015 or later, is assumed to operate at a net thermal efficiency of 51%. In accord with the literature, for both power stations an economic lifetime of 40 years and a construction time of 4 years are supposed (BEI 2004: 8–5, A–3, IEA and NEA 2005: 35f, Schneider 1998: 17, The University of Chicago 2004: 6–6).

5.3.1.2 Cost Assumptions The cost assumptions for the fossil-fuelled reference power stations considered in this study are taken from IEA and NEA (2005), BEI (2004), EWI and Prognos (2005) and Schneider (1998).13 • IEA and NEA (2005) provides detailed cost estimates for a number of power stations to be built or approved in Germany by 2010, in particular a pulverised-fuel hard-coal steam plant with supercritical conditions and a net thermal efficiency of 46% and a combined cycle gas turbine (CCGT) plant with a net thermal efficiency of 60%. The cost estimates are taken from different studies and the literature and provided after clearance with different manufactures and electric utilities. • BEI (2004) provides estimates of cost ranges for a number of different types of power stations for 2003 and 2020 to be built in Germany, based on its own data as well as the consultation of experts from industry and lobbies. It refers to general hard-coal and CCGT power stations with net thermal efficiencies for 2003 (2020) of 45 (51) and 57 (60)%, respectively. The values of the specific investment costs for 2020 derive by adding 10% to the cost ranges for 2003. • EWI and Prognos (2005) provides discussion and projections for the availability and prices of various energy carriers, the development of power plant and abatement technologies, as well as of power plant capacities and electricity generation with a particular focus on Germany until 2030. It provides cost estimates only for some general kinds of fossil-fuelled power plants for 2005 and 2030 and more detailed information on fossil fuel prices. • Schneider (1998) contains an extensive review of the cost estimations in the literature of his time, in particular for different types of hard-coal power stations. Capital costs. A plant’s main capital cost parameters, apart from financing costs, are its specific investment and its specific decommissioning costs (subsection 5.2.1). IEA and NEA (2005: 120) provides the specific investment costs of the pulverised-fuel hard-coal power station under consideration the, both internationally and as compared to BEI (2004), comparatively low estimate of 820 k¤/MWe. It assumes 34.5 k¤/MWe for the specific decommissioning costs. BEI (2004: A–3) estimates specific investment costs of 850–1,000 k¤/MWe for 2003, and of 935–1,100

13

IEA and NEA (1998) does not contain data for Germany.

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k¤/MWe for 2020. It disregards decommissioning costs.14 The figures indicated in Schneider (1998: 18) are without exception above the 2003 cost range of BEI (2004). For the present study, with respect to the technical assumptions met above, for the established and the new coal-fired reference power stations specific investment costs of 925 and 1020 k¤/MWe, respectively, are assumed. The higher value in the case of the new plant takes into account the use of supercritical cycles with increased efficiency. The specific decommissioning costs are assumed to amount to 34.5 k¤/MWe in both cases. Operation and maintenance (O&M) costs. Specific O&M costs for coal-fired power plants are indicated by IEA and NEA (2005) and Schneider (1998). While IEA and NEA (2005: 120) refers to specific fixed annual O&M costs of 36.6 k¤/MWe and specific variable O&M costs (without fuel costs) of 2.7 ¤/MWh, Schneider (1998: 23–30) assumes for subcritical coal-fired power plants of his time specific fixed annual O&M costs of 60 kDM/MWe and specific variable O&M costs of 3 DM/MWh (prices of 1991). It is to be noted that O&M costs generally rise in real terms during the economic life of a power station, to which the different cost components contribute in different ways (Schneider 1998: 23f). While the development of labor costs is linked with the development of real wages and of social insurance, the maintenance part of the O&M costs generally rises considerably with the age of a power plant. In the present study, for the established coal-fired reference power plant specific fixed annual O&M costs of 40 k¤/MWe and specific variable O&M costs (without fuel costs) of 4 ¤/MWh are assumed, for the new plant 36.6 k¤/MWe and 2.7 ¤/MWh, respectively. These figures indicate the mean values over the plants’ economic life. Fuel costs. The prices for hard coal are, both internationally and for Germany, expected to slowly rise in the period of consideration, i.e. 2015–55 (EWI and Prognos 2005: 68f, 296, IEA and NEA 2005: 37, 205). The increase is reinforced by increasing oil prices for transport. The projected prices are the prices at the power plant, i.e. include processing and transport costs. Projected coal prices are expressed in ¤/energy unit to reflect real energy content of the coal taking into account varying calorific values of different coals.15 The present study follows the price indications given in EWI and Prognos (2005: 296) for Germany, as shown in Table 5.2. The values for 2040 and 2050 have been extrapolated using the escalation factor expressed in the older estimations in IEA and NEA (2005: 121). After 2050, they are expected to continue to rise by the same annual amount as in the 2015–2050 mean. This assumption takes into account the increasing scarcity as well as that no general availability constraint is expected to be reached until then (EWI and Prognos 2005: ch. 2). 14 Decommissioning costs are more important in the case of nuclear energy, which is not considered in BEI (2004). 15 EWI and Prognos (2005) and IEA and NEA (2005) indicate fossil-fuel prices in monetary unit per gigajoule, where 3.6 GJ are equivalent to 1 MWh.

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Table 5.2 Hard coal prices at the plant (¤/MWh) (EWI and Prognos 2005: 296, IEA and NEA 2005: 121, own calculations) Year 2015 2020 2025 2030 2040 2050

Hard coal ¤/MWh 6.552 6.552 6.624 6.696 7.334 7.972

In the case of the established coal-fired reference power station, the coal price is assumed to follow its actual expected development as expressed in Table 5.2. For the new technology, a constant mean coal price of 7.13 ¤/MWh is assumed for commissioning in 2015. For later commissioning dates, the mean coal price is derived, equivalently, as the 40-years arithmetical mean based on the above indications.

5.3.1.3 Pollution and Pollution-control Systems During combustion, the impurities of coal are released as necessary joint products of electricity generation. In addition to CO2 , nitrogen oxides (NOx ) are formed by the combustion process itself by reactions with nitrogen contained in the coal and in the combustion air. Toxic by-products found in combustion gases include sulphur dioxide, nitrogen oxides, halogens, unburned hydrocarbons, and metals. From the noncombustible portion of coal feed and unburned carbon ash remains, half of which is typically collected in the bottom of the boiler. The remainder is carried along in the combustion gases as fly ash. Today various environmental control systems are incorporated into plant design to directly limit the formation of pollutants or remove them from flue gases. Pollution-control systems for coal-fired plants are generally the same regardless of the steam pressure employed. While sulphur dioxide is usually controlled by fluegas desulphuration systems, nitrogen oxides are abated by modifications to the coal combustion system itself. For particulate matter, electrostatic precipitators or fabric filters are alternatively applied. For CO2 , currently carbon-capture-and-storage (CCS) technologies are developed as a major end-of-pipe approach to abate completely carbon emissions of (large) power stations (EWI and Prognos 2005: 121–125, WI et al. 2007). CCS involves the three distinct processes of capturing CO2 from the gas streams emitted during electricity production, transporting the captured CO2 in pipelines or tankers, and storing CO2 underground in deep saline aquifers, depleted oil and gas reservoirs, or unminable coal seams. CO2 can be captured either before or after combustion using a range of existing and emerging technologies. In conventional processes, CO2 is captured from the flue gases produced during combustion (post-combustion

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capture). Among post-combustion capture technologies, chemical absorption via aqueous alkaline solvents such as monoethanolamine (MEA) is best known. It is expected to be among the first available by 2015. However, it is also possible to first convert the hydrocarbon fuel into CO2 and hydrogen, remove the CO2 from the fuel gas and combust the hydrogen (pre-combustion capture). CO2 capture is most effective when used in combination with large-scale, high-efficiency power plants. Pollution control and the pollutant control levels constitute key cost factors. Plants with more efficient steam cycles have marginally less expensive pollutioncontrol systems as less coal is burned per unit of electrical output. However, the tighter the emission limits, the more expensive are the construction and operation of pollution-control systems and the more energy they will consume. CO2 capture rises investment costs, reduces net thermal efficiency of a plant and rises necessary fuel consumption. At the same time, less emissions imply reduced emission costs imposed by environmental policy. With regard to pollution and pollution-control systems, the present study concentrates on CO2 as primary climate gas and carbon capture and storage (CCS) as its major upcoming end-of-pipe abatement technology. Following BEI (2004: A–9), for hard coal a CO2 emission factor of 0.338 t CO2 /MWh is assumed.16 EWI and Prognos (2005: 125) estimates for the MEA post-combustion abatement technology for coal-fired power plants cost ranges of 25–45, 10–15, and 2–10 ¤/t CO2 for CO2 capture, transport over 200 km, and storage, respectively, and thus a specific CCS full cost range of 37–70 ¤/t CO2 . In the present study, a homogeneous end-of-pipe CO2 abatement technology for complete emission abatement with fixed abatement unit costs (AUC) in a range of 10–60 ¤/t CO2 is assumed. AUC of 37–70 ¤/t CO2 are regarded as the relevant range of abatement unit costs for the coal-fired plants considered.

5.3.2 Gas-fired Reference Power Plant The two basic types of gas-fired power plants most frequently used in OECD countries are gas turbines and combined cycle gas turbines (CCGT). While gas turbines, due to their comparatively low capital, variable O&M, and fuel costs as well as emissions, are almost solely used for peak load, CCGT plants are usually used for mid- or baseload depending on economic circumstances.

5.3.2.1 Basic Technology and Plant Features Gas, or combustion, turbine cycles burn the fuel gas at over 1,300 °C. Combinedcycle gas turbines (CCGT) combine gas and steam turbines. They use the hot engine exhaust stream from the gas turbine to raise steam for electricity production from 16

The emission factor indicates the mean mass of pollutant per energy unit (calorific value) of the fuel input (Rebhan 2002: 208).

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a steam turbine. About two thirds of the electricity generated by a CCGT plant stem from the gas turbine cycle, one third from the steam turbine cycle (Schneider 1998: 5). While in 2000 gas turbines alone reached a thermal efficiency of about 35%, for 2010-2020 thermal efficiencies of about 40% are projected (BEI 2004: 6-9f). CCGT plants have currently thermal efficiencies between 50 and 58%. Until 20102020, using advanced gas turbines, with higher combustion temperatures, steamcooled turbine blading, and more complex steam cycles, efficiencies of over 60% are expected (BMWA 2003: 29, BEI 2004: 6-10). More than for other types of power plants, the realisation of high thermal efficiencies depends on plant size as well as the current capacity factor. Highest thermal efficiencies are realised above a net installed capacity of 100 MW. Partial load operation shrinks thermal efficiency to some extent (BEI 2004: 8-2). Apart from that, gas turbine thermal efficiencies are affected by ambient temperatures. As ambient air temperature increases, plant output decreases due to reduced mass flow through the turbine itself. As with other plant types, the design point efficiencies are typically higher than the average efficiency obtainable on an annually averaged basis because of variations in ambient conditions and in off-design point operating regimes. While heat recovery steam generators have typically used two steam pressure levels to maximise the heat recovery from the gas turbine exhaust stream, boilers on advanced turbines will take advantage of higher exhaust stream temperatures by using three levels. Moreover, the boilers used to recover heat from the turbine exhaust (heat recovery steam generators) and the steam turbines are relatively standardised. The use of standardised components allows manufacturers to market modular power plants with reduced design and construction costs. The construction time of a new plant usually expands over 2 to 3 years. For Germany usually 2 years are assumed (IEA and NEA 2005: 40, Schneider 1998: 17). Due to the high loading of the gas turbine part the economic lifetime of a gas-fired plant is generally assumed to stay below those of coal-fired or nuclear power plants. It is generally assumed between 20 and 30 years (IEA and NEA 2005: 35, BEI 2004: 8–9). While this study considers a net installed capacity of 1.5 GW, well above 100 MW, a gas-fired plant’s net thermal efficiency is still affected by a reduced capacity factor and fluctuations of ambient air temperature. In accord with the new coalfired and the nuclear power plant, the commissioning of the CCGT reference plant is projected for 2015 or later. It is assumed to operate at baseload with a net thermal efficiency of 60%. The construction time is assumed to amount to 2 years, the economic lifetime to 25 years.

5.3.2.2 Cost Assumptions The cost assumptions for the CCGT reference power station are taken from IEA and NEA (2005), BEI (2004) and EWI and Prognos (2005). As noted above, the first two studies consider CCGT plants with net thermal efficiencies of 60% built

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or approved by 2010, or 57 (60)% for 2003 (2020), respectively, both for Germany. EWI and Prognos (2005) is consulted for gas price projections. Capital costs. IEA and NEA (2005: 120) estimates specific investment costs for a CCGT power station of 440 k¤/MWe, and specific decommissioning costs of 15.8 k¤/MWe. BEI (2004: A–3) provides the specific investment costs an estimated range of 400–550 k¤/MWe for 2003. Assuming again the specific investment costs to grow by 10% due to technical progress, it indicates an estimated range of 440–605 k¤/MWe for 2020. In this study, for the CCGT reference power station specific investment costs of 500 k¤/MWe and specific decommissioning costs of 15.8 k¤/MWe are assumed. O&M costs. Following the indications in IEA and NEA (2005: 120), the specific fixed annual O&M costs of the CCGT reference power station are assumed to amount to 18.8 k¤/MWe, the specific variable O&M costs to 1.6 ¤/MWh. Fuel costs. Despite decreasing real costs for transport via pipeline or liquefied natural gas (LNG), determining roughly half of the gas price, due to worsening reservoirs and high transport costs rising real gas prices are expected in the period of consideration, i.e. 2015–55 (EWI and Prognos 2005: 29, 67–69, 296, IEA and NEA 2005: 41, 205). The gas-price assumptions in this study refer to the indications given in EWI and Prognos (2005: 296) for Germany and are shown in Table 5.3. The projected prices are the prices at the power plant. They do not include the natural gas tax.17 The values for 2040 and 2050 have been extrapolated using the escalation factor expressed in the older estimations in IEA and NEA (2005: 121). After 2050, they are expected to continue to rise by the same annual amount as in the 2015– 2050 mean. This assumption takes into account the increasing scarcity as well as that no general availability constraint is expected to be reached until then (EWI and Prognos 2005: ch. 2). Table 5.3 Natural gas prices at the plant (¤/MWh) (EWI and Prognos 2005: 296, IEA and NEA 2005: 121, own calculations) Year 2015 2020 2025 2030 2040 2050

Natural gas ¤/MWh 13.968 14.580 15.192 16.020 18.230 20.163

For the CCGT reference power station, for commissioning in 2015 a constant mean gas price of 17.16 ¤/MWh is assumed. For later commissioning dates, the mean gas price is derived, equivalently, as the 40-years arithmetical mean based on the above indications. 17

In Germany, in 1999 ecotaxes have been introduced including a natural gas tax, amounting to 5.5 ¤/MWh at the last step since 2003. However, in 2003 gas power stations with a net thermal efficiency of over 57.5% have been exempted from this tax for a period of 10 years after commissioning.

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5.3.2.3 Pollution and Pollution-control Systems Similar to coal-fired plants, in gas-fired power plants, apart from CO2 , nitrogen oxides are produced during the combustion process. However, natural gas normally has little or no sulphur. The pollutants controlled and environmental protection measures associated with coal combustion are similar for gas-fired electric generation technologies. While new gas turbines use low-NOx burners to partially reduce the production of NOx in gas turbine combustors,18 gas-fired power stations do not need flue gas desulphurisation systems. Carbon can be captured and stored in a way equivalent to that described for hard coal above. Concentrating on CO2 and carbon capture and storage (CCS), in the present study, following (BEI 2004: A–9), for natural gas a CO2 emission factor of 0.2 t CO2 /MWh is assumed. For the MEA post-combustion abatement technology, EWI and Prognos (2005: 125) estimates in the case of CCGT power plants cost ranges of 20–40, 10–15, and 2–10 ¤/t CO2 for CO2 capture, transport over 200 km, and storage, respectively, and thus a specific CCS full cost range of 32–65 ¤/t CO2 . For analytical comparability, the homogeneous end-of-pipe CO2 abatement technology for complete emission abatement with fixed abatement unit costs (AUC) in a range of 10–60 ¤/t CO2 (subsection 5.3.1) is assumed to be applicable, with the same AUC as for coal, also to the CCGT power plant considered. AUC of 32–65 ¤/t CO2 are regarded as the relevant range of abatement unit costs for the CCGT power plant considered.

5.3.3 Nuclear Reference Power Plant The nuclear reference power plant for which cost estimates are considered in the present study is part of Generation III+.19 Due to particularly high turn-on/turn-off 18

Also injection of steam or water into the combustors can be used to reduce NOx production. However, this reduces thermal efficiency and is thus less common in new machines. 19 Generally, four generations of nuclear power plants are distinguished (The University of Chicago 2004). Following the first generation of the 1950s and 1960s, Generation II reactors, deployed in the 1970s and 1980s, are those in commercial use today. They include light-water reactors (LWR), comprising in turn pressurised-water reactors (PWRs) and boiling-water reactors (BWRs), and pressurised-heavy-water reactors (PHWRs). Generation III reactors, also referred to as advanceddesign reactors, with an improved reliability, economics and safety include, e.g., the advanced boiling-water reactor (ABWR) and the AP600 (pressurised-water) passive-design reactor. The more innovative Generation III+ reactors include AP1000 (a capacity upgrade from AP600), the Pebble Bed Module (PBMR) (a gas-cooled reactor), the SWR 1000 (which combines the conventional BWR with passive safety features) as well as the European Pressurised-Water Reactor (EPR) (a large BWR designed to meet German and French safety standards). Developed since the 1990s, Generation III+ reactors can be deployed by 2010. Generation IV reactors, to be deployed by 2030, include LWRs incorporating advanced engineering to increase safety and reduce operational costs, or the gas-turbine modular helium reactor (GT-MHR) which is gas-cooled and has passive safety features. Developers still aim at improving economics, safety in operation and as regards proliferation, and at minimising waste production.

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costs nuclear power plants are usually operated at baseload. As Generations III and III+ constitute advanced, directly modified versions of the reactors of Generation II, in the following only the basic types of light-water reactors (LWR) and pressurisedheavy-water reactors (PHWRs) are briefly described.

5.3.3.1 Basic Technology and Plant Features Different reactor types are basically characterised by the choice of a neutron moderator and a cooling medium which lead to different fuel designs. Both pressurisedand boiling-water reactors use light water (ordinary water) as moderator and coolant. In PWRs water is maintained liquid by high pressure. In BWRs water is allowed to boil in the reactor core. In either type, the heat removed from the core is ultimately used to raise steam which drives an ordinary steam turbine generator. Both reactor types require enriched uranium fuel (containing more 235U, the fissile isotope, than natural uranium) in order to maintain a chain reaction in spite of the absorption of neutrons by the moderator. Fuels used in LWRs of current generation use uranium enriched at some 3 to 5% in 235U (natural uranium contains 0.7% of 235U). LWRs can also use fuel containing recycled materials, plutonium and uranium, recovered through reprocessing of spent fuel. Pressurised-heavy-water reactors use heavy water (deuterium oxide) as coolant and moderator. This choice makes it possible to utilise natural uranium as fuel. The use of pressure tubes rather than a single large pressure vessel around the core facilitates refuelling while the reactor is in operation. To minimise capital cost, particularly that of the reactor pressure parts, while still maximising fuel efficiency, in nuclear plants less severe steam conditions have been chosen than in fossil-fuelled plants. In PWRs, the steam temperature is, e.g., generally less than 350°C. Net thermal efficiencies of operating plants typically range between 33 and 37% (IEA and NEA 2005, MIT 2003: 119f). Nuclear construction projects divide into several phases (The University of Chicago 2004: 5-17f). The start-up phase consists of early site permitting, design certification, plant licensing, site preparation, and procurement of long lead-time components such as pressure vessels and steam generators. Procurement continues during the construction phase. The final phase is start-up and testing. Though nuclear units commissioned in the 2000s in Japan and Korea were built in 4 to 5 years, for new nuclear power plants today usually 5 to 7 years are expected. In particular, the construction time of the first plant of a new build is longer than of later. Traditionally, the economic life of a nuclear power plant has been assumed to amount to 40 years. Advanced reactors are designed to last 50 to 60 years. For the nuclear reference power plant, oriented towards the European PressurisedWater Reactor (EPR), in this study a net thermal efficiency of 37%, a construction time of 6 years and an economic life of 40 years are assumed (IEA and NEA 2005: 26, 43, 119).

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93

5.3.3.2 Cost Assumptions The expected costs of nuclear power under liberalised market conditions are the object of an ongoing, in part controversial debate in the literature. As uncertaintygenerating factors, e.g., the lack of recent construction experience, regulatory and political obstacles related to obtaining construction and operating licenses for new plants, and the long payback period associated with high capital costs and large plant size are mentioned (Roques et al. 2006). The cost assumptions for the nuclear reference power station are taken from Enquetekommission (2002), IEA and NEA (2005), The University of Chicago (2004) and MIT (2003).20 • Enquetekommission (2002) highlights the situation of nuclear power in Germany. It discusses the specific investment costs of a EPR in Germany for new deployment in the 2000s with respect to various public and industry data. • IEA and NEA (2005) provides detailed cost estimates oriented at the EPR, as a nuclear reference power station possibly to be approved in Germany by 2010. The estimates are taken from different studies and the literature and provided after clearance with different manufactures and electric utilities. • The University of Chicago (2004) studies the prospects and economics of nuclear power with a particular focus on the United States by the mid-2010s. It provides detailed information on technologies currently available and an extensive treatment of financing issues and considers differences in financial policies for plants coming on line by that time. • MIT (2003) is concerned with nuclear power as a general energy option for the United States by 2050, discussing diverse issues such as fuel cycle and waste management options, safety, non-proliferation, public attitudes, and recommended government action. In its cost analysis, it only considers a general LWR as nuclear reference power station. Capital costs. Capital costs constitute the by far most important component in the cost structure of nuclear power plants. Associated with the different kinds of new builds, a variety of figures is available in the literature. Studying the specific investment costs of five Generation III+ power plants, which may be erected in the U.S. by 2010-20, The University of Chicago (2004: ch. 3), e.g., distinguishes three levels of specific investment costs. Overnight costs of 1,200 $/kWe are described for the ABWR or the ACR-700 reactor designs, 1,500 $/kWe for the AP1000 (assuming its entire FOAK costs to be paid on the first plant). For the two European designs, SWR 1000 and EPR, an overnight cost of 1,800 $/kWe is estimated. MIT (2003: 132, 135) takes comparatively high 2,000 $/kWe as a general estimate for the overnight costs of the fictional 1,000 MWe plant it investigates commissioned in the U.S. in 2002. Enquetekommission (2002) and The University of Chicago (2004: chs. 4, 9) estimate construction cost reductions between the first and the second to fifth plant of a new build of 3–10% due to learning effects based on historical evidence. For Germany, Enquetekommission (2002) provides 1,800 k¤/MWe as 20

Note that neither BEI (2004) nor EWI and Prognos (2005) particularly treat nuclear energy.

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minimum specific investment costs for a EPR in the NOAK case including the interest payment during design and construction, but judges 2,200–3,000 k¤/MWe, including FOAK costs, as more realistic under market conditions. IEA and NEA (2005: 120) indicates for Germany, oriented towards the EPR, specific investment costs (NOAK case) of 1,550 k¤/MWe, and specific decommissioning costs of 155 k¤/MWe, where the specific investment costs also include the costs incurred during the time between plant shut-down and plant decommissioning. In view of the wide range of figures in the literature and the uncertainty associated with new construction due to the lack of recent construction experience and regulatory and political obstacles, this study considers two scenarios for the specific nuclear investment costs. The low-cost scenario (Nl ) assumes specific investment costs of 1,800 k¤/MWe, the high-cost scenario (Nh ) 2,600 k¤/MWe. The Nl scenario, thus, considers a moderate lower bound oriented towards the indications in Enquetekommission (2002) and IEA and NEA (2005), the Nh scenario a moderate upper bound judgment according to the more pessimistic Enquetekommission (2002) figures. For both cases, the specific decommissioning costs are assumed to amount to 155 k¤/MWe. O&M costs. Following the indications in IEA and NEA (2005: 120), the specific fixed annual O&M costs of the nuclear reference power station are assumed to amount to 30.0 k¤/MWe, the specific variable O&M costs to 3.6 ¤/MWh. The specific fixed annual O&M costs also contain the insurance costs. Fuel costs. The nuclear fuel cycle divides into three parts, the front-end (before fuel loading in the reactor), electricity generation in the power station, and the backend (following unloading of spent fuel from the reactor). The nuclear fuel costs comprise the front-end and back-end costs. For LWRs the main front-end fuel cycle steps are uranium mining and milling, conversion, enrichment, and fuel fabrication. For PHWRs the enrichment step is not necessary. As enrichment accounts for some 40% of the levelised front-end fuel cost, PHWR fuel cycle costs are lower than those of LWRs. At the back end of the fuel cycle two options are available, direct disposal of spent fuel or reprocessing. In the first case, spent fuel is conditioned after a period of cooling into a form adequate for final disposal in a high level radioactive waste repository. In the second case, spent fuel is reprocessed to separate materials (plutonium and uranium). They can be used again in reactor fuel from residual waste fission products which are conditioned after interim storage for cooling to be disposed of in a high level waste repository. As the front end may extend over a period of up to five years prior to the use of the fuel in the reactor, the outlays during this period incur interest costs and the fuel costs comprise an overnight component. The front-end component of the nuclear fuel costs are calculated from their levelised value. Back-end costs include in particular high level waste disposal costs. Until final repositories are in operation, they are treated as future financial liabilities by operators raisig respective funds during operation. As the costs for reprocessing slightly exceed those for direct disposal, direct disposal, or a one-through fuel cycle, is considered. Nuclear fuel costs are expected to stay constant over the next decades (Enquetekommission 2002, The University of Chicago 2004: ch. 7, app. 5).

5.3 Technical and Economic Parameters

95

The present study follows the indications for the total nuclear fuel cycle unit costs for Germany in IEA and NEA (2005: 44), which are supposed to be invariant under different discount rates. The total nuclear fuel cycle unit costs are assumed to amount to 4.0 ¤/MWh.

5.3.3.3 Pollution and Pollution Control Whereas no direct CO2 emissions are associated with electricity generation in nuclear power plants, different further aspects of nuclear energy are often suggested to entail external costs (Enquetekommission 2002, NEA 2003).21 These include health and environmental impacts of radioactivity releases in routine operation, financial liabilities arising from decommissioning and dismantling of nuclear facilities, radioactive waste disposal, and severe accidents. Existing regulation takes precautions with respect to all of these aspects.22 Notably, it imposes stringent limits to atmospheric emissions and liquid effluents from nuclear facilities, and requires the containment and confinement of solid radioactive waste to ensure its isolation from the biosphere as long as it may be harmful for human health and the environment. Future costs associated with decommissioning of nuclear facilities constitute a component of the capital costs and are thus included in the investment costs (section 5.2). Also high level waste disposal costs, until final repositories are in operation, are treated as future financial liabilities and constitute a part of the fuel costs. Operators raise respective funds to cover disposal costs during operation. With regard to effects of severe nuclear accidents, a special legal regime, the third-party liability system, has been implemented to provide insurance coverage for any potential damage that might occur. Under current regulation, the capital and operating costs of nuclear power plants and fuel-cycle facilities thus internalise the most part of the potential external costs. For the case of Germany, it is to be noted that the question of nuclear waste treatment and final disposal is, however, not yet fully decided on political level (Bundesamt f¨ur Strahlenschutz 2008, Enquetekommission 2002). Uncertainties are, moreover, still associated with the valuation of severe accidents, and, more generally, that of low-probability high-consequence negative events, and thus the object of an ongoing discussion, in particular in the economics literature. More recent studies have been refining the respective tools and considerations. For example, Eeckhoudt et al. (2000) integrate risk aversion based on an expected-utility approach into the assessment of the external costs of a severe nuclear accident, showing with reference to French data that they restrict to about 50% of the total external costs of the nuclear fuel cycle without accident. Kunreuther et al. (2001) have addressed people’s capacity to judge low-probability high-consequence events showing that fairly rich 21

Life-cycle assessments show for nuclear power similarly low greenhouse-gas, and in particular CO2 , emissions as for renewable energy sources. For gas they are about 13, for coal about 30 times higher (Owen 2004, Fritsche et al. 2007). 22 As noted above, the EPR has been designed to particularly meet French and German environment and safety standards.

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context information must be available to people in order to feel competent to subjectively judge differences between low probabilities. Schneider and Zweifel (2004) account for this result when studying Swiss consumers’ willingness to pay for increased financial security provided by an extension of coverage of nuclear operators’ mandatory liability insurance, as one way to internalise the risks associated with a severe accident. They find a clearly positive willingness to pay, indicating the welfare-enhancing character of a respective coverage extension. Itaoko et al. (2006) show in turn, based on a choice experiment conducted in Japan, that the willingness to pay for mortality-risk reductions associated with nuclear power considerably exceeds that associated with fossil fuel power generation, and therefore, contrary to the common assumption, in particular differs for different technologies. Still more research in this respect needs to be done, notably for Germany, in order to provide a well-pondered basis for political decisions.23 The persisting uncertainties and ongoing, though advancing discussions provide another reason for the consideration of the two nuclear-cost scenarios below.

5.4 Policy Parameters While, as mentioned in subsections 5.1.1 and 5.1.4, environmental and technology policies are in general considered as induced in the same way as in the theoretical part, the underlying distortions remain in this part of the study in both cases exogenous to the analysis. Rather, their effect is studied in form of relevant sensitivity ranges of resulting policy interventions. This section explains the treatment and implementation of environmental and technology policies, respectively, in the following analysis.

5.4.1 Environmental Policy Environmental policy becomes relevant for the utility in form of a positive emission price. As shown in chapter 3, theoretically its equilibrium level is jointly determined by the households’ preferences, the firms’ technologies, the market structures, and the economy’s initial endowment of resources. For the analysis below it does not matter whether this price is implemented via an emission tax or a permit trading scheme. Therefore, for convenience, and in accord with the theoretical part, the analysis below associates the CO2 price with an emission tax, τe . τe (t) indicates the constant mean real price per tonne CO2 for the period t under consideration. It directly imposes the emission costs to the polluting utility. The sensitivity range for τe in the analysis below is oriented towards the CO2 prices which have been occurring under the EU emission trading scheme to which 23

See also the ethical discussion of nuclear waste treatment by Taebi and Kloosterman (2008).

5.4 Policy Parameters

97

the EU Member States, including Germany, are subject since 2005. Displaying a relatively volatile behavior due to the newly installed market, in its first phase 2005– 2007 CO2 prices have been ranging between 6 and 30 ¤/t, with a core range of about 15–25 ¤/t (e.g., Borak et al. 2006, ECX 2007, Sijm et al. 2005, 2006, UhrigHomburg and Wagner 2007).24 In the second period the supply of EU allowances (EUA) will be reduced as compared to the first, and later on generally continue to decrease. Therefore, for an at best similarly decreasing demand, non-decreasing prices might be expected. However, notably in view of ongoing discussions concerning, e.g., the initial allowance allocation, the banking option, and polluter participation more generally, concrete projections for 2015 and later remain difficult. The penalty levels for illegal emissions, fined with 40 ¤/t in the first trading period and 100 ¤/t from the second period onwards, set a clear upper bound for the expected price development.25 For the environmental-policy parameter, τe , in this study a sensitivity range of 0–60 ¤/t is considered. The range of 5–30 ¤/t is taken as its relevant range in the period under consideration, i.e. the range in which CO2 prices are expected to stay most likely.

5.4.2 Technology Policy A power-plant construction project should yield at least the return of an alternative investment on financial markets. As a rule, this is generally equivalent to having a positive net present value. As introduced in section 5.2, the decisive factor for the calculation of the present value of a planned investment project is the real imputed interest rate, r. The (real) imputed interest rate of a particular investment project derives as the mean of the (real) rates of return on equity and debt weighted with the fractions of equity and debt financing. However, as set out in section 2.1, for various reasons financial markets are in general distorted. These distortions constitute a case for the social and private rates of time preference to differ. To study the effect of distorted time preferences in this applied analytical setting, in line with the reasoning in chapter 2, a series of simplifying assumptions is met. First, the analysis concentrates on the real imputed interest rate as the calculation factor via which the distortions factually materialise. More particularly, it focuses on one private (benchmark) level of it, r p , as deriving from the utility’s market observations, and a set of socially optimal ones, rs . Second, building on the theoretical part, the distortion is taken for granted. The analysis focuses on its effect, for given

24

At present, studies on the issue have not left the working-paper status. Note that in this study no distinction is made between spot and forward prices. Preliminary results indicate that the latter exceed the first and that forward markets lead the price discovery process. 25 An analysis of the relationship between discounting and the social costs of carbon is beyond the scope of this study. See Guo et al. (2006) for a summary and discussion of respective analyses.

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reasonable private and social levels of the rates.26 Third, as used in the following, the term technology policy designates, in contrast to the theoretical part, the bundle of policy measures necessary to correct all distortions resulting from the diverging interest rates. Fourth, still an investment subsidy, τi , is considered as the only technology-policy instrument. It is now calculated as an output subsidy directly paid on the electricity provided at the busbar. Corresponding to the larger notion of technology policy in this part, its amount now quantifies in fact the whole of the resulting distortions. It thus indicates only the clear upper bound of the policy instrument introduced in section 3.4. Finally, for convenience, no distinction is made with respect to the particular financing conditions of specific technologies. This corresponds to the common practice in the literature, but clearly needs differentiation if policy measures are met based on this reasoning (section 8.3).27 In the literature, the financing and discounting issues have been treated in varying degrees of intensity. For example, the series of six studies including IEA and NEA (1998, 2005) published since 1983 by the OECD have considered (since the second report of 1986), in addition to the 5%, a 10% discount-rate scenario. IEA and NEA (2005: 183) judges the 5% discount rate for the U.S. as approximately consistent with the evaluation of relatively low-risk utility investments in the former regulated environment. It considers the 10% rate as an appropriate general proxy for powerplant investments in deregulated markets, pointing to the corresponding evaluation of comparable, relatively risky US airline or telecommunication investments. With respect to upcoming US nuclear power investments, both MIT (2003: ch. 5) and The University of Chicago (2004: ch. 5) calculate with r p = 0.125. For Germany, in IEA and NEA (2005: 122–123) the general 5 and 10% rates are simply adopted. Similarly, BEI (2004: 8-2) uses an 8% imputed interest rate. Schneider (1998: 51) has studied more closely the financing conditions of new conventional power plants in the upcoming decade, finally considering scenarios with low 5.7, probable 8.9, high 12.2% real imputed interest rates. EWI and Prognos (2005: 295) uses a rate of 10%, referring to Enzensberger (2003) who found r p ∈ [0.08, 0.12] for respective investments in Germany.28 Social discount rates, on the other hand, have thus far been determined in different ways. While France has been applying for the evaluation of public projects an 8% real rate derived with respect to the marginal product of capital, Germany has been using a 3% rate based on the federal government’s average real refinancing rate over the past five years. In the UK, until 2003 a 6% rate was applied based on considerations of both capital costs and social time preferences. However, after re-basing it then entirely on social time preferences, it dropped to 3.5%. Evans and Sezer (2004, 2005) have recently applied the latter approach to major EU and OECD countries, finding, e.g., for Denmark a real rate of 2.4, for France of 3.2, 26 This proceeding notably reflects the given research need at this place (section 8.3). See, apart from section 2.1, for treatments of financial-market imperfections notably Hubbard (1998), Kocherlakota (1996), Mehra and Prescott (2003) and in the references cited therein. 27 Cf. IEA and NEA (2005: app. 6), MIT (2003: ch. 5), Roques et al. (2006) and The University of Chicago (2004: ch. 5) for useful treatments of the issue. 28 Note that Enquetekommission (2002) does not contain a treatment of the discounting issue.

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99

for Germany of 4.3, for Ireland of 6.8, for Japan of 5.0, for the UK of 4.0, and for the U.S. of 4.6%.29 The variation between the rates is mainly due to differences in the national per capita growth rates in the considered years of 1970–2001. Denmark and Ireland display minimum and maximum, respectively. As the particular rates for power-plant financing and the social discount rates have been derived with respect to both different models and different data, it only stands to investigate how the present rates are actually consistent with the rates occuring on undistorted financial markets. Probably, the present figures will ultimately rather describe the lower bound for the socially optimal discounting of private power-plant investments. In this study, for the private level of the real imputed interest rate, as deriving from given market conditions, r p = 0.1 is assumed. For its social level, a sensitivity range of rs ∈ [0.02, 0.08] is considered. For convenience, the rates are supposed not to differ for different technologies. The term technology policy stands now for the policy mix necessary to correct all of the distortions resulting from the diverging interest rates. The investment subsidy, τi , quantifies, correspondingly, the whole of the resulting distortions. With respect to the respective policy instrument introduced in section 3.4, it may thus only indicate a clear upper bound.

5.5 Conclusion In this chapter, the analytical foundations of the applied analysis were set out with respect to analytical setting, financial model, technical and economic parameters of reference power plants and abatement technology, as well as the two policies and respective parameters. The two following chapters study the threefold trade-off of the investing utility under environmental policy (section 1.1), taking account of the additional aspect of distorted time preferences, in two steps. Chapter 6 analyses first its choice among the three new generation technologies, before chapter 7 focuses on the optimal moments of transition from the established polluting to the new less polluting technologies. In each case, first the case of the absence, then that of the availability of the end-of-pipe abatement technology are considered.

29 For their results, they empirically determine the three components of the Ramsey rule (equation (2.4) above). This revealed-preference approach has the advantage to use a well-established theory and clear estimation procedures, and to rely on widely available data. Alternative experimental approaches, some of which have been considered in subsection 2.1.1, or opinion surveys, such as Weitzman (2001), can in general only refer to specific goods or provide very general indications.

Chapter 6

Technology Choice Under Environmental and Technology Policies

This chapter studies, based on the technical, economic and financing assumptions set out in chapter 5, the single and combined influence of environmental and technology policies on the utility’s choice of a new electric generation technology, first for the case of the absence of a CO2 abatement technology (section 6.2). Section 6.3 analyses how results change if a CO2 abatement technology is available. Section 6.4 summarises and discusses the results.

6.1 No-policy Benchmark Table 6.1 shows the unit costs of electricity at the busbar of the three alternative new reference power plants in the benchmark case without policies. They have been calculated using a private real imputed interest rate of r p = 0.1. Note again that throughout the analysis it is abstracted from the natural gas tax currently levied in Germany.

Table 6.1 Unit costs of electricity at busbar of new plant alternatives in no-policy benchmark (¤/MWh) (own calculations) rp 0.1

C 37.12

UCT2 G Nl 40.33 46.05

Nh 58.16

In the no-policy benchmark, the new hard-coal power plant constitutes the leastcost alternative. The CCGT power plant displays medium, the nuclear power plant, already in the Nl scenario, the by far highest unit costs of electricity. As the effect of the policies on the unit costs of electricity of the technologies depends on the varied contributions of the different cost components distinguished C. Heinzel, Distorted Time Preferences and Structural Change in the Energy Industry, Sustainability and Innovation, DOI 10.1007/978-3-7908-2183-3 6, © Physica-Verlag Heidelberg 2009

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in subsections 5.2.1–5.2.2, their composition in the no-policy benchmark is displayed in Table 6.2. Striking are the high capital-investment, comparatively high Table 6.2 Shares of capital investment, O&M, fuel, and decommissioning costs in unit costs of electricity of new plant alternatives in no-policy benchmark, discounted to year of commissioning (percent) (own calculations)

CC OMC FC DC

C 41.6 20.5 37.7 0.2

Shares in UCT2 G Nl 18.8 59.2 10.2 16.5 70.9 23.5 0.1 0.8

Nh 67.7 13.1 18.6 0.6

decommissioning and relatively low fuel costs in the case of nuclear under both scenarios, as well as the high fuel and relatively low capital-investment costs in the case of gas. In the case of coal, capital-investment costs are slightly more important than fuel costs. O&M costs contribute in each case in a moderate way. The contribution of the decommissioning costs amounts in all cases to less than 1%.

6.2 Technology Choice Without Abatement Technology This section studies, first separately, then combined, the influence from environmental and technology policies on the utility’s technology choice.

6.2.1 Sensitivity Under Environmental Policy How do the unit costs of electricity and the technology ranking change if an emission tax τe , as described in subsection 5.4.1, is levied? Figure 6.1 displays the behavior of the unit costs of electricity of the reference power plants for CO2 prices ranging from 0 to 60 ¤/t in steps of 5 ¤. For τe ≤ 9.75 ¤/t, hard coal remains the cheapest alternative before gas and nuclear, with UCT2 of up to 43.61 ¤/MWh. For τe ∈ (9.75, 17.0(53.5)] ¤/t, gas dominates coal and nuclear in the Nl (Nh ) scenario. For τe > 17.0 (53.5) ¤/t, nuclear is the least-cost option before gas and coal in the Nl (Nh ) scenario, fixing the UCT2 minimum level at 46.05 (58.16) ¤/MWh. As compared to the no-policy benchmark, the technology ranking is reversed in the Nl (Nh ) scenario for τe > 17.0 (53.5) ¤/t. Thus, in the Nl scenario environmental policy alone reverses the technology ranking of the no-policy benchmark within the relevant CO2 price range of 5–30 ¤/t. In the Nh scenario only coal and gas reverse their order within the relevant range, nuclear becomes the least-cost option for τe > 53.5 ¤/t.

6.2 Technology Choice Without Abatement Technology

103

80,00 75,00 70,00

UCT2

65,00 60,00 55,00 50,00 45,00 40,00 35,00

0

5

10

15

20

25 C

30 te G

35 N_l

40

45

50

55

60

N_h

Fig. 6.1 Unit costs of electricity of new plant alternatives for varying CO2 -price levels (¤/t) under r p = 0.1 (¤/MWh) (own calculations).

Table 6.3 Shares of CO2 emission costs in and increases of unit costs of electricity of new plant alternatives (percent) for varying CO2 -price levels (¤/t) (own calculations) CO2 price 5 10 15 20 25 30 35 40 45 50 55 60

EC share in UCT2 G Nl / Nh 8.2 4.0 0 15.2 7.6 0 21.1 11.0 0 26.3 14.2 0 30.9 17.1 0 34.9 19.9 0 38.5 22.4 0 41.7 24.8 0 44.6 27.1 0 47.2 29.2 0 49.5 31.3 0 51.7 33.2 0

C

UCT2 increase G Nl / Nh 8.9 4.1 0 17.9 8.3 0 26.8 12.4 0 35.7 16.5 0 44.6 20.7 0 53.6 24.8 0 62.5 28.9 0 71.4 33.1 0 80.4 37.2 0 89.3 41.3 0 98.2 45.5 0 107.1 49.6 0 C

Table 6.3 shows the emission-cost shares in the unit costs of electricity of the different alternatives and the UCT2 increases, for varying CO2 -price levels. Note that the shares of capital investment, O&M, fuel, and decommissioning costs shrink proportionally to the EC share. Within the relevant CO2 price range, in the case of coal the emission-cost share rises to about one third and the UCT1 by more than 50%, in the case of gas to about one fifth and by about a quarter, respectively. By the end of the τe range considered, in the case of coal the emission-cost share rises

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to over 50% and the UCT1 by over 100%, in the case of gas to about one third and by almost 50%, respectively. At the same time, in the case of nuclear the unit costs of electricity are unaffected by environmental policy. The varied impact of environmental policy on the unit costs of electricity of the different technologies reflects the differences in emission in emission factors between the fuels and in efficiencies between the technologies. Accordingly, gas becomes, despite its high fuel-cost share, dominant over coal for higher CO2 -price levels due to its lower emission factor and higher efficiency. Moreover, for nuclear power, being free of CO2 emissions from production, there must be in both scenarios a certain CO2 -price level at which its ecological advantage also turns into an economic advantage.

6.2.2 Sensitivity Under Technology Policy As described in subsection 5.4.2, the term technology policy designates in this part of the study the bundle of policies necessary to correct all of the distortions resulting from the diverging interest rates. The hypothetic investment subsidy, τi , quantifies the resulting distortions. Figure 6.2 shows the behavior of the unit costs of electricity of the new plant alternatives for social imputed interest rates, rs , ranging from 8.0 to 2.0% in steps of 0.5 percentage points. Under technology policy, in both scenarios, coal remains the cheapest alternative as in the no-policy benchmark over the whole rs range considered. In the Nl scenario, gas and nuclear change their place as second cheapest technology for rs < 0.054. In the Nh scenario, the technology ranking remains unaltered as compared to the no-policy benchmark over the rs range considered. Thus, as compared to the no-policy benchmark, technology policy alone does neither change the status of coal as the cheapest alternative, nor, in the Nh scenario, the general technology ranking. In the Nl scenario, it makes nuclear energy advantageous over gas as second cheapest technology under a certain level of the social imputed interest rate. Table 6.4 shows the shares of the capital-investment costs in the unit costs of electricity of the different alternatives and the UCT2 decreases, for varying rs levels. Only the CC shares are displayed, as the impact of the lower (social) imputed interest rates is among the different cost components the strongest on them, due to their inclusion of the financing costs of plant construction and commissioning, and, therefore, direct dependance on r. The shares of O&M, fuel, and decommissioning costs in the UCT2 rise accordingly, with slightly varying proportions. The decommissioning costs with falling rs slightly gain in relative importance due to their different levelisation.1 In the case of coal, over the whole rs range considered the CC share now stays below the fuel-cost share, and for rs = 0.02, reduced by For rs ∈ [0.02, 0.08], the OMC shares in the UCT2 range between 21.8–25.5, 10.5–11.2, and 18.0–22.7 (14.4–19.1)% in the cases of coal, gas, and nuclear in the Nl (Nh ) scenario, the FC shares between 39.9–46.8, 72.8–77.8, and 25.5–32.2 (20.5–27.1)%, respectively. The DC shares, in turn, rise to 0.3–0.6, 0.1–0.2, and 1.1–2.6 (0.9–2.1)%, respectively.

1

6.2 Technology Choice Without Abatement Technology

105

55,00 50,00

UCT2

45,00 40,00 35,00 30,00 25,00

0,08 0,075 0,07 0,065 0,06 0,055 0,05 0,045 0,04 0,035 0,03 0,025 0,02 rs C

G

N_l

N_h

Fig. 6.2 Unit costs of electricity of new plant alternatives for varying levels of social imputed interest rate (¤/MWh) (own calculations). Table 6.4 Shares of capital-investment costs in and decreases of unit costs of electricity of new plant alternatives (percent) for varying levels of social imputed interest rate (own calculations) rs 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020

C 38.0 37.1 36.2 35.2 34.3 33.4 32.4 31.5 30.6 29.7 28.8 27.9 27.1

CC share in UCT2 G Nl 16.6 55.4 16.1 54.4 15.5 53.4 15.0 52.3 14.5 51.3 14.0 50.2 13.5 49.1 13.0 48.0 12.5 46.9 12.1 45.8 11.6 44.7 11.2 43.6 10.8 42.5

Nh 64.2 63.3 62.3 61.3 60.3 59.3 58.2 57.2 56.1 55.0 53.9 52.8 51.6

C 5.7 7.1 8.4 9.7 10.9 12.1 13.3 14.5 15.6 16.6 17.6 18.6 19.5

UCT2 decrease G Nl 2.6 8.0 3.2 9.9 3.8 11.7 4.4 13.5 4.9 15.3 5.5 17.0 6.0 18.6 6.5 20.2 7.0 21.7 7.5 23.1 8.0 24.5 8.4 25.9 8.8 27.1

Nh 9.2 11.4 13.5 15.6 17.6 19.6 21.5 23.3 25.1 26.7 28.4 29.9 31.4

one third, almost equals the O&M-cost share. In the case of gas, the CC share decreases by up to 40%, falling, for rs = 0.02, even below the O&M-cost share. The high fuel-cost share further increases. In the case of nuclear in the Nl (Nh ) scenario, the high CC share now decreases below 50 (60)% in the mean over the parameter range considered, for rs = 0.02 even considerably below (to almost) 50%. For rs ∈ [0.02, 0.08], below (to almost) 50%. For rs ∈ [0.02, 0.08], the UC T2 decrease by, approximately, 6–20, 2.5–9, and 8–27 (9–31)% in the cases of coal, gas, and nuclear in the Nl (Nh ) scenario, respectively. The varied impact of technology policy on the unit costs of electricity of the different technologies, therefore, depends on

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the share of the capital-investment costs in the UCT2 , clearly dominating its slight counteracting effect on the decommissioning costs. Accordingly, its impact is the strongest in the case of nuclear in the Nh scenario, before nuclear in the Nl scenario, coal and gas. By which amount are the unit costs of electricity of the single technologies distorted? Table 6.5 shows the τi levels for varying levels of the social imputed interest rate, rs . τi is calculated as the difference between the unit costs of electricity at the private and social levels of the imputed interest rate. For coal, gas, as Table 6.5 Distortion of unit costs of electricity of new plant alternatives for varying levels of social imputed interest rate, absolute deviation from (¤/MWh) and in shares of distorted level (own calculations) UCT2 distortion rs 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020

C 2.12 2.62 3.11 3.59 4.05 4.51 4.94 5.37 5.77 6.17 6.54 6.90 7.24

absolute G Nl 1.04 3.68 1.29 4.55 1.53 5.40 1.76 6.23 1.99 7.03 2.21 7.81 2.43 8.56 2.63 9.29 2.83 9.99 3.03 10.65 3.21 11.30 3.39 11.91 3.55 12.48

Nh 5.36 6.63 7.87 9.07 10.25 11.38 12.49 13.55 14.57 15.56 16.50 17.40 18.25

C 0.057 0.071 0.084 0.097 0.109 0.121 0.133 0.145 0.156 0.166 0.176 0.186 0.195

shares G N1 0.026 0.080 0.032 0.099 0.038 0.117 0.044 0.135 0.049 0.153 0.055 0.170 0.060 0.186 0.065 0.202 0.070 0.217 0.075 0.231 0.080 0.245 0.084 0.259 0.088 0.271

Nh 0.092 0.114 0.135 0.156 0.176 0.196 0.215 0.233 0.251 0.267 0.284 0.299 0.314

well as nuclear in the Nl (Nh ) scenario, the distortions range between 2.12–7.24, 1.04–3.55, and 3.68–12.48 (5.36–18.25) ¤/MWh or 5.7–19.5, 2.6–8.8, and 8.0– 27.1 (9.2–31.4)% of the distorted UCT2 , respectively. The payments per unit under a corresponding hypothetic policy regime would thus, e.g., stay considerably below the actual payments under the German “Erneuerbare-Energien-Gesetz” (Renewable Energy Sources Act).2 This act prescribes feed-in tariffs only for renewable energy technologies oriented at the level of their unit costs of production. According to it, suppliers of renewable energy receive 457–624, 55–91, and 71.6–150 ¤/MWh for power from photovoltaics, wind energy, and geothermal energy, respectively. On average, the electricity supplied from renewable energies is thus implicitly subsidized by about 56 ¤/MWh (IfnE and DIW 2006).

2 The “Erneuerbare-Energien-Gesetz” was first enacted in April 2000, succeeding the 1991 “Stromeinspeisegesetz”, the first act to promote the introduction of renewable energies in Germany by subsidies, and amended in August 2004. Its stated purpose is to increase the share of electricity from renewable energies to at least 12.5% in 2010 and 20% in 2020.

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6.2.3 Sensitivity Under Environmental and Technology Policies Combined What is the utility’s optimal technology choice when both environmental and technology policies are enacted? Figures 6.3 and 6.4 show the combined influence of environmental and technology policies on the UCT2 behavior, in the Nl and the Nh scenarios, respectively, over the CO2 price range considered for a private imputed interest rate r p = 0.1 and exemplary social imputed interest rates, rs , of 0.08, 0.05, 0.02. 50,00

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Fig. 6.3 Unit costs of electricity of new plant alternatives for varying CO2 -price levels under r p = 0.1 and social imputed interest rates of 0.08, 0.05, 0.02 in Nl scenario (¤/MWh) (own calculations)

In the Nl scenario, for rs ∈ [0.02, 0.08] coal remains the first option until τe ∈ [5.5, 11.0] ¤/t. Above τe ∈ [5.5, 11.0] ¤/t, nuclear directly follows coal as most economic option. Gas vanishes as least-cost option irrespective of the CO2 -price level over the whole rs range. As compared to the no-policy benchmark, the technology ranking reverses over the rs range considered for τe ∈ [13.0, 21.0] ¤/t and higher. In the Nh scenario, for rs ∈ [0.04, 0.08] coal remains the least-cost option until τe ∈ [13.0, 18.5] ¤/t, for rs ∈ [0.02, 0.04) until τe ∈ [15.0, 18.5) ¤/t. For rs ∈ [0.04, 0.08] gas is the least-cost option for τe in intervals of (13.0, 40.5]–18.5 ¤/t, for rs < 0.04 it vanishes as first option irrespective of the CO2 -price level. For rs ∈ [0.04, 0.08] nuclear follows gas as the most economic option above τe ∈ [18.5, 40.5] ¤/t, for rs ∈ [0.02, 0.04) directly coal above τe ∈ [15.0, 18.5) ¤/t. As compared to the no-policy benchmark, the technology ranking reverses over the rs range considered above τe ∈ [15.0, 40.5] ¤/t.

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Fig. 6.4 Unit costs of electricity for varying CO2 -price levels under r p = 0.1 and social imputed interest rates of 0.08, 0.05, 0.02 in Nh scenario (¤/MWh) (own calculations).

Thus, as compared to the case of environmental policy alone, the additional enactment of technology policy expands the upper bound of the CO2 price range for coal as least-cost option, from 9.75 ¤/t before, for rs = 0.08 to 11.0 (13.0) ¤/t in the Nl (Nh ) scenario, in the Nh scenario for rs down to 0.04 even to 18.5 ¤/t. Down to rs = 0.02, in the Nl scenario it shrinks until 5.5 ¤/t, passing by its level of environmental policy alone (τe = 9.75 ¤/t) at rs = 0.0675. In the Nh scenario, for rs = 0.02 it remains expanded until 15.0 ¤/t. As compared to the case of environmental policy alone, where it was the first option for any τe ∈ (9.75, 17.0(53.0)] ¤/t in the Nl (Nh ) scenario, gas vanishes as least-cost option irrespective of the CO2 -price level over the whole rs range considered in the Nl scenario, and for rs < 0.04 in the Nh scenario. Only in the Nh scenario, for rs ∈ [0.04, 0.08] it persists as least-cost option for τe intervals restricted to (13.0, 40.5]–18.5 ¤/t. Instead of for τe > 17.0 (53.5) ¤/t as under environmental policy alone, nuclear power in the Nl (Nh ) scenario now becomes the least-cost option over the rs range considered above τe ∈ [5.5, 11.0] ([15.0, 40.5]) ¤/t. The technology ranking reverses, as compared to the no-policy benchmark, over the rs range considered in the Nl scenario for τe around the middle of the relevant range and higher, in the Nh scenario for τe from around the middle of the relevant range until beyond and higher. The impact of the additional enactment of technology policy to environmental policy reflects its effect in the case of technology policy alone. There, it was the stronger the higher the share of capital-investment costs of a particular technology. Accordingly, here, coal generally tends to be favored, though less than nuclear. Gas persists as least-cost option only in the Nh scenario, for more moderate levels of technology policy. However, also there for rs ∈ [0.04, 0.0625) it is succeeded by nuclear already within the relevant CO2 price range.

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6.3 Technology Choice With Abatement Technology How do the results of the previous section change, if a CO2 abatement technology becomes available? As described in section 5.3, carbon-capture-and-storage (CCS) technologies constitute a major upcoming end-of-pipe approach for complete carbon abatement. In this section a sensitivity range of abatement unit costs (AUC) of 10–60 ¤/t is considered. Obviously, this kind of abatement constitutes a relevant option only if environmental policy is enacted.

6.3.1 Sensitivity Under Environmental Policy The availability of an end-of-pipe abatement technology with fixed AUC fixes the UCT2 for any τe ≥ AUC at the level they have for that AUC level. Graphically, it curbs the with increasing CO2 price rising UCT2 curves at the level they have for the given AUC. Figure 6.5 shows the behavior of the unit costs of electricity of the new plant alternatives under environmental policy for AUC levels between 10 and 60 ¤/t in steps of 10 ¤. In both scenarios, irrespective of the AUC level coal remains the least-cost option until τe ≤ 9.75 ¤/t. For τe ∈ (9.75, 17.0(53.5)] ¤/t, gas is the most economic option in the Nl (Nh ) scenario irrespective of the AUC level, as for AUC ∈ [10.0, 17.0(53.5)] ¤/t and τe > 9.75 ¤/t. For τe , AUC > 17.0 (53.5) ¤/t nuclear power is the first 65,00 60,00

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option in the Nl (Nh ) scenario. As compared to the no-policy case, the technology ranking is reversed for τe , AUC > 17.0 (53.5) ¤/t. Thus, while the availability of the abatement technology does not affect the leastcost range of coal, it fixes gas as first option in the Nl scenario, if the AUC are low, and in the Nh scenario even for high AUC, considerably beyond the relevant τe range, also for any τe ≥ AUC. Nuclear is excluded from being the first option for low (even for high) AUC in the Nl (Nh ) scenario irrespective of the CO2 price, and dominates only for τe and AUC above these ranges.

6.3.2 Sensitivity Under Environmental and Technology Policies Combined How does the additional enactment of technology policy change the utility’s technology choice? Figures 6.6 and 6.7 show, for the Nl and Nh scenarios, respectively, the unit costs of electricity of the plant alternatives under environmental and technology policies combined for AUC between 10 and 40 or 60 ¤/t in steps of 10 ¤and social imputed interest rates of 0.08 and 0.02. 50,00

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Fig. 6.6 Unit costs of electricity for varying CO2 -price levels and abatement unit cost levels between 10 and 60 ¤/t in steps of 10 ¤ under r p = 0.1 and social imputed interest rates of 0.08, 0.02 in Nl scenario (¤/MWh) (own calculations).

In the Nl scenario, for rs ∈ [0.07, 0.08] coal remains the least-cost option until AUC ∈ [10.0, 11.0] ¤/t irrespective of the τe level, as until τe ∈ [10.0, 11.0] ¤/t irrespective of the AUC level. For rs ∈ [0.02, 0.07) coal is the least-cost option until

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τe ∈ [5.5, 10.0) ¤/t, irrespective of the abatement option. Nuclear dominates for rs ∈ [0.07, 0.08] above τe , AUC ∈ [10.0, 11.0] ¤/t, for rs ∈ [0.02, 0.07) it dominates above τe ∈ [5.5, 10.0) ¤/t. For rs ∈ [0.02, 0.08] gas has no role to play as first option. The technology ranking is reversed as compared to the no-policy benchmark over the rs range considered for τe , AUC ∈ [13.0, 21.0] ¤/t and higher. In the Nh scenario, for rs ∈ [0.04, 0.08] coal remains the least-cost option until AUC ∈ [13.0, 18.5) ¤/t irrespective of the τe level, as until τe ∈ [13.0, 18.5) ¤/t irrespective of the AUC level. For rs ∈ [0.02, 0.04) coal is the least-cost option until AUC ∈ [15.0, 18.5) ¤/t irrespective of the τe level, as until τe ∈ [15.0, 18.5) ¤/t irrespective of the AUC level. For rs ∈ [0.04, 0.08] gas is the least-cost option for AUC in intervals of [13.0, 40.5]–18.5 ¤/t and above τe ∈ [13.0, 18.5] ¤/t, as for τe in intervals of [13.0, 40.5]–18.5 ¤/t and above AUC ∈ [13.0, 18.5] ¤/t. For rs ∈ [0.02, 0.04) it vanishes as first option irrespective of the τe and AUC levels. For rs ∈ [0.04, 0.08] nuclear dominates above τe , AUC ∈ [18.5, 40.5] ¤/t following gas, for 60,00

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Fig. 6.7 Unit costs of electricity for varying CO2 -price levels and abatement unit cost levels between 10 and 60 ¤/t in steps of 10 ¤ under r p = 0.1 and social imputed interest rates of 0.08, 0.02 in Nh scenario (¤/MWh) (own calculations).

rs ∈ [0.02, 0.04) it dominates above τe , AUC ∈ [15.0, 18.5) ¤/t, directly following coal. The technology ranking is reversed as compared to the no-policy benchmark over the rs range considered above τe , AUC ∈ [15.0, 40.5] ¤/t. Thus, as compared to the case of environmental policy alone, due to the expanded least-cost ranges for coal the availability of the abatement technology is now also relevant for coal, namely for very low AUC and high rs levels in the Nl scenario and for slightly higher AUC levels over the whole rs range considered in the Nh scenario. The least-cost areas for gas are restricted to rs ∈ [0.04, 0.08] in the Nh scenario and AUC levels from very low until beyond the relevant CO2 price range but

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considerably lower than before. Nuclear energy dominates both in the Nl scenario and for low rs ranges in the Nh scenario already for low AUC and τe at that level or higher, and is excluded from being the first option over the whole τe range considered also for AUC levels beyond the relevant CO2 price range only for relatively high rs levels in the Nh scenario. The additional enactment of technology policy to environmental policy when an end-of-pipe abatement technology is available expands the scope in which the abatement option is relevant, though only for very low AUC levels, also to coal. At the same time, it restricts it for gas to only higher rs levels in the Nh scenario for less high levels of the AUC than in the case of environmental policy alone. As compared to the case of the combined enactment of environmental and technology policies without abatement technology the availability of the abatement option fixes, as coal for very low AUC levels in both scenarios, gas in the Nh scenario as leastcost option even until relatively high AUC levels for all τe above relatively low. The scope of nuclear as least-cost option is, accordingly, restricted by these cases in the two scenarios.

6.4 Summary and Discussion of Results This section summarises the results of this chapter and discusses them in the light of the findings of the previous studies cited in subsection 5.1.3. First the no-policy benchmark and the cases of environmental policy without and with abatement option are considered, then the impact of technology policy. Finally, the results are reconsidered from the perspective of the two nuclear-cost scenarios.

6.4.1 No-policy Benchmark The technology ranking, derived on the basis of the technical, economic and financing assumptions of chapter 5, for the case that no policies are enacted clearly shows hard coal as the least-cost option, before gas and nuclear in both scenarios. That is, reflecting on the rentability of generation technologies for new commissioning in Germany in about 2015, the utility would rank in the no-policy case the alternatives considered in this order. The ranking of coal before gas in the no-policy case corresponds to the respective ranking in BEI (2004) and IEA and NEA (2005), whence there for 2020 and 2010, respectively. However, while BEI (2004) does not consider nuclear power, in IEA and NEA (2005) nuclear energy ranks as second option, close to coal, in the corresponding r = 0.1 scenario, and clearly first for an imputed interest rate of 0.05. The ranking of nuclear power as third option in the two scenarios of the present no-policy benchmark is an outcome of the more pessimistic judgment of the

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capital-investment costs in the Nl and the Nh scenario and the consideration of the newer, lower, coal- and gas-price estimations as expressed in EWI and Prognos (2005).3

6.4.2 Results Under Environmental Policy Without and With Abatement Option In the case that a positive CO2 price is implemented via environmental policy, coal remains the least-cost option until a level of 9.75 ¤/t, then gas takes over, succeeded by nuclear for prices of over 17.0 (53.5) ¤/t in the Nl (Nh ) scenario. As compared to the no-policy benchmark, the technology ranking is thus reversed in the Nl scenario within the relevant τe range of 5–30 ¤/t. In the Nh scenario only coal and gas reverse their order within the relevant range, nuclear becomes the least-cost option for τe > 53.5 ¤/t. The availability of an end-of-pipe abatement option for complete emission abatement with AUC ∈ [10.0, 60.0] ¤/t, while leaving the results for coal unaffected, changes qualitatively those for gas and nuclear for sufficiently low AUC levels. Notably, AUC of 10.0–17.0 (53.5) ¤/t fix gas as first option for any CO2 price within these ranges and higher and thus exclude nuclear in the Nl (Nh ) scenario for any CO2 price from being the least-cost option. The AUC ranges to fix a fossil-fuelled technology as least-cost option for respective τe levels coincide, thus, only for gas in the Nh scenario with about the two lower thirds of its expected AUC range of 32–65 ¤/t. For coal, they stay considerably below its relevant range of 37–70 ¤/t. In both cases, the relevant AUC levels lie, moreover, fully beyond the relevant τe range. As mentioned above, the cited studies consider the impact of environmental policy only for particular cases. BEI (2004: sec. 8.7) finds that gas becomes profitable over hard coal from CO2 prices of about 30–35 ¤/t for r = 0.08, IEA and NEA (2005: 123) for prices of about 30 ¤/t for r = 0.05. Thus, in the two studies the prices for the transition from coal to gas are higher than in the present study, though at the upper bound of the relevant τe range. EWI and Prognos (2005: ch. 9), projecting the continuation of status-quo environmental and technology policies notably with a linearly rising CO2 price between 2010–2030 from 5–15 ¤(2000)/t, forecasts a cut back of gross installed capacity in the case of hard coal from about 25 to below 10% and a rise of gas from about 17 to 34% between 2000–2030. These estimations occur as roughly consistent with the present results under environmental policy alone. As long as τe ≤ 15 ¤/t, this also holds, when the nuclear option is taken into account, even in the Nl scenario. The impact of a new (CCS) end-of-pipe abatement option has only marginally been discussed in the cited studies. Notably, the AUC associated with the IGCC power plant with CO2 capture included in IEA and NEA (2005: 119–123) only cover the costs for CO2 capture but not for transportation and storage. WI et al. 3 Note that, as expressed in subsection 5.1.3, due to slight differences in the financial models and the high number of parameters, the concrete UCel levels, though largely similar, in general, cannot be compared but with qualifications across different studies.

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(2007: 206) shows the unit costs of electricity of a coal-fired power plant with CCS abatement for 2020 to immediately exceed those of a gas-fired plant with CCS facility irrespective of the CO2 price, because in the case of coal CC and OMC rise relative to the plant without CCS in absolute terms considerably stronger than in the case of gas. It finds CCS abatement in 2020 for about τe = 15 ¤/t as by far not profitable.

6.4.3 Results in Cases with Technology Policy While the importance of the discount rate has often been emphasised in the literature and results are sometimes considered for different levels (subsection 5.4.2), never deviations from its social level have been analysed as a cause of correcting optimal technology-policy interventions. This subsection summarises and discusses the impact of a respective technology policy for the cases that no other policy is enacted and that it is enacted in addition to environmental policy without and with abatement option. 6.4.3.1 Technology Policy Alone Technology policy generally lowers the unit costs of electricity of the different technologies, the more the higher their capital-investment costs. For the considered range of social imputed interest rates of rs ∈ [0.02, 0.08] and a private rate of r p = 0.1, its sole enactment leaves the technology ranking as compared to the no-policy case unaffected, except a reversal between nuclear and gas for medium policy levels in the Nl scenario. For the present data, the optimal subsidy payments amount to 2.12–7.24, 1.04–3.55, and 3.68–12.48 (5.36–18.25) ¤/MWh for coal, gas, and nuclear in the Nl (Nh ) scenario, respectively. They thus would stay, e.g., considerably below the feed-in-tariff levels prescribed by the German “ErneuerbareEnergien-Gesetz” for current from renewable energy sources.

6.4.3.2 Technology Policy Complementing Environmental Policy As compared to the case of environmental policy alone, the additional enactment of technology policy slightly expands the least-cost range of coal in the Nl scenario at the expense of gas for low technology-policy levels, but reduces it for higher ones. In the Nh scenario it is expanded over the whole rs parameter range considered until medium τe levels. Gas, before the first option in the Nl (Nh ) scenario for τe ∈ (9.75, 17.0(53.0)] ¤/t, vanishes as such irrespective of the τe level over the whole rs range considered in the Nl scenario, as for higher technology-policy levels in the Nh scenario, and persists as least-cost option only until medium technology-policy levels in the Nh scenario in restricted τe intervals until only medium levels of τe . Nuclear power is, instead of for τe > 17.0 (53.5) ¤/t as before, the first option over

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115

the rs range considered from low or medium until higher τe levels in the Nl or Nh scenario, respectively. Accordingly, the technology ranking reverses, as compared to the no-policy benchmark, over the rs range considered in the Nl scenario from medium, and in the Nh scenario from medium until higher τe levels, instead of around (considerably below) the τe > 17.0 (53.5) ¤/t in the Nl (Nh ) scenario in the case of environmental policy alone. The impact of the additional enactment of technology policy to environmental policy reflects its effect in the case of technology policy alone. Coal generally tends to be favored, though less than nuclear. Gas persists as least-cost option only in the Nh scenario, for more moderate levels of technology policy. However, also there it is succeeded by nuclear already for medium technology-policy levels within the relevant CO2 price range. With end-of-pipe abatement technology available, the additional enactment of technology policy expands the scope of relevance of the abatement option, due to its expanded least-cost ranges, also to coal, namely in the Nl scenario for very low AUC and high rs levels and in the Nh scenario for slightly higher AUC levels over the whole rs range considered. For gas, it is restricted to rs ∈ [0.04, 0.08] in the Nh scenario and AUC levels from very low until beyond the relevant CO2 price range but considerably lower than before. Accordingly, nuclear energy dominates both in the Nl scenario and for low rs levels in the Nh scenario already for low AUC and τe at that level or higher, and is excluded from being the first option over the whole τe range considered also for AUC levels beyond the relevant CO2 price range only for relatively high rs levels in the Nh scenario. Under environmental and technology policies combined, taking into account nuclear power as a renewed option, the position of coal seems generally slightly stronger that projected in EWI and Prognos (2005: ch. 9). Its concrete prospects depend, however, strongly on the realising nuclear costs. The favorable EWI and Prognos (2005) results for gas are not sustained anymore. Gas could keep its strong position only in the case of the availability of an abatement option with relatively low, but realistic AUC for relatively high τe and rs and high nuclear costs.

6.4.4 Results According to Nl and Nh Scenarios This subsection finally reconsiders the results under the perspective of the two nuclear-cost scenarios, highlighting especially the position of nuclear power and importance of its capital-investment costs in the relative economics of the different generation technologies. In the no-policy benchmark, nuclear power displays the, by far, highest unit costs of electricity, before coal and gas, already in the low-cost scenario. In the Nl scenario, under environmental policy alone, nuclear becomes the first option for τe > 17.0 ¤/t, following gas, which is the least-cost option for τe ∈ (9.75, 17.0] ¤/t. Technology policy particularly favors nuclear power because of its high capitalinvestment costs. Its sole enactment makes nuclear cheaper than gas but not than coal, for medium to high policy levels (rs ∈ [0.02, 0.054)). In the case of its

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additional enactment to environmental policy, nuclear is the first option over the rs range considered already above τe ∈ [5.5, 11.0] ¤/t. The end-of-pipe abatement option excludes, under environmental policy alone, nuclear from being the first option for any τe , if AUC ∈ [10.0, 17.0] ¤/t. If technology policy is enacted in addition, nuclear dominates for high rs levels (rs ∈ [0.07, 0.08]) already above τe , AUC ∈ [10.0, 11.0] ¤/t, and for rs ∈ [0.02, 0.07) above τe ∈ [5.5, 10.0) ¤/t, i.e. even irrespective of the AUC. In the Nh scenario, the nuclear results are considerably less favorable. Here, it is the first option under environmental policy alone only for τe > 53.5 ¤/t, following gas, which is the least-cost option for τe ∈ (9.75, 53.5] ¤/t. Technology policy alone does not affect its status as least favorable option. If technology policy is enacted in addition to environmental policy, nuclear is the first option over the rs range considered above τe ∈ [15.0, 40.5] ¤/t, and thus in part, for medium policy levels (rs ∈ [0.02, 0.0625)), already in the relevant τe range. The end-of-pipe abatement option excludes, under environmental policy alone, nuclear from being the first option for any τe , if AUC ∈ [10.0, 53.5] ¤/t. If technology policy is enacted in addition, nuclear is still excluded from being the first option over the whole τe range considered for relatively high rs levels (rs ∈ [0.04, 0.08]), if AUC ∈ [18.5, 40.5] ¤/t, i.e. also for AUC levels beyond the relevant τe range. Only for rs ∈ [0.02, 0.04) it dominates above τe , AUC ∈ [15.0, 18.5) ¤/t. The present analysis differentiates the results concerning the ranking of nuclear power in Enquetekommission (2002) and IEA and NEA (2005), underlining the particular importance of the level of capital-investment costs which ultimately realises. While in the Nl scenario nuclear dominates already from τe levels below the middle of the relevant range, in the Nh scenario it becomes the first option only for τe levels considerably beyond the relevant range. The consideration of interest-rate distortions changes these results in favor of nuclear power. While in the Nl scenario it dominates, over the rs range considered, already from low τe levels, also in the Nh scenario, except for low technology-policy levels, it now becomes the first option for τe levels in the relevant range. The end-of-pipe abatement option excludes nuclear from being the first option, for any τe , if the AUC stay below its least-cost ranges. Only in the Nh scenario, for the case of environmental policy alone and, under (additional) technology policy, for relatively high rs levels, AUC ranges to fix a fossil-fuelled technology (here, gas) as first option for all τe within these ranges and higher (partially) overlap with the AUC ranges as currently expected.

6.5 Conclusion This chapter studied the utility’s optimal technology choice and its variation under environmental and technology policies, separately and combined, in the cases where an end-of-pipe CO2 abatement technology is unavailable and available. The main results are briefly restated in the following points. 1. Environmental policy reverses the no-policy technology ranking of coal before gas and nuclear for τe > 17.0 ¤/t in the Nl , and for τe > 53.5 in the Nh scenario.

6.5 Conclusion

117

2. Technology policy lowers the unit costs of electricity of the different technologies, the more the higher their capital-investment costs. Its sole enactment leaves, for r p = 0.1 and rs ∈ [0.02, 0.08], the no-policy technology ranking unaffected, apart from a reversal between nuclear and gas for rs < 0.054 in the Nl scenario. 3. The distortion induced by the split of the social and private levels of the imputed interest rate amounts to about 1.0–12.5 (18.5) ¤/MWh or 2.5–27.0 (31.5)% of the distorted UCT2 at the busbar in the Nl (Nh ) scenario. 4. The additional enactment of technology policy to environmental policy generally favors coal, but less than nuclear. Gas persists as least-cost option only in the Nh scenario until higher technology-policy levels (rs ∈ [0.04, 0.08]) in restricted τe intervals until medium levels of τe . Otherwise it vanishes as such, making nuclear the cheapest option above τe ∈ [5.5, 11.0] ([15.0, 40.5]) ¤/t in the Nl (Nh ) scenario. 5. The end-of-pipe abatement option affects the results for coal only if also technology policy is enacted for AUC ∈ [10.0, 11.0] ([13.0,18.5]) ¤/t and rs ∈ [0.07, 0.08] (irrespective of rs ) in the Nl (Nh ) scenario. Gas is, already under environmental policy, fixed for sufficiently low AUC levels (10.0–17.0 (53.5) ¤/t) in the Nl (Nh ) scenario as least-cost option for any τe within these ranges and higher. Technology policy restricts the relevance of the abatement option for gas to rs ∈ [0.04, 0.08] in the Nh scenario in restricted AUC intervals. Nuclear is excluded as first option for any τe , where the abatement option is relevant for coal or gas. 6. For coal and gas, the relevant AUC ranges lie fully beyond the relevant τe range (subsections 5.3.1–5.3.2, 5.4.1). The derived AUC ranges to fix a technology as least-cost option for respective τe levels coincide only for gas in the Nh scenario with parts of its expected AUC range (32–65 ¤/t), also for technology policy. Otherwise, they stay below the relevant ranges, for coal considerably. 7. In the no-policy benchmark, nuclear power displays the by far highest unit costs of electricity. Under environmental policy, it is the first option for τe > 17.0 (53.5) ¤/t in the Nl (Nh ) scenario. Technology policy particularly favors it because of its high capital-investment costs, without making it the first option. Under environmental and technology policies combined, nuclear is the first option over the rs range considered above τe ∈ [5.5, 11.0] ([15.0, 40.5]) ¤/t. The end-of-pipe abatement option excludes it, under environmental policy alone, from being the first option for any τe , if AUC ∈ [10.0, 17.0(53.5)] ¤/t. Under additional technology policy, it dominates in the Nl scenario for rs ∈ [0.07, 0.08] already above τe , AUC ∈ [10.0, 11.0] ¤/t, and for rs ∈ [0.02, 0.07) above τe ∈ [5.5, 10.0) ¤/t. In the Nh scenario, it is excluded from being the first option over the whole τe range considered for rs ∈ [0.04, 0.08], if AUC ∈ [18.5, 40.5] ¤/t, and only dominates for rs ∈ [0.02, 0.04) above τe , AUC ∈ [15.0, 18.5) ¤/t. In the next chapter, the investment conditions for the new technologies are projected on a temporal scale. This allows to account, in addition, for the effect of environmental policy and the abatement option on the unit costs of electricity of the polluting established technology, and for the temporal dimension of the structural change.

Chapter 7

Optimal Moments of Transition Under Environmental and Technology Policies

This chapter studies, based on the technical, economic and financing assumptions set out in chapter 5, the single and combined influence of environmental and technology policies on the utility’s choice of the optimal moment of transition from its established to the new power plants. Again, the two cases of the absence (section 7.3) and the availability of a CO2 abatement technology (section 7.4) are distinguished. Section 7.5 summarises and discusses the results.

7.1 Determination of the Optimal Moment of Transition Beginning in 2015, the utility has at any moment the choice between continuing to produce electricity with its established polluting power plant and switching to one of the new less polluting technologies. As stated in Propositions 3.1 and 3.3 of chapter 3 with respect to the model of section 3.1, there is investment in the new technology, if and only if its unit costs of energy are below those of the established technology. Accordingly, the optimal economic life of the established plant, and thus the optimal moment of transition, is determined by the relationship of the unit costs of electricity of the established and the new power plants. In contrast to the assumption of constant unit costs of energy over a potentially infinite lifetime of the established technology as met in the theoretical part, in actuality a plant’s unit costs of eletricity rise over time. At the same time, the levelised unit costs of the new plant stay constant ceteris paribus, or vary, e.g., for constant capital and O&M costs, only according to the fuel-price development. The period of analysis begins in t1 = 0, the first year in which the new power plants could be commissioned, and extends until tn , the moment of transition to the highest-cost alternative in the nopolicy benchmark. t1 is chosen such that in the no-policy benchmark the units costs of electricity of any new technology exceed those of the established (already operating) power plant, UCT2 > UCT1 . The optimal economic life of the established plant, and thus the optimal moment of transition, may be determined as follows.

C. Heinzel, Distorted Time Preferences and Structural Change in the Energy Industry, Sustainability and Innovation, DOI 10.1007/978-3-7908-2183-3 7, © Physica-Verlag Heidelberg 2009

119

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7 Optimal Moments of Transition Under Environmental and Technology Policies

Definition 7.1 (Optimal moment of transition). Given strictly monotonously rising UCT1 (t) and monotonous and less steep UCT2 (t) than UCT1 (t) in the time interval [t1 ,tn ], the optimal moment of transition from production with the established technology, T1 , to production with the new technology, T2 , topt , is the moment t ∈ [t1 ,tn ] from which the unit costs of electricity of the established technology equal or exceed those of the new, i.e. UCT1 (t) ≥ UCT2 (t) .

(7.1)

Obviously, under these conditions an optimal moment of transition exists. Lemma 7.1 states the sufficiency of these conditions for the optimal moment of transition to be unique. Lemma 7.1 (Unicity of optimal moment of transition). Given strictly monotonously rising UC T1 (t) in the time interval [t1 ,tn ], a monotonous and less steep UCT2 (t) shape, t ∈ [t1 ,tn ], is sufficient for the optimal moment of transition to production with the new power plant to be unique. Thus, UC T1 (t) < UCT2 (t) in t = t1 implies a positive replacement time, i.e. trepl = topt ∈ (t1 ,tn ], UC T1 (t) ≥ UCT2 (t) in t = t1 immediate replacement. For the analysis in this chapter the unit costs of the established power plant are calculated as indicated in subsection 5.2.4, based on the empirical data of subsection 5.3.1. For their derivation an OMC f ix (t) value in t = tend = 14.0, the end of the established power plant’s economic life, of 80.0 k¤/MWe has been chosen, implying OMCvar (14) = 12.797 ¤/MWh.1 For the new power plants, for convenience, the technologies, and with them capital and O&M costs, are assumed to stay constant over time while fuel prices follow their real expected development. Generally, in the time under consideration, the prices of coal and gas are expected to increase, while the fuel prices associated with nuclear energy will tend to remain constant (section 5.3). Accordingly, the unit costs of electricity of the new coal and the gas technologies smoothly rise over time, whereas those of nuclear stay constant at their levels in t = 0 (2015) in both scenarios. Figure 7.1 shows the schedules of the unit costs of electricity of the the established and the new power plants from the time t = 0, in which the analysis begins, to t = tn , the moment of transition to the highest-cost alternative (in the hypothetical case that the other alternatives are not available) in the no-policy benchmark. The shapes of UCT1 and UC T2 thus satisfy the conditions of Lemma 7.1. As the policies do neither change the monotonicity nor, qualitatively, the relation of the slopes of the UCT1 and UCT2 curves, this result also holds in any of the cases below.

By implication of the indications in subsection 5.2.4, the value of either OMC f ix (tend ) or OMCvar (tend ) has to be freely chosen.

1

7.2 No-policy Benchmark

121

60,00 55,00

UCT1,UCT2

50,00 45,00 40,00 35,00 30,00 25,00 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

t C (old)

C (new)

G

N_l

N_h

Fig. 7.1 Unit costs of electricity of the established and new power plants under r p = 0.1 in nopolicy benchmark (¤/MWh) (own calculations).

7.2 No-policy Benchmark According to Definition 7.1, the optimal moments of transition from the established to one of the new generation technologies, topt , derive as the moments in which the unit costs of the established technology and those of the new technology equal each other. As stated in section 7.1, the UC T1 and UC T2 curves comply with the conditions of Definition 7.1. Table 7.1 displays the results for the no-policy benchmark. Note that, as indicated in subsection 5.2.4, the UCT1 shape is calibrated such as to equal the unit costs of the new coal-fired power plant in t = tend = 14.0. Table 7.1 Optimal moments of transition in cases of sole availability of any single new plant alternative, in years of operation of established plant from year in which analysis begins, i.e. 2015 (own calculations) Optimal transition moment C G Nl Nh 14.0 17.8 17.9 22.5

While the new coal-fired power plant succeeds its predecessor after 40 years of operation of the latter, the other new generation technologies would replace the existing plant, in case of their sole availability, only after the end of its expected economic life, namely the CCGT plant after 43.8 and the nuclear plant, in the Nl (Nh ) scenario, after 43.9 (48.5) years of operation.

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7 Optimal Moments of Transition Under Environmental and Technology Policies

For the given data the technology ranking of section 6.1 thus immediately translates into the present replacement-time ranking among the new plant alternatives. This is, however, a particular case. For a different behavior of particular cost components of the new technologies or the UCT1 over time, the ranking in general differs.

7.3 Optimal Moments of Transition Without Abatement Technology This section analyses how the optimal moments of transition vary under environmental and technology policies, separately and combined, if no CO2 abatement technology is available.

7.3.1 Sensitivity Under Environmental Policy As studied for the ranking of the new technologies in subsection 6.2.1, under environmental policy also the optimal moments of transition from the established to the new power plants as well as, in general, the order in which the new power plants would replace the established vary. Figure 7.2 shows the behavior of the optimal moments of transition for varying CO2 -price levels. 22,0 20,0 18,0 16,0

trepl

14,0 12,0 10,0 8,0 6,0 4,0 2,0 0,0 0

5

10

15

20

C (new) (0.1)

25

30 te

G (0.1)

35

40

N_l (0.1)

45

50

55

60

N_h (0.1)

Fig. 7.2 Optimal moments of transition to new plant alternatives for varying CO2 prices (¤/t) under r p = 0.1 (own calculations).

7.3 Optimal Moments of Transition Without Abatement Technology

123

In the Nl scenario, the new coal-fired power plant remains the first option to replace the old one until τe = 11.5 ¤/t, with trepl ∈ [12.6, 14.0]. For τe > 11.5 ¤/t, nuclear replaces the established plant, with trepl ∈ [0.0, 12.5], immediately (i.e. in t = 0) for τe ≥ 23.5 ¤/t. Gas has no role to play as first option, irrespective of the CO2 price. The replacement-time ranking reverses as compared to the no-policy benchmark for τe > 17.5 ¤/t. In the Nh scenario, the new coal-fired plant remains the first option until τe = 17.75 ¤/t, with trepl ∈ [11.8, 14.0]. For τe ∈ (17.75, 53.5] ¤/t, gas replaces the established plant, with trepl ∈ [0, 11.8), immediately for τe ≥ 28.75 ¤/t. For τe > 53.5 ¤/t, nuclear is the first alternative, replacing the old plant immediately, as it would – in the hypothetic case of its sole availability – already for τe ≥ 39.75 ¤/t. The replacement-time ranking reverses as compared to the no-policy benchmark for τe > 53.5 ¤/t. Thus, in the Nl scenario coal persists as first option only until relatively low CO2 prices, gas plays no role as first option. In the Nh scenario coal persists as first option until medium CO2 prices and gas has an advantage as compared to nuclear until after the end of the relevant CO2 price range. Table 7.2 displays the reductions of the optimal replacement times induced by environmental policy in years of operation of the established plant and in shares of the replacement times of the no-policy benchmark. As already Figure 7.2, the table shows that environmental policy generally reduces the replacement times as compared to the no-policy benchmark. Between single technologies, its impact differs, Table 7.2 Shortening of replacement times as compared to no-policy benchmark in cases of sole availability of any single new plant alternative for varying CO2 prices (¤/t), in years of operation of established plant and in shares of initial times (own calculations) CO2 price 5 10 15 20 25 30 35 40 45 50 55 60

C 0.6 1.2 1.8 2.5 3.1 3.7 4.4 5.1 5.7 6.4 7.2 7.8

Replacement-time shortening absolute shares G N1 Nh C G N1 1.1 1.8 2.3 0.043 0.062 0.101 2.3 3.8 2.7 0.086 0.129 0.212 3.8 8.4 4.2 0.129 0.213 0.469 8.3 13.5 5.9 0.179 0.466 0.754 13.3 17.9 7.9 0.221 0.747 1.000 17.8 17.9 12.0 0.264 1.000 1.000 17.8 17.9 17.0 0.314 1.000 1.000 17.8 17.9 22.5 0.364 1.000 1.000 17.8 17.9 22.5 0.407 1.000 1.000 17.8 17.9 22.5 0.457 1.000 1.000 17.8 17.9 22.5 0.514 1.000 1.000 17.8 17.9 22.5 0.557 1.000 1.000

Nh 0.102 0.120 0.187 0.262 0.351 0.533 0.756 1.000 1.000 1.000 1.000 1.000

however, importantly, both in absolute and relative terms. While in the case of coal the replacement time reduces within the relevant τe range of 5–30 ¤/t by 3.7 periods or 26.4% and even for τe = 60 ¤/t only by 7.8 periods or 55.7%, in the cases of gas it shortens by 17.8 and in that of nuclear in the Nl (Nh ) scenario by 17.9 (22.5) periods or 100%. The new coal-fired power plant, thus, succeeds its predecessor even

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7 Optimal Moments of Transition Under Environmental and Technology Policies

for τe = 60 ¤/t only in t = 6.2, whereas for gas, and for nuclear in the Nl scenario immediate replacement is reached already within the relevant τe range, for nuclear in the Nh scenario still at almost 40 ¤/t. The differences among the technologies mainly depend on the varied differences in emission factors and net thermal efficiencies between the established and the new technologies. Notably in the case of coal, while both coal-fired power plants have the same emission factor, as compared to the unit costs of electricity of the new plant those of the established plant rise with increasing τe slightly more due to its lower net thermal efficiency. However, the trepl shapes over the τe range considered, moreover, depend on the varied shapes of the specific UCel curves over time. In particular, their behavior differs, due to the particular UCT1 shape over time, depending on whether the optimal moments of transition lie beyond or within the expected economic lifetime of the established plant. The respective deterrance is to be taken into account when interpreting these data.2

7.3.2 Sensitivity Under Technology Policy Corresponding to the dynamic setting of this chapter, two further assumption are met with respect to the implementation of the hypothetic investment subsidy, τi , to correct the distortions induced by the diverging private and social imputed interest rates. It is, first, assumed to be newly introduced in t = 0 and, second, to be paid only on electricity produced with the new technologies. The first assumption implies that it is not relevant for the established technology before t = 0, the second that it has also no direct relevance for T1 in t = 0 or later.3 Figure 7.3 shows the behavior of the optimal moments of transition for social imputed interest rates ranging from 8.0 to 2.0%. Under technology policy, in both scenarios coal remains the first technology to replace the established power plant over the whole rs range considered, with trepl ∈ [2.7, 11.0]. In the Nl scenario, the replacement-time ranking between gas and nuclear is, as compared to the no-policy benchmark, reversed for rs ≤ 0.08, in the Nh scenario for rs < 0.034. Thus, as compared to the no-policy benchmark, technology policy alone does not change the status of coal as the first option to replace the established plant over the whole rs range considered. However, nuclear energy becomes the second technology instead of gas in the Nl scenario over the whole rs range, and in the Nh scenario under a certain level of the social imputed interest rate. 2

See, for further remarks on the interpretation of the trepl indications, subsection 7.5.1. Note that, as calculated according to subsection 5.2.4, for t ∈ {t1 , ...,tend − 1} the UCT1 (t) also depend on an imputed interest rate, which from a welfare-theoretic point of view should comply with its socially optimal level. Due to the sunk capital costs and its with rising t decreasing importance, the distortion has, however, only a marginal effect. Notably, at the highest in t = 0, for a private imputed interest rate of r p = 0.1 and rs = 0.08, 0.05, 0.02 the UCT1 (t) are underestimated by 1.1, 2.7, 4.5%, respectively. Therefore, the present analysis abstracts from this effect.

3

7.3 Optimal Moments of Transition Without Abatement Technology

125

22,0 20,0 18,0 16,0

trepl

14,0 12,0 10,0 8,0 6,0 4,0 2,0 0,0 0,08 0,075 0,07 0,065 0,06 0,055 0,05 0,045 0,04 0,035 0,03 0,025 0,02

rs C (new)

G

N_l

N_h

Fig. 7.3 Optimal moments of transition to new plant alternatives for varying levels of social imputed interest rate (own calculations). Table 7.3 Shortening of replacement times as compared to no-policy benchmark in cases of sole availability of any single new plant alternative for varying CO2 prices (¤/t), in years of operation of established power plant and in shares of initial times (own calculations) rs 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020

C 3.0 3.7 4.5 5.2 5.8 6.6 7.3 7.9 8.6 9.3 9.8 10.5 11.3

Replacement-time shortening absolute shares G N1 Nh C G N1 0.5 1.7 1.9 0.214 0.028 0.095 0.6 2.2 2.3 0.264 0.034 0.123 0.7 2.6 2.8 0.321 0.039 0.145 0.8 3.1 3.3 0.371 0.045 0.168 1.1 3.5 3.8 0.421 0.062 0.196 1.2 4.1 4.3 0.471 0.067 0.229 1.3 5.0 4.8 0.521 0.073 0.279 1.4 5.9 5.2 0.564 0.079 0.330 1.5 6.8 5.7 0.614 0.084 0.380 1.6 7.6 6.2 0.664 0.090 0.425 1.7 8.4 6.7 0.700 0.096 0.469 1.9 9.2 7.2 0.750 0.107 0.514 2.0 10.0 7.6 0.807 0.112 0.559

Nh 0.084 0.102 0.124 0.147 0.169 0.191 0.213 0.231 0.253 0.276 0.298 0.320 0.338

Table 7.3 displays the reductions of the optimal replacement times induced by technology policy in years of operation of the established plant and in shares of the replacement times of the no-policy benchmark. As Figure 7.3, it shows that technology policy – like environmental policy – generally reduces the replacement times as compared to the no-policy benchmark. Notably, for rs ∈ [0.02, 0.08] in the case of coal the replacement times are reduced, as compared to the no-policy case, by

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7 Optimal Moments of Transition Under Environmental and Technology Policies

3.0–11.3 periods or 21.4–80.7%, for gas by 0.5–2.0 periods or 2.8–11.2%, and for nuclear in the Nl (Nh ) scenario by 1.7–10.0 (1.9–7.6) periods or 9.5–55.9 (8.4– 33.8)%. Thus, the impact of technology policy is the strongest for coal, before nuclear in the Nl scenario, nuclear in the Nh scenario, and gas. In no case technology policy induces immediate replacement. Apart from the cases of coal (by construction) and of nuclear for rs < 0.057 in the Nl scenario, the replacement times even remain beyond the established plant’s expected economic life. For all technologies but coal, the effect is, thus, considerably less strong than under environmental policy. The varied effect of technology policy on the replacement times of the different technologies is a combined outcome of, first, its varied effect on the unit costs of electricity of the different new technologies and, second, the particular shapes of the different UCel curves, especially the UCT1 curve. As derived in subsection 6.2.2, the (negative) influence of technology policy on the UCT2 is the stronger the higher the technology-specific share of capital-investment costs. This negative impact on the UCT2 materialises here in the higher replacement-time reductions the flatter the UCT1 curve at the place in question. For the rs levels considered, the effect is accordingly, in general, the strongest for coal, before nuclear in the Nl scenario, nuclear in the Nh scenario, and gas. An exception to this rule is nuclear in the Nl scenario. For rs ∈ [0.02, 0.057], where its optimal moments of transition lie beyond the expected economic life of the established power plant, it is, in absolute terms, less strongly affected than in the Nh scenario. Moreover, for rs < 0.057, where its optimal moments of transition lie within the expected economic life of the established power plant, it is, at the margin, in absolute terms, at least as strongly affected as coal, and usually more.4 Note that, due to the higher fuel costs as compared to t = 0, and accordingly higher unit costs of electricity, in the cases of coal and gas the induced distortions, and thus policy levels, slightly exceed those indicated in Table 6.5 above.

7.3.3 Sensitivity Under Environmental and Technology Policies Combined How do the optimal moments of transition and the optimal replacement order change, if both environmental and technology policies are enacted? Figures 7.4 and 7.5 show for the Nl and the Nh scenario, respectively, the combined influence of environmental and technology policies on the behavior of the optimal moments of transition to the new plant alternatives for r p = 0.1 and exemplary social imputed interest rates, rs , of 0.08, 0.05, 0.02 over the CO2 price parameter range considered.

4 Due to the discrete evaluation and complexity of the data, at the margin slight deviations from these rankings occur.

7.3 Optimal Moments of Transition Without Abatement Technology

127

18,0 16,0 14,0

trepl

12,0 10,0 8,0 6,0 4,0 2,0 0,0 0

5

10

C (new) (0.1) C (new) (0.08,0.05,0.02)

15

te

20

G (0.1) G (0.08,0.05,0.02)

25

30

N_l (0.1) N_l (0.08,0.05,0.02)

Fig. 7.4 Optimal moments of transition to new plant alternatives for varying CO2 prices (¤/t) under r p = 0.1 and social imputed interest rates of 0.08, 0.05, 0.02 in Nl scenario (own calculations).

In the Nl scenario, for rs ∈ [0.02, 0.08] coal remains the first option until τe ∈ [6.0, 9.75] ¤/t, with trepl ∈ [1.9, 11.0]. Above τe ∈ [6.0, 9.75] ¤/t, nuclear is the first option, with trepl ∈ [0.0, 9.6]. Gas vanishes as first option irrespective of CO2 price and rs levels. As compared to the no-policy benchmark, the replacement-time ranking reverses over the rs parameter range considered for τe ∈ [18.75, 21.0] ¤/t and higher. In the Nh scenario, for rs ∈ [0.05, 0.08] coal is the first option until τe ∈[18.5, 20.0) ¤/t, with trepl ∈ [3.8, 11.0], for rs ∈ [0.02, 0.05) until τe ∈ [15.0, 20.0) ¤/t, with trepl ∈ [0.4, 3.7).5 For rs ∈ [0.05, 0.08], gas is the first option for τe in intervals of [18.5,40.5]–20.0 ¤/t, with trepl ∈ [3.6, 8.7]. For rs < 0.05, it vanishes as first option for any CO2 price. For rs ∈ [0.05, 0.08] nuclear follows gas as first option above τe ∈ (20.0, 40.5] ¤/t, for rs ∈ [0.02, 0.05) directly coal for τe ∈ (15.0, 20.0] ¤/t and higher, with trepl ∈ [0.0, 3.6]. As compared to the no-policy benchmark, the replacement-time ranking reverses over the rs parameter range considered above τe ∈ [20.0, 40.5] ¤/t. Thus, as compared to the case of environmental policy alone, the additional enactment of technology policy reduces in the Nl scenario the upper bound of the CO2 price range for coal as first option, from 11.5 ¤/t before, to 6.0–9.75 ¤/t Note that, due to the stop of the analysis in t = 0, the graphs display, in general, a ‘last-round’ effect for the points between t = 0 and the one before. Therefore, in these ranges the points of intersection between different curves shown in the graphs may be deterred (such as here for the transition from coal to nuclear for r = 0.02 at τe = 15). In the text, the accurate figures are indicated.

5

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7 Optimal Moments of Transition Under Environmental and Technology Policies 22,0 20,0 18,0 16,0

trepl

14,0 12,0 10,0 8,0 6,0 4,0 2,0 0,0 0

5

10

15

C (new) (0.1) C (new) (0.08,0.05,0.02)

20

te

25

G (0.1) G (0.08,0.05,0.02)

30

35

40

N_h (0.1) N_h (0.08,0.05,0.02)

Fig. 7.5 Optimal moments of transition to new plant alternatives for varying CO2 prices (¤/t) under r p = 0.1 and social imputed interest rates of 0.08, 0.05, 0.02 in Nh scenario (own calculations).

for rs ∈ [0.02, 0.08]. In the Nh scenario, it expands it, from 17.75 ¤/t before, for rs ∈ [0.05, 0.08] to 18.5–20.0 ¤/t, and reduces it in turn for rs ∈ [0.02, 0.05) down until 15.0 ¤/t, passing by its level of environmental policy alone at rs = 0.035. The range in which gas dominates in the Nh scenario is reduced, from τe ∈ (17.75, 53.5] in the case of environmental policy alone, to intervals of [18.5,40.5]–20.0 for rs ∈ [0.05, 0.08]. It vanishes as first option now not only in the Nl scenario but also for rs ∈ [0.02, 0.05) in the Nh scenario. Instead of for τe > 11.5 (53.5) ¤/t as under environmental policy alone in the Nl (Nh ) scenario, nuclear power in the Nl scenario now becomes the first option over the rs range considered above τe ∈ [6.0, 9.75] ¤/t, in the Nh scenario for rs ∈ [0.05, 0.08] above τe ∈ (20.0, 40.5] ¤/t, and for rs ∈ [0.02, 0.05) for τe ∈ (15.0, 20.0] ¤/t and higher. The replacement times reduce as compared to the no-policy benchmark in the case of coal in the Nl (Nh ) scenario by 3.0–12.1 (3.0–13.6) periods or 21.4–86.4 (21.4–97.1)%, for nuclear by 8.3–17.9 (18.9–22.5) periods or 46.4–100 (84.0–100)%, and for gas in the Nh scenario by 9.1–14.2 periods or 51.1–79.8%. They are thus, as compared to the case of environmental policy alone, expanded in both scenarios for coal, from 10 (15)%, and for nuclear, from 29.6–100% in the Nl scenario, and with respect to the τe range in the Nh scenario. For gas they decrease from 33.1–100%. The impact of the additional enactment of technology policy to environmental policy reflects the combined effect at work in the case of its sole enactment, on the different UCT2 and due to due to the particular shapes of the different UC el curves, and especially the UCT1 curve. There, it was general the strongest for coal, before nuclear in the Nl scenario, nuclear in the Nh scenario, and gas. An exception was, in

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particular, that nuclear power in the Nl scenario for rs < 0.057, its optimal moments of transition lying within the expected economic life of the established power plant, is, at the margin, in absolute terms, in general more strongly affected than coal. Accordingly, here, the least-cost range of coal is in the Nl scenario restricted in favor of nuclear, while in the Nh scenario it expands at the expense of gas. The least-cost range of gas, which persists as first option only for more moderate levels of technology policy in the Nh scenario, is furthermore restricted from above by nuclear, succeeding it for rs ∈ [0.05, 0.0625) already within the relevant CO2 price range.

7.4 Optimal Moments of Transition With Abatement Technology This section studies how the optimal moments of transition vary under environmental and technology policies, separatedly and combined, if a CO2 abatement technology is available.

7.4.1 Sensitivity Under Environmental Policy The availability of an end-of-pipe abatement technology with fixed abatement unit costs (AUC) now fixes both UCT1 and UCT2 for any τe ≥ AUC at the level they have at that AUC level. Graphically, it curbs the with increasing CO2 price falling replacement-time curves at the level they have for the given AUC. Figure 7.6 shows the behavior of the optimal moments of transition to the new plant alternatives under environmental policy for AUC levels between 10 and 40 ¤/t in steps of 10 ¤under r p = 0.1. In the Nl scenario, coal remains the first option for AUC ≤ 11.5 ¤/t irrespective of the τe level, as for τe ≤ 11.5 ¤/t irrespective of the AUC level, with trepl ∈ [12.6, 14.0] in each case. For τe , AUC > 11.5 ¤/t, nuclear is the first alternative. Gas is never the first option. The replacement-time ranking is reversed as compared to the no-policy benchmark for τe , AUC > 11.5 ¤/t. In the Nh scenario, coal remains the first option for AUC ≤ 17.5 ¤/t irrespective of the τe level, as for any τe ≤ 17.5 ¤/t irrespective of the AUC level, with trepl ∈ [11.9, 14.0] in each case. For AUC ∈ (17.5, 53.5] ¤/t, gas is the first alternative for any τe > 17.5 ¤/t, as for τe ∈ (17.5, 53.5] ¤/t if AUC > 17.5 ¤/t, with trepl ∈ [0.0, 11.9] in each case. Nuclear is the first option for τe , AUC > 53.5 ¤/t. The replacement-time ranking is reversed as compared to the no-policy case for τe , AUC > 53.5 ¤/t. Thus, as compared to the case without abatement technology, its availability makes coal in the Nl (Nh ) scenario, in addition to the range of τe ≤ 11.5 (< 17.5) ¤/t, persist as first alternative for any τe if AUC ≤ 11.5 (< 17.5) ¤/t, the replacement time being reduced by 10 (15)%. In the Nl scenario, it is followed by nuclear

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7 Optimal Moments of Transition Under Environmental and Technology Policies 22,0 20,0 18,0 16,0

trepl

14,0 12,0 10,0 8,0 6,0 4,0 2,0 0,0 0

5

10 C (new) (0.1)

15

20 te G (0.1)

25 N_l (0.1)

30

35

40

N_h (0.1)

Fig. 7.6 Optimal moments of transition to new plant alternatives for varying CO2 prices and abatement unit cost levels between 10 and 40 ¤/t in steps of 10 ¤ under r p = 0.1 (own calculations).

as first alternative for τe , AUC > 11.5 ¤/t, the replacement time being reduced by 29.6–100%. In the Nh scenario, gas is, in addition to the case of τe ∈ [17.75, 53.5] ¤/t and AUC ≥ 17.75 ¤/t, the first option for AUC ∈ [17.75, 53.5] ¤/t and any τe ≥ 17.75 ¤/t, the replacement time being reduced by 33.1–100% in each case. Nuclear is in the Nh scenario the first alternative only for τe , AUC > 53.5 ¤/t. In the Nl and Nh scenarios for very low AUC levels both gas and nuclear are excluded as first option for all τe , in favor of coal. In the Nh scenario gas is the first option for AUC from low to levels considerably beyond the upper bound of the relevant τe range, and τe equal to the lower bound of this AUC range and higher, directly following coal, and thus excluding nuclear as first option for all τe . While in the Nl scenario nuclear is the first option already from low AUC and medium τe within the relevant range, in the Nh scenario it thus dominates only for relatively high AUC and τe considerably beyond the upper bound of its relevant range. Note that by fixing the UCel of both the new technologies and the established technology, the AUC also fix the replacement times for any τe ≥ AUC at the level they have for those AUC, in particular also in the cases of nuclear. Hence, the introduction of the end-of-pipe abatement technology extends, for τe > AUC, the economic life of the established plant and delays the structural change, amplifying the overall operating time of old and new plants together.

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7.4.2 Sensitivity Under Environmental and Technology Policies Combined How do the optimal moments of transiton and optimal replacement order change if, in addition, technology policy is enacted? Figures 7.7 and 7.8 show for the Nl and the Nh scenario, respectively, the behavior of the optimal moments of transition to the new plant alternatives under environmental and technology policies combined for AUC levels between 10 and 30 or 40 ¤/t in steps of 10 ¤under r p = 0.1. In the Nl scenario, for rs ∈ [0.02, 0.08] coal remains the first option until τe ∈ [6.0, 9.75] ¤/t, with trepl ∈ [1.9, 11.0]. Above τe ∈ [6.0, 9.75] ¤/t, nuclear is the first option, with trepl ∈ [0.0, 9.6]. Neither the end-of-pipe abatement option nor the CCGT technology option influence the determination of the first option. The replacement-time ranking is reversed as compared to the no-policy case for τe , AUC ∈ [18.75, 21.0] ¤/t and higher. 18,0 16,0 14,0

trepl

12,0 10,0 8,0 6,0 4,0 2,0 0,0 0

5

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C (new) (0.1) C (new) (0.08,0.02)

15

te

G (0.1) G (0.08,0.02)

20

25

30

N_l (0.1) N_l (0.08,0.02)

Fig. 7.7 Optimal moments of transition to new plant alternatives for varying CO2 prices and abatement unit cost levels between 10 and 30 ¤/t in steps of 10 ¤ under r p = 0.1 and social imputed interest rates of 0.08, 0.02 in Nl scenario (own calculations).

In the Nh scenario, for rs ∈ [0.05, 0.08] coal is the first option until AUC ∈ [18.5, 20.0) ¤/t irrespective of the τe level, as until τe ∈ [18.5, 20.0) ¤/t irrespective of the AUC level, with trepl ∈ [3.8, 11.0]. For rs ∈ [0.02, 0.05), coal remains the first option until AUC ∈ (15.0, 20.0] ¤/t irrespective of the τe level, as until τe ∈ (15.0, 20.0] ¤/t irrespective of the AUC level, with trepl ∈ [0.4, 3.7]. For rs ∈ [0.05, 0.08] gas is the first option for AUC in intervals of [18.5,40.5]–20.0 ¤/t and τe in intervals of [18.5,40.5]–20.0 ¤/t and higher, as for τe in intervals of

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[18.5,40.5]–20.0 ¤/t and AUC in intervals of [18.5,40.5]–20.0 ¤/t and higher, with trepl ∈ [3.6, 8.7]. For rs < 0.05 it vanishes as first option irrespective of the τe and AUC levels. For rs ∈ [0.05, 0.08] nuclear dominates above τe , AUC ∈ (20.0, 40.5] ¤/t, for rs ∈ [0.02, 0.05) above τe , AUC ∈ (15.0, 20.0] ¤/t, with trepl ∈ [0.0, 3.6]. The replacement-time ranking is reversed as compared to the no-policy benchmark above τe , AUC ∈ [20.0, 40.5] ¤/t and higher. Thus, as compared to the case of environmental policy alone, due to the restricted τe range of coal as first option in favor of nuclear, the abatement option is now irrelevant in the Nl scenario. In the Nh scenario, while the τe range of coal as first option is slightly expanded at the expense of gas, the range of gas as first option is 22,0 20,0 18,0 16,0

trepl

14,0 12,0 10,0 8,0 6,0 4,0 2,0 0,0 0

5

10

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C (new) (0.1) C (new) (0.08,0.02)

20

te

25

G (0.1) G (0.08,0.02)

30

35

40

N_h (0.1) N_h (0.08,0.02)

Fig. 7.8 Optimal moments of transition to new plant alternatives for varying CO2 prices and abatement unit cost levels between 10 and 40 ¤/t in steps of 10 ¤ under r p = 0.1 and social imputed interest rates of 0.08, 0.02 in Nh scenario (own calculations).

restricted to rs ∈ [0.05, 0.08] and AUC levels from low until beyond the relevant price range but considerably lower than before. Nuclear energy is thus excluded from being the first option over the whole τe range considered, also for AUC levels beyond the relevant CO2 price range, only for relatively high rs levels in the Nh scenario. Both in the Nl scenario and for low rs ranges in the Nh scenario, it dominates already for low AUC and any τe at that level or higher. The additional enactment of technology policy to environmental policy, when the end-of-pipe abatement option is available, restricts the scope of relevance of the abatement option to the Nh scenario, and there, while slightly expanding it for coal, further restricts it for gas to only higher rs levels for less high AUC. As compared to the case of the combined enactment of environmental and technology policies without abatement technology, the availability of the abatement option fixes now in the Nh scenario coal until low AUC levels and gas even until relatively high AUC

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levels for all τe above relatively low as first option. The scope of nuclear as first option is, accordingly, restricted only in the Nh scenario.

7.5 Summary and Discussion of Results The present chapter complements the static analysis of the previous by accounting for the temporal dimension of the structural change. The projection of the investment conditions for the new technologies on a temporal scale notably allows to take into account also the impact of environmental policy and the abatement option on the unit costs of electricity of the polluting established technology. This section summarises the results and discusses them in the light of those of chapter 6. Again, first the no-policy benchmark and the cases of environmental policy without and with abatement option are considered, then the impact of technology policy. Finally, the results are reconsidered from the perspective of the two nuclear-cost scenarios.

7.5.1 No-policy Benchmark The no-policy benchmark displays for coal, gas, and nuclear in the Nl (Nh ) scenario, respectively, replacement times of 14.0 (by construction), 17.8, and 17.9 (22.5) periods. The 14.0 periods in the case of the new coal-fired power plant coincide with the end of the expected economic lifetime of the established coal-fired power plant. Thus, the special case occurs that, notably despite the rising prices of coal and gas over time (e.g., Figure 7.1), the technology ranking of the no-policy case in t = 0 (section 6.1) immediately translates into the ranking of the optimal moments of transition from the old to one of the new technologies. Note that, especially due to the stylised determination of the UCT1 shape and the constant-technology assumption for the new power plants, the time indications in this chapter should not be given a literal interpretation in terms of years. Their derivation being based on an internally consistent model, they give, however, an impression of the relative configuration in time of the optimal moments of transition to production with the different new generation technologies under the assumed conditions.

7.5.2 Results Under Environmental Policy Without and With Abatement Option Environmental policy reduces the replacement times in any case, as the established technology is more polluting than the new ones. More particularly, in the case of coal it is reduced by up to 3.7 periods or 26.4% within the relevant τe range (5–30

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¤/t), and by 7.8 periods or 55.7% until τe = 60 ¤/t. For gas as well as nuclear in the Nl scenario, it induces immediate replacement already within the relevant τe range, for nuclear in the Nh scenario still at almost 40 ¤/t. As regards the replacementtime ranking, coal remains the first option to replace the established plant in the Nl scenario until τe = 11.5 ¤/t directly followed by nuclear, and in the Nh scenario until τe = 17.75 ¤/t directly followed by gas, which is succeeded in turn by nuclear only for τe > 53.5 ¤/t. The replacement-time ranking reverses as compared to the no-policy benchmark for τe > 17.5 (53.5) ¤/t in the Nl (Nh ) scenario. The differences occurring for the technologies mainly depend on the varied differences in emission factors and net thermal efficiencies between the established and the new technologies. Moreover, particularly due to the particular UCT1 shape, the shapes of the replacement-time curves differ depending on whether the optimal moments of transition lie beyond or within the expected economic lifetime of the established plant. The availability of the end-of-pipe abatement option for complete emission abatement with AUC ∈ [10.0, 60.0] ¤/t fixes for any τe ≥ AUC, with UCT1 and UCT2 , also the replacement times at the level they have for those AUC. The abatement option thus extends for any τe > AUC the economic life of the established plant, and delays the structural change, amplifying ceteris paribus the overall operating time of old and new plants together. More particularly, it makes coal in the Nl (Nh ) scenario, in addition to the mentioned ranges, persist as first option irrespective of τe for very low AUC levels, with replacement-time reductions by 1.4 (2.1) periods or 10 (15)%. Similarly, in addition to the mentioned ranges, gas is fixed as first option in the Nh scenario even from low until high AUC levels for any CO2 price from a medium level within the relevant range and higher, the replacement time being reduced by 5.9–17.8 periods or 33.1–100%. Accordingly, nuclear is the first option in the Nl scenario already from low AUC and medium τe within the relevant range, with replacement-time reductions by 5.3–17.9 periods or 29.6–100%. However, in the Nh scenario it dominates only for relatively high AUC and τe considerably beyond the upper bound of its relevant range, in t = 0. As compared to the respective results for the technology ranking in chapter 6, in the Nl scenario the τe range in which coal dominates is slightly expanded, from 9.75 to 11.5 ¤/t, and gas vanishes as first option for any τe . In the Nh scenario, the upper bound of the range of coal as first option rises from 9.75 to 17.75 ¤/t, however, the upper bound of gas as first option remains at τe = 53.5 ¤/t. The end-of-pipe abatement option becomes thus in this chapter relevant for coal in the Nl scenario, for very low AUC levels. In the Nh scenario, its scope of relevance is slightly expanded at the expense of gas, the upper bound of the relevant range of which, however, remains the same. In the present setting, the abatement option is, in addition, also relevant in the case of nuclear, as also its application to the established technology is taken into account. It fixes for τe ≥ AUC with the UC T1 also always the replacement times to the new technologies at the level they have for those AUC. The differences to the previous chapter arise, apart from the specifics implied by the taking into account of the established technology, notably with respect to gas especially due to the, as rising over time, generally higher gas prices.

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7.5.3 Results in Cases with Technology Policy This subsection summarises and discusses the impact of technology policy for the case that no other policy is enacted, and for the cases of its combination with environmental policy without and with abatement option.

7.5.3.1 Technology Policy Alone Technology policy generally reduces the replacement times as compared to the nopolicy benchmark, as it only affects the financing of the new technologies, adjusting it to the lower socially optimal discount rate. Over the rs range considered (rs ∈ [0.02, 0.08]), the replacement times reduce in the case of coal by 3.0–11.3 periods or 21.4–80.7%, for gas by 0.5–2.0 periods or 2.8–11.2%, and for nuclear in the Nl (Nh ) scenario by 1.7–10.0 (1.9–7.6) periods or 9.5–55.9 (8.4–33.8)%. In no case it induces immediate replacement. Apart from the cases of coal (by construction) and of nuclear (for rs < 0.057) in the Nl scenario, the replacement times even remain beyond the established plant’s expected economic life. In any case, except coal, its effect is considerably less strong than under environmental policy. As regards the replacement-time ranking, over the whole rs range considered coal keeps its status as first option as in the no-policy benchmark. Only nuclear replaces gas as second technology, in the Nl scenario over the whole rs range, in the Nh scenario under a certain rs level. The varied effect of technology policy on the replacement times of the different technologies is an outcome of both its varied effect on the different UCT2 (as considered in subsection 6.2.2) and the particular shapes of the UCel curves, especially the UCT1 curve. The generally negative impact on the UCT2 materialises in the higher replacement-time reductions the flatter the UCT1 curve at the place in question. For the rs levels considered, the effect is, in general, the strongest for coal, before nuclear in the Nl scenario, nuclear in the Nh scenario, and gas. Exceptional is nuclear in the Nl scenario, which is for rs ∈ [0.02, 0.057] (i.e. trepl ≥ 14.0) in absolute terms less strongly affected than in the Nh scenario, and for rs < 0.057 (trepl < 14.0) at the margin in absolute terms at least as strongly affected as coal, and usually more. Comparing with the previous chapter, the relative impact of technology policy on the replacement times is stronger than that on the UCT2 alone in any case, except that of nuclear in the Nh scenario where it is similar.6 The generally stronger impact on the replacement times is due to the rising shape of the UCT1 over time. In contrast to the technology ranking for t = 0 (subsection 6.2.2) and to the no-policy benchmark, gas is, in particular due to the higher fuel prices, in the Nl scenario never the second option and remains in the Nh scenario the second option only down to

Notably, for rs ∈ [0.02, 0.08] in the case of coal the replacement times { UCT2 } are reduced, as compared to the no-policy cases, by 21.4–80.7 {5.7–19.5}%, for gas by 2.8–11.2 {2.6–8.8}%, and for nuclear in the Nl (Nh ) scenario by 9.5–55.9 {8.0–27.1} (8.4–33.8 {9.2–31.4})%.

6

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rs = 0.034. For all technologies but coal, the effect of technology policy alone on the the replacement times is, moreover, considerably less strong than under environmental policy alone. alone.

7.5.3.2 Technology Policy Complementing Environmental Policy The combination of environmental and technology policies mutually reinforces the reductions of replacement times as induced by the single policies. As compared to the no-policy benchmark, they now reduce in the Nl (Nh ) scenario for coal by 3.0–12.1 (3.0–13.6) periods or 21.4–86.4 (21.4–97.1)%, for nuclear by 8.3– 17.9 (18.9–22.5) periods or 46.4–100 (84.0–100)%, and for gas in the Nh scenario by 9.1–14.2 periods or 51.1–79.8%. As compared to environmental policy alone, the reductions thus expand in both scenarios for coal from 10 (15)% and for nuclear from 29.6–100%, but decrease for gas from 33.1–100%. As regards the replacement-time ranking, the additional enactment of technology policy reduces the upper bound of the CO2 price range for coal as first option in the Nl scenario, from 11.5 ¤/t before, to 6.0–9.75 ¤/t for rs ∈ [0.02, 0.08]. In the Nh scenario, it expands, from 17.75 ¤/t before, for rs ∈ [0.05, 0.08] to 18.5–20.0 ¤/t, however decreases in turn for rs ∈ [0.02, 0.05) down until 15.0 ¤/t. Gas remains vanished as first option in the Nl scenario. In the Nh scenario, its respective range reduces from τe ∈ (17.75, 53.5] before, to intervals of [18.5,40.5]–20.0 for rs ∈ [0.05, 0.08] and vanishes, also here, for rs ∈ [0.02, 0.05). Nuclear power now becomes the first option, instead of for τe > 11.5 (53.5) ¤/t in the Nl (Nh ) scenario, in the Nl scenario for rs ∈ [0.02, 0.08] above τe ∈ [6.0, 9.75] ¤/t, and in the Nh scenario for rs ∈ [0.05, 0.08] above τe ∈ (20.0, 40.5] ¤/t and for rs ∈ [0.02, 0.05) for τe ∈ (15.0, 20.0] ¤/t and higher. The impact of the additional enactment of technology policy reflects the combined effects at work in the case of its sole enactment. While in the Nl scenario the τe range of coal as first option is restricted in favor of nuclear, in the Nh scenario it expands at the expense of gas. The range of gas as first option, persisting as such only for more moderate technology-policy levels in the Nh scenario, is moreover restricted from above by nuclear, which succeeds it for rs ∈ [0.05, 0.0625) already within the relevant τe range. The end-of-pipe abatement option is, in contrast to the case of environmental policy alone, now irrelevant in the Nl scenario, due to the restricted τe range for coal as first option in favor of nuclear. In the Nh scenario, while the τe range for coal as first option is slightly expanded at the expense of gas from below, that for gas is further restricted to rs ∈ [0.05, 0.08] and AUC levels from low until beyond the relevant CO2 price range but considerably lower than before from above by nuclear. Nuclear energy is thus excluded from being the first option over the whole τe range considered also for AUC levels beyond the relevant CO2 price range only for relatively high rs levels in the Nh scenario. In the Nl scenario and for low rs ranges in the Nh scenario, it dominates already for low AUC and any τe at that level or higher.

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Comparing with the previous chapter, gas also persists as first option only in the Nh scenario, however, now in more restricted rs and τe ranges in favor of nuclear. While before the scope of relevance of the end-of-pipe abatement option expanded only under environmental and technology policies combined, for low AUC, in both scenarios also to coal, restricting in turn for gas to certain rs levels and AUC intervals only in the Nh scenario, it is now relevant only in the Nh scenario, for coal for low AUC and gas only for certain more restricted rs levels in similar AUC intervals. In both comparisons, the derived AUC ranges to fix a technology as first option for respective τe levels coincide only for gas in the Nh scenario with parts of its expected AUC range (32–65 ¤/t), also for technology policy. Otherwise, they stay below the relevant ranges, for coal considerably.

7.5.4 Results According to Nl and Nh Scenarios This subsection finally reconsiders the results under the perspective of the two nuclear-cost scenarios, highlighting especially the position of nuclear power and importance of its capital-investment costs in the relative economics of the different generation technologies. In the no-policy benchmark, nuclear power displays the longest replacement times before coal and gas. Environmental policy has generally the strongest impact for nuclear before gas and coal. In the Nl scenario, while reducing the replacement time of coal by only up to 3.7 periods or 26.4% within the relevant τe range, it induces in the cases of gas and nuclear immediate replacement already within this range. As regards the replacement-time ranking, nuclear is for τe > 11.5 ¤/t the first option to replace the established plant, following coal directly. The impact of technology policy is in general the strongest for coal before nuclear and gas, due to the particular shapes of the UCel curves. Over the rs range considered (rs ∈ [0.02, 0.08]), the replacement times reduce for nuclear by 1.7–10.0 periods or 9.5–55.9%, as compared to 3.0–11.3 periods or 21.4–80.7% for coal and 0.5–2.0 periods or 2.8–11.2% for gas. While coal keeps its status as first option as in the no-policy benchmark, nuclear replaces gas as second option over the whole rs range. Under environmental and technology policies combined, the effects of the single policies generally add up. The replacement times reduce as compared to the no-policy case for coal by 3.0– 12.1 periods or 21.4–86.4%, for nuclear by 8.3–17.9 periods or 46.4–100%. Over the rs range considered nuclear power becomes the first option above τe ∈ [6.0, 9.75] ¤/t, directly following coal. If the end-of-pipe abatement option is available, nuclear is the first option, under enviromental policy alone, already for τe , AUC > 11.5 ¤/t, with replacement-time reductions by 5.3–17.9 periods or 29.6–100%. Under additional technology policy, the end-of-pipe abatement option is irrelevant due to the restricted τe range for coal as first option in favor of nuclear. In the Nh scenario, the nuclear results are again less favorable. Environmental policy induces immediate replacement for nuclear at almost 40 ¤/t. Nuclear is the first option only for τe > 53.5 ¤/t, following gas. Under technology policy, over the

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rs range considered the replacement times reduce for nuclear by 1.9–7.6 periods or 8.4–33.8%, following gas as second option for rs < 0.034. Under environmental and technology policies combined, the replacement times reduce as compared to the nopolicy benchmark now for coal by 3.0–13.6 periods or 21.4–97.1%, for gas by 9.1– 14.2 periods or 51.1–79.8%, and for nuclear by 18.9–22.5 periods or 84.0–100%. Nuclear power becomes the first option for rs ∈ [0.05, 0.08] above τe ∈ (20.0, 40.5] ¤/t following gas, for rs ∈ [0.02, 0.05) for τe ∈ (15.0, 20.0] ¤/t and higher directly following coal. If the end-of-pipe abatement option is available, nuclear dominates, under environmental policy alone, only for τe , AUC > 53.5 ¤/t, in t = 0. Under additional technology policy, nuclear dominates over the rs range considered above τe , AUC ∈ (15.0, 40.5] ¤/t. Corresponding to the respective no-policy technology ranking in chapter 6, also here it displays in the no-policy case the longest replacement times before coal and gas. In the Nl (Nh ) scenario it now dominates from considerably lower (the same) τe levels. It is the second option before gas, instead of only under a certain rs level in the Nl scenario, over the whole of the considered rs range (under a certain rs level). Under combined policies, it dominates over the rs range from a restricted low (the same, but over rs restricted) τe interval. In the latter case, the end-of-pipe abatement option is now irrelevant.

7.6 Conclusion This chapter studied the utility’s choice of the optimal moment of transition from its established to the new power plants and its variation under environmental and technology policies, separately and combined, in the cases where an end-of-pipe CO2 abatement technology is unavailable and available. The main results are briefly restated in the following points. 1. Environmental policy reduces the replacement times as compared to the nopolicy benchmark in any case, for, the established technology is more polluting than the new ones. Its impact is generally the strongest for nuclear before gas and coal. Gas is in the Nl scenario never the first option to replace the established plant. The replacement-time ranking reverses for τe > 17.5 (53.5) ¤/t in the Nl (Nh ) scenario. 2. Technology policy also generally reduces the replacement times as compared to the no-policy benchmark. Its impact is in general the strongest for coal before nuclear and gas, due to the particular shapes of the UCel curves. While coal keeps its no-policy status as first option in any case, nuclear replaces gas as second option over the whole rs range (for rs < 0.034) in the Nl (Nh ) scenario. 3. Under environmental and technology policies combined, the replacement-time reductions as induced by the single policies add up. The impact is the strongest on nuclear before coal and gas. As compared to environmental policy alone, the τe range of coal as first option is restricted in the Nl scenario in favor of nuclear, and expands in the Nh scenario. Gas persists as first option only in the Nh scenario

7.6 Conclusion

139

until higher technology-policy levels (rs ∈ [0.05, 0.08]) in restricted τe intervals until medium levels of τe . Otherwise it vanishes as such, making nuclear the first option above τe ∈ [6.0, 9.75] ([15.0,40.5]) ¤/t in the Nl (Nh ) scenario. 4. The end-of-pipe abatement option fixes for τe ≥ AUC, with UCT1 and UCT2 , also the replacement times at their level for those AUC. For τe > AUC, it thus extends the economic life of the established plant and delays the structural change. Under environmental policy, it affects the results for coal in Nl and Nh scenario for very low AUC. Gas is fixed as first option in the Nh scenario for AUC ∈ (17.5, 53.5] ¤/t for any τe within this range and higher. The additional enactment of technology policy restricts its scope of relevance to the Nh scenario. Nuclear is excluded as first option for any τe , where the abatement option is relevant for coal or gas. 5. The derived AUC ranges to fix a technology as least-cost option for respective τe levels coincide only for gas in the Nh scenario with parts of its expected AUC range (32–65 ¤/t), also for technology policy. Otherwise, they stay below the relevant ranges, for coal considerably. 6. In the no-policy benchmark, nuclear power displays the longest replacement times before coal and gas. Environmental policy induces for nuclear immediate replacement within the relevant τe range (at almost 40 ¤/t) in the Nl (Nh ) scenario. It makes it the first option for τe > 11.5 (53.5) ¤/t. Technology policy reduces the replacement times for nuclear over the rs range by 1.7–10.0 (1.9– 7.6) periods or 9.5–55.9 (8.4–33.8)%, making it the second option before gas over the whole of the considered rs range (for rs < 0.034). Under environmental and technology policies combined, the replacement times reduce for nuclear as compared to the no-policy case by 8.3–17.9 (18.9–22.5) periods or 46.4–100 (84.0–100)%, making it the first option over the rs range above τe ∈ [6.0, 9.75] ([15.0,40.5]) ¤/t. With the end-of-pipe abatement option, nuclear dominates, under enviromental policy alone, for τe , AUC > 11.5 (53.5) ¤/t, the replacement times reducing by 5.3–17.9 periods or 29.6–100% (in t = 0). Under additional technology policy, the abatement option is irrelevant (nuclear the first option above τe , AUC ∈ (15.0, 40.5] ¤/t). The present results confirm, extend, and differentiate those of the previous chapter. As the prices of gas and, but considerably lesser, of coal increase over time, the results are generally more favorable for nuclear. The no-policy technology ranking and the ranking of the (positive) UCT2 impact of environmental policy immediately translate into the present ranking of replacement times in the no-policy case and of the (negative) replacement-time impact of environmental policy, respectively. However, due to the varied fuel prices, in the Nl scenario the first-option ranges of coal and nuclear expand whereas gas vanishes, in the Nh scenario coal is considerably stronger. Due to the particular UCel shapes, the (negative) technology-policy impact is now, on the replacement times, in general the strongest for coal before nuclear and gas, such that in the option ranking again the position of gas weakens. Under environmental and technology policies combined, gas also persists as first option only in the Nh scenario, now in more restricted rs and τe ranges in favor of nuclear. The endof-pipe abatement option is now, under environmental policy alone, for low AUC,

140

7 Optimal Moments of Transition Under Environmental and Technology Policies

in both scenarios also relevant for coal but for gas only in the Nh scenario, still until high AUC. Under additional technology policy, its scope of relevance restricts to the Nh scenario, for coal for low AUC and gas for even more restricted rs levels in similarly restricted AUC intervals. Also now, the derived AUC ranges to fix a technology as first option for respective τe levels coincide only for gas in the Nh scenario with parts of its expected AUC range (32–65 ¤/t), also for technology policy. Otherwise, they stay below the relevant ranges, for coal considerably.

Chapter 8

Conclusions

The aim of the present study was to analyse the welfare-theoretic implications of diverging social and private time preferences and a time-to-build feature in capital accumulation for the conditions of structural change in the energy industry, when emissions are negatively valued and an end-of-pipe abatement technology is available. The results of theoretical and applied part were summarised in chapter 4 and at the ends of chapters 6 and 7, respectively. In this chapter they are put in perspective (section 8.1). Section 8.2 considers general policy conclusions. Section 8.3 states issues for further research.

8.1 Putting the Analysis in Perspective Two of the most prolific economic authors of the past, Schumpeter and GeorgescuRoegen, described economic development as an evolutionary process – being characterized by qualitative change occurring possibly at all levels of an economy – and unfolding in historical, i.e. unique, irreversible, time (Heinzel 2006). Already Schumpeter (1950: 82) alluded that changing nature may be one cause of evolutionary economic development. Georgescu-Roegen’s (1971) two major points were that, by being subject to the laws of nature, the economy is not only inevitably subject to qualitative change, but also fundamentally exposed to the development of the natural environment. The two authors’ descriptions have become most palpable in the issue of anthropogenic climate change. Its complex relationship to qualitative change and time poses as a particular issue. This study has been analysing aspects of both of these facets. The question of how to accomplish the transition to a low-carbon energy industry in a socially optimal way involves in particular different kinds of technological changes, e.g., changes of the gradual kind, via refinement of existing technologies, and changes of the structural kind, via replacement of existing technologies. From a welfareeconomics perspective, the transition to a low-carbon energy industry underlies the C. Heinzel, Distorted Time Preferences and Structural Change in the Energy Industry, Sustainability and Innovation, DOI 10.1007/978-3-7908-2183-3 8, © Physica-Verlag Heidelberg 2009

141

142

8 Conclusions

usual environmental-economic trade-off between production of a desired good and the, gradually necessary, by-production of pollution. The time dimension complicates this trade-off in a number of ways. The transformation of the energy industry is subject to particular rigidities in relation with the particularly long economic lives, the extended construction times, and the high investment costs of power plants. (Revealed) human time preferences and, after the liberalization of energy markets, especially the private rate of time preference, determining the level of investment in an economy, have thus a particular role to play. They may be distorted, however. The analysis in this study has been focusing on distortions of revealed human time preferences and a time-lag in capital accumulation in the presence of an emission externality. Though the two features have been present in environmental economics, their implications for private investments, notably including their mutual relationship, have thus far not been investigated from a welfare-economics perspective. While the initial focus of the theory of environmental policy on the static internalisation of environmental externalities has meanwhile been complemented by a systematic research on dynamic incentives of environmental policy as well as an expanding literature on induced technological change and the environment, and discounting itself has long been an issue in debates on environmental and energy policies, the consideration of the welfare-theoretic implications of distorted time preferences for private investments contributes, in vein with the increasingly dynamic investigation, to an analysis of directly time-related second-best issues. In the light of this aspect, notably certain old issues owe new attention, such as the choice among different new generation options and end-of-pipe abatement, now in interplay with structural change. In addition, with its question concerning the welfare and policy implications of split social and private time preferences for private investments the study sheds some light on a relatively few considered aspect in the economic discounting debate. The research need detected in this respect, on both theoretical and applied level, is quite extensive (section 8.3). While the analysis in this study has been concentrating on the economic sphere, it clearly applies, and may be extended, also to the natural environment. Such an extension would matter for the present results, however, only in magnitude. For the consideration of a stock pollutant – in equivalence to the economic capital good – the split of time-preference rates would imply an underestimation of future damages from emissions today by the individual households as compared to the social planner (subsection 4.2.5). As a consequence, in the unregulated market economy the unit costs of production of the polluting established technology would be further underestimated, amplifying the disadvantageous effect for structural change of the split time preferences. A reinforcing effect on the distortion of the conditions of structural change is to be expected, if also the time-lagged dynamics of the pollutant-stock accumulation is taken into account. The environmental impact, in form of climate change, with its long causation history and most severe damages occurring only in the future, is particularly stretched in time.

8.2 Policy Conclusions

143

8.2 Policy Conclusions The welfare-economics approach of this study leads to a number of typical but also to new policy conclusions. Generally, the study argues for a non-distortionary, welfare-enhancing, multioptional, and general policy approach, which takes into account the long-run consequences of present action. The idea of remedying market distortions and of internalising external effects always implies an enhancement of overall economic efficiency and thus the level of welfare in an economy. The particular focus has been on the importance of time-preference distortions for structural technological change. Given its analytical setting, the analysis provides a new, general reason for an intervention of technology policy and for the combination of environmental and technology policies in the transition to a low-carbon energy industry under liberalised market conditions. Details are important for more concrete conclusions. While on welfare-theoretic grounds distorted time preferences always provide a case for a welfare-enhancing policy intervention, it is to be directed towards the source of the distortion. The split of private and social time-preference rates itself may only be the direct point of reference, if and only if the underlying market failure cannot directly or differently be remedied. Therefore, already for the correction of the distortions induced by the split of the rates in general a policy mix is necessary. The developed rationale applies independantly of the particular type to any kind of technology, as long as the split of time-preference rates affects its financing in a relevant way. It gives, hence, in itself no support for policies which favor or exclude single types of technology, such as, e.g., renewable energy sources on the one hand (as prescribed under the German 2000 Renewable Energy Sources Act) or nuclear energy on the other. The distortion induced by the split, and with them the implied policy levels, vary, however, across different technologies depending on different specific parameter values. The discussion of the relative economics of conventional generation technologies including, in addition, CCS abatement was based on projected data for the German energy industry in the second half of the 2010s. It shows that the relative prospects of coal and gas particularly depend on the prevailing and expected fuel prices. Nuclear energy occurs, while under environmental policy alone only in the low-cost scenario, for the additional implementation of the social imputed interest rate, for probable policy levels, also in the high-cost scenario as a both ecologically and economically relevant option in the German generation mix in the period under consideration, notably with respect to new construction. Note again that despite advancing research uncertainties persist with respect to the social valuation of certain nuclear risks, and that the waste-treatment issue is still not yet fully resolved on political level. Finally, the rentability of CCS abatement depends, apart from the actual abatement unit costs, especially on the strength of environmental policy. The results concerning the CO2 -price ranges for an end-ofpipe abatement option to be relevant confirm other studies projecting as yet only a minor role for it in the considered period. Concentrating on baseload electricity generation with conventional technologies, the analysis did not include renewable energy sources. Due to their particularly high capital-investment costs, accounting

144

8 Conclusions

for interest-rate distortions is likely to also improve their market position. However, given their current state of development, also for correct pricing their unit costs do not seem likely to reach a competitive level in the period considered. Before concrete policy measures are met, however, more research has to be done in different ways, as set out in the next section. For energy policy, the consideration of time-preference distortions and respective regulations add to the long list of regulatory, organisational and technological issues which have come up after liberalisation. Among them, the design and composition of generation capacity is the decisive one for emission abatement. Any measure in this direction would substantiate how policies are to be constituted for the win-win hypothesis of optimal environmental regulation a` la Porter to apply.

8.3 Issues for Further Research The major aim of this study was to add some clarification to a fairly complex issue, the welfare and policy implications of a split of private and social time-preference rates for structural change in the energy industry. The analysis has been pointing to further research need in different ways, both with respect to the energy sector, where the issue is of a particular importance, and with respect to private investments in general, to which it clearly extends. The main theoretical questions this study raises concern the causes of the split of social and private time preferences, their quantitative contribution to the split, and the specific policy implications with respect to each cause. In chapter 2, it was set out that none of these questions has, thus far, been subject to a systematic analysis. Notably, more causes should be assessed, and, more generally, any cause should closely be analysed with respect to its welfare-theoretic implications. A number of further complexities, excluded from the present analysis but important as soon as it comes to the implementation of respective policies, should be taken into account in future research. They include the relationship between the time horizon and the level of the discount rate, the variance in the discounting of specific commodities, and the (distorted) valuation of resource stocks and future damages. Also, certain anomalies, as stated in more recent research (subsection 2.1.1), owe further attention. For the particular case considered in this study, the quantification of the concrete level of the generally derived investment subsidy requires a detailed analysis of the relevant causes of the split, which was beyond the scope of this study. Only two implementation regimes for the investment subsidy were considered, its payment on the labor input in the production of the capital good for the new energy technology (section 3.4) and its payment as an output subsidy on the electricity from the new power plant provided at the busbar (subsection 5.4.2). With respect to its possible implementation, further alternative regimes should be studied in a more encompassing analysis, taking into account also the implied redistribution of welfare rents, and incentive and transaction-cost issues.

8.3 Issues for Further Research

145

With special regard to the energy sector, for its implementation technologyspecific financing conditions are to be taken into account. The determination of the unit costs of electricity of the different generation technologies should explicitly account for the various important risks, e.g. concerning fuel prices, technological development, materials availability, and policy changes. As regards particular technologies, apart from the continuing research need with respect to the nuclear option (subsection 5.3.3, section 8.2), the extension of the applied analysis especially to renewable energy sources is desirable. This would allow for a more complete comparison among the relevant technological options. Interesting differentiations to the present results could, finally, derive from the relaxation of the, not anymore realistic, assumption of energy as a homogeneous output, as well as, e.g., the extension of the analysis in chapter 7 to real option values as associated with the waiting to invest in new technologies and their variance under over-time changing framework conditions.

Appendix A

A.1 Concavity of Hamiltonian Along Optimal Path In the following, it is shown that the maximised Hamiltonian H 0 is jointly concave in the variables x, e, and k along the optimal path. H 0 is the Hamiltonian H as defined in equation (3.12) in which the optimal paths for a and i are substituted. Although the optimal paths for a and i cannot be derived, they can be eliminated by employing the necessary conditions for an optimal solution. The Hamiltonian (3.12) can be written as:

1 k(t) − x(t) − qe (t)e(t) H = [U(x(t)) − D(e(t))]exp[−ρ t] + qx(t) κ + qk (t + σ )i(t) − qk (t)γ k(t) + qi(t)i(t) + ql1 +

1 − λκ k(t) − i(t) 1 + a(t)

(A.1)

1 − λκ k(t) − i(t) qx (t) + qe (t) 1 − G(a(t)) . 1 + a(t)

From the necessary condition (3.13d), it is known that qx (t) + qe (t) 1 − G(a(t)) ql (t) = qk (t + σ ) + qi(t) − 1 . 1 + a(t) 1 + a(t)

(A.2)

Inserting equation (A.2) into equation (A.1) yields the maximised Hamiltonian H 0 , in which the control variables a and i are eliminated:

1 H 0 = [U(x(t)) − D(e(t))] exp[−ρ t] + qx(t) k(t) − x(t) − qe (t)e(t) κ

λ + qk (t + σ ) 1 − k(t) − qk (t)γ k(t) . (A.3) κ Obviously, H 0 is concave, as it is the sum of concave functions. 147

148

A Appendix to Part I

A.2 Optimal Transition Dynamics and Stationary States The optimal system dynamics of the optimisation problem (3.11) splits into three cases. The first case corresponds to the corner solution i(t) = 0 ∀t. In this case, there is no system dynamics at all. The system will remain at any time t in a stationary state where the labor endowment is fully used up by energy production via the established technology and by abatement. In the second case, the optimal system dynamics is an interior solution, i.e. i(t) > 0 and l1 (t) > 0 ∀t holds along the optimal path. Then, the system dynamics is governed by the following system of differential equations:

di(t) exp[−ρσ ] = Φ1 (t) (γ + ρ )D (t)G (t) + λ D (t+σ )G (t+σ ) + U (t+σ ) dt κ (A.4a) + Φ2 (t) [i(t−σ ) − γ k(t)] ,

exp[− da(t) ρσ ] = Φ3 (t) (γ + ρ )D(t)G (t) + λ D (t+σ )G (t+σ ) + U (t+σ ) dt κ + Φ4 (t) [i(t−σ ) − γ k(t)] , (A.4b) dk(t) = i(t−σ ) − γ k(t) , (A.4c) dt where Φn (t) (n = 1, . . . , 4) are functions of i(t), a(t) and k(t), as shown in appendix da(t) dk(t) A.3 below. As di(t) dt , dt and dt also depend on advanced (i.e. at a later time) and on retarded (i.e. at an earlier time) variables, equations (A.4) form a system of functional differential equations.1 In general, this system is not analytically soluble (not even in the linear approximation around the stationary state). However, it is shown in appendix A.3 that the unique stationary state, given by the following implicit equations:

U (x ) = D (e ) G (a ) (1 + a) + 1 − G(a) (A.5a)

γ + ρ = exp[−ρσ ] i = γ k ,

λ D (e )G (a) + U (x ) , κ D (e )G (a )

(A.5b) (A.5c)

is a saddle point. Hence, for all sets of initial conditions there is a unique optimal path which converges towards the stationary state. In general, these optimal paths are oscillatory and exponentially damped.2 1

For an introduction to functional differential equations see Asea and Zak (1999: section 2) and Gandolfo (1996: chapter 27). A detailed exposition of linear functional differential equations is given in Bellman and Cooke (1963) and Hale (1977). 2 The system of functional differential equations (A.4) may also exhibit so-called limit-cycles, i.e. the optimal paths oscillate around the stationary state without converging towards or diverging from it (e.g. Feichtinger et al. 1994, Asea and Zak 1999, Liski et al. 2001 and Wirl 1995, 1999, 2002).

A.3 Saddle-Point Stability of Interior Solution

149

In the third case, which corresponds to the corner solution l1 (t) = 0, the established technology will eventually be fully replaced by the new technology, and all labor is used to employ and maintain the capital stock k. Thus, if the restriction l1 (t) ≥ 0 is binding, there exists a direct link between capital stock k and investment i: κ (A.6) k(t) = (1 − i(t)) . λ Differentiating with respect to time t and inserting into the equation of motion for the capital stock (3.11d), yields the following linear first-order differential-difference equation of the retarded type, which governs the system dynamics: di(t) λ + γ i(t) + i(t−σ ) = γ . dt κ

(A.7)

The solution to this equation is analysed in detail in Winkler et al. (2005). In general, the optimal paths converge oscillatorily and exponentially damped towards the stationary state, which is given by i =

κγ , λ + κγ

k =

κ . λ + κγ

(A.8)

A.3 Saddle-Point Stability of Interior Solution In order to show the saddle point property of the stationary state in the case of an interior solution, i.e. if i(t) > 0 and l1 (t) > 0 ∀t along the optimal path, consider the following general maximisation problem: ∞

max

a(t),i(t) 0

F(i(t), a(t), k(t)) exp[−ρ t] dt

(A.9a)

subject to k˙ = i(t−σ ) − γ k(t) , t ∈ [−σ , 0) , i(t) = ξ (t) = 0,

(A.9b) (A.9c)

which is equivalent to the optimisation problem (3.11) in the case of an interior solution with 1 − λκ k(t) − i(t) 1 − λκ k(t) − i(t) k(t) . F =U − D 1 − G(a(t)) + 1 + a(t) κ 1 + a(t) (A.10) The corresponding present-value Hamiltonian reads H = F(t) exp[−ρ t] + q(t+σ )i(t) − q(t)γ k(t) , where q denotes the shadow price for the state variable k.

(A.11)

150

A Appendix to Part I

If the maximised Hamiltonian (A.11) is strictly concave, which is assumed in the following, the following conditions are necessary and sufficient for an optimal solution:3 q(t+σ ) = −Fi (t) exp[−ρ t] , Fa (t) = 0 , q(t) ˙ = −Fk (t) exp[−ρ t] + γ q(t) , lim q(t)k(t) = 0 .

(A.12a) (A.12b) (A.12c) (A.12d)

t→∞

Differentiating equations (A.12a) and (A.12b) with respect to time t, inserting da(t) (A.12a), (A.12c) and (A.9b) into the resulting equations, and solving for di(t) dt , dt and

dk(t) dt

yields the following set of functional differential equations: Faa (t) di(t) = [(γ + ρ )Fi(t) + exp[−ρσ ]Fk (t+σ )] dt Δ F(t) Fia (t)Fak (t) − Faa(t)Fik (t) [i(t−σ ) − γ k(t)] , + Δ F(t) Fia (t) da(t) = [(γ + ρ )Fi(t) + exp[−ρσ ]Fk (t+σ )] dt Δ F(t) Fia (t)Fik (t) − Fii (t)Fak (t) [i(t−σ ) − γ k(t)] , + Δ F(t) dk(t) = i(t−σ ) − γ k(t) , dt

(A.13a)

(A.13b)

(A.13c)

where Δ F(t) ≡ Fii (t)Faa (t) − Fia(t)2 . Introducing the following abbreviations:

Φ1 (t) =

Faa (t) , Δ F(t)

Φ3 (t) = −

Fia (t) , Δ F(t)

Φ2 (t) =

Fia (t)Fak (t) − Faa(t)Fik (t) , Δ F(t)

Φ4 (t) =

Fia (t)Fik (t) − Fii (t)Fak (t) , Δ F(t)

and inserting Fi (t) and Fk (t+σ ) yields the system of differential equations (A.4). da(t) dk(t) In the stationary state, di(t) dt = dt = dt = 0 holds. Thus, the unique stationary state (i , a , k ) is determined by the three implicit equations: Fi (i , a , k ) , Fk (i , a , k ) 0 = Fa (i , a , k ) ,

γ + ρ = − exp[−ρσ ]

i = γk .

(A.14) (A.15) (A.16)

Inserting Fi , Fa and Fk yields the equations (A.5). 3

In the following, for presentational convenience, partial derivatives are denoted by subscripts and only the time argument is stated explicitly.

A.3 Saddle-Point Stability of Interior Solution

151

In order to investigate the stability properties of optimisation problem (A.9) in a neighborhood around the stationary state (i , a , k ), the system of functional differential equations (A.13) is linearised around the stationary state. Therefore, first the following new variables are introduced: ˆ = i(t) − i , i(t)

a(t) ˆ = a(t) − a ,

ˆ = k(t) − k . k(t)

(A.17)

Applying the first-order Taylor approximation of the system (A.13) around the stationary state (i , a , k ) yields:

ˆ d i(t) Fia Fk ˆ σ ) − Fii Fk i(t) ˆ + Fak a(t+ ≈ Φ1 exp[−ρσ ] Fik i(t+ ˆ σ) − a(t) ˆ dt Fi Fi

Fik Fk ˆ ˆ ˆ ˆ σ ) − γ k(t) + Fkk k(t+ k(t) + Φ2 i(t− , (A.18a) σ) − Fi

Fia Fk d a(t) ˆ ˆ σ ) − Fii Fk i(t) ˆ + Fak a(t+ ˆ σ) − a(t) ˆ ≈ Φ3 exp[−ρσ ] Fik i(t+ dt Fi Fi

Fik Fk ˆ ˆ ˆ + Fkk k(t+σ ) − k(t) + Φ4 iˆ(t−σ ) − γ k(t) , (A.18b) Fi ˆ d k(t) ˆ , ˆ σ ) − γ k(t) ≈ i(t− dt

(A.18c)

where all functions are evaluated at the stationary state (i , a , k ). Similar to the case of ordinary linear first-order differential equations, the elementary solutions for iˆ, aˆ and kˆ are exponential functions, and the general solution is given by the superposition of the elementary solutions ˆ ≈ ∑ in exp[znt] , i(t) n

a(t) ˆ ≈ ∑ an exp[znt] , n

ˆ ≈ ∑ kn exp[znt] , k(t)

(A.19)

n

where the in , an and kn are constants, which can (at least in principle) be unambiguously determined by the set of initial conditions and the transversality condition. The eigenvalues zn are the roots of the characteristic polynomial Q(z). The characteristic polynomial Q(z) for the system of differential-difference equations (A.18) is given by the determinant of the Jacobian of (A.18) minus the identity matrix times z: A11 − z A12 A13 , A22 − z A23 (A.20a) Q(z) = A21 A31 A32 A33 − z

152

A Appendix to Part I

where A11 = Φ1 Fik exp[σ (z − ρ )] − exp[−σ z] + Fii(γ + ρ ) Fia Fak exp[−σ z] , + Δ F A12 = Φ1 Fak exp[σ (z − ρ )] + Fia(γ + ρ ) , Fia Fak A13 = Φ1 Fkk exp[σ (z − ρ )] + Fik (2γ + ρ ) − γ, ΔF A21 = Φ2 Fik exp[σ (z − ρ )] − exp[−σ z] + Fii(γ + ρ ) Fii Fak − exp[−σ z] , Δ F A22 = Φ2 Fak exp[σ (z − ρ )] + Fia(γ + ρ ) , Fii Fak A23 = Φ2 Fkk exp[σ (z − ρ )] + Fik (2γ + ρ ) + γ, ΔF

(A.20b)

(A.20c) (A.20d) (A.20e)

(A.20f) (A.20g)

A31 = exp[−σ z] , A32 = 0 ,

(A.20h) (A.20i)

A33 = −γ .

(A.20j)

Thus, one obtains for the characteristic polynomial Q(z): Q(z) = − (z − γ − ρ )(z + γ ) + Φ2 (z − γ − ρ ) exp[−σ z] − (z + γ ) exp[σ (z − ρ )] 2 Faa Fkk − Fak exp[−σ ρ ] . (A.21) ΔF Q(z) is a quasi-polynomial, which exhibits an infinite number of complex roots. In order to determine whether the stationary state is a saddle point, the signs of the real parts of the characteristic roots have to be known. Therefore, it is shown that the characteristic polynomial Q(z) has an infinite number of roots with negative real part and an infinite number of roots with positive real part and, thus, the stationary state is a saddle point. Note, first, that the characteristic roots of Q(z) are symmetric around ρ /2, i.e., if z0 is a characteristic root, then ρ − z0 is also a characteristic root (one can easily verify that Q(z0 ) = Q(ρ − z0 )). Second, in order to apply Theorem 13.1 of Bellman and Cooke (1963: 441), consider the new variable y = σ z and multiply Q with σ 2 exp[y] Q(y) = (y − σ γ − σ ρ )(y + σ γ ) exp[y] − σ Φ2 (y − σ γ − σ ρ ) −

+

2 Faa Fkk − Fak − (y + σ γ ) exp[2y − σ ρ ] + σ 2 exp[y − σ ρ ] . (A.22) ΔF

A.3 Saddle-Point Stability of Interior Solution

153

As Q(y) has no principal term, i.e. a term, where the highest power of y and the highest exponential term appear jointly,4 Q(y) has “an unbounded number of zeros with arbitrarily large positive real part” (ibid). However, as the characteristic roots are symmetric around ρ /2, this implies that Q(y) has also an unbounded number of roots with arbitrarily large negative real part.

4

In this case, the principal term would be a term with y2 exp[2y].

Appendix B

B.1 Summary of Technical, Financing, and Cost Parameters

Table B.1 Assumptions for technical, financing, and cost parameters in year of commissioning of established and first year of availability for operation of new reference power plants as explained in sections 5.2–5.4, prices of 2005 (various sources) Parameters Technical parameters Year of commissioning Economic life Net installed capacity Net thermal efficiency CO2 emission factor Capacity factor Electricity generated in t Annual fuel consumption Financing parameters Cost accounting term of depreciation Planning horizon Private imputed interest rate Cost parameters Specific investment costs Specific decommissioning costs Specific annual O&M costs (fix) Specific O&M costs (var.) Mean fuel price Abatement unit costs

Unit years MWe t/MWh TWh TWh

C (old)

C (new)

G

Nl / Nh

1990 40 1,500 0.45 0.338 0.85 10.5 23.3

2015 40 1,500 0.51 0.338 0.85 10.5 20.6

2015 25 1,500 0.60 0.200 0.85 10.5 17.5

2015 40 1,500 0.37 0.0 0.85 10.5 28.3

years years

20 25

20 25

20 25

20 25

-

0.1

0.1

0.1

0.1

k¤/MWe

925

1,025

500

1,800/2,600

k¤/MWe

34.5

34.5

15.8

155.0

k¤/MWe ¤/MWh ¤/MWh ¤/t

40.0 4.0 6.55 37–70

36.6 2.7 7.13 37–70

18.8 1.6 17.16 32–65

30.0 3.6 4.00 0

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