Figure 18: Firm 2’s best response correspondence for ex-ante low demand Figure 18 illustrates firm 2’s best response correspondence. The capacity game equilibria is obtained by intersecting each firm’s best response correspondence. Appendix 3.2: Proof of Theorem 3 The case where D > reduces the number of options firm 2 has in declaring capacity, and eliminates the regime. All best responses from section 4.1 are applicable here, only there are now less cases to analyse. If firm 2 declares D > K2 , firm 1’s best response is to declare K1 D, and if firm 2 declares > K2 0, firm 1’s best response is to declare > K1 (D – K2). The best response correspondence for firm 1 is Firm 2’s best responses are as follows, keeping in mind K2 D is no longer an option. If firm 1 declares K1 D, firm 2’s best response is to declare K2 . If firm 1 declares D > K1 , firm 2’s best response is to declare K2 . Finally, if firm 1 declares > K1 0 firm 2’s best response is to declare K2 (D – K1). Firm 2’s best response correspondence is The capacity game equilibria is obtained by intersecting each firm’s best response correspondence. Appendix 3.3: Proof of Theorem 4 When D > > 0, the result is a further reduction of firm 2’s capacity options. Firm 1’s best response is to declare > K1 (D – K2). Firm 2’s best response if > K1 (D – K2), is to declare its actual capacity, because its profits in the area, , are strictly increasing in K2. Appendix 3.4: Proof of Theorem 5 The case where D > reduces the number of options firm 1 has in declaring capacity, and eliminates the possibility of the regime occurring. For K2 D, firm 1 prefers to declare > K1 , and be in profit region 2, than declare > K1 0, and be in profit region 4 if >
(8-19) Firm 1’s profit in region 2 is increasing in K1, so assume K1 = for that area. Firm 1’s profit in the high pricing region is also increasing in K1, so assume K1 = . Comparing the profits gives . This is defined as true for the case under study, so if firm 2 declares K2 D, firm 1’s best response is to declare K1 =. If firm 2 declares D > K2 , the analysis for the previous case comes in to play again, and firm 1’s best response is to declare K1 =. Finally, if firm 2 declares > K2 0, firm 1’s best response is to bid > K1 (D – K2). To summarise, the best response correspondence for firm 1 is: Firm 2’s best response will now be determined. If firm 1 declares D > K1 , firm 2’s best response is to declare K2 , and for > K1 0 its best response is to declare K2 (D – K1). The best response correspondence for firm 2 is: The capacity game equilibria is obtained by intersecting each firm’s best response correspondence. Appendix 3.5: Proof of Theorem 7 For K2 , firm 1’s best response is . For > K2 0, firm 1’s best response is K1 (D – K2). Firm 1’s best response correspondence is For K1 , firm 2’s best response is K2 . For > K1 0, firm 2’s best response is K2 (D – K1). Firm 2’s best response correspondence is The capacity game equilibria is obtained by intersecting each firm’s best response correspondence. Bibliography Baldwin, T. (2004), “Government Changes to NZ Electricity Industry”, The New Zealand Herald, 25 September, 2003.
Mathematical Principles of the Theory of Wealth, Macmillan & Company, New York, 1897. Cullen, M. and P. Hodgson (2003), “Electricity Supply Security”. Retrieved: March 15th, 2004 from http://www.beehive.govt.nz/hodgson/electricity-commission/ discussion.cfm. Fabra, von der Fehr, and Harbord (2004), Designing Electricity Auctions”, CSEM Working Paper 122, University of California Energy Institute. Green, R. (1996), “Increasing Competition in the British Electricity Spot Market”, The Journal of Industrial Economics, Vol. 44, No. 2, June, 205-216. Green, R. (2004), “Did English Generators Play Cournot? Capacity withholding in the Electricity Pool”, CMI Working Paper 41. Green, R. and D. Newbery (1992), “Competition in the British Electricity Spot Market”, The Journal of Political Economy, Vol. 100, No. 5, October, 929-953. Hodgson, P. (2002), “Electricity Post Winter Review”. Retrieved 17th March, 2004, from http://www.winterreview.govt.nz. Kühn, K. and M. Machado (2004), “Market Power and Vertical Integration in the Spanish Electricity Market”, CEPR Working Paper No. 4590. Klemperer, P. and M. Meyer (1989), “Supply Function Equilibria in Oligopoly Under Uncertainty”, Econometrica, Vol. 57, No. 6, November, 1243-1277. Kreps, D. and A, Scheinkman (1983), “Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes”, The Bell Journal of Economics, Vol 14, No. 2, Autumn, 326-337.
Mansur, E. (2003), “Vertical Integration in Restructured Electricity Markets: Measuring Market Efficiency and Firm Conduct,” Working Paper Series ES 32, Yale School of Management. “Mighty River Power: About Electricity.” Retrieved 10th September, 2004, from http://www.mightyriverpower.co.nz/about_electricity/. New Zealand Business Roundtable (2003), “Submission on the Inquiry into the New Zealand Electricity Industry”. Retrieved: March 17th, 2004, from http://www.nzbr.org.nz/documents/submissions/submissions-2003/electricity_ submission.pdf. “Overview of Nuclear Energy”, World Nuclear Association. Retrieved 10th September, 2004, from http://www.world-nuclear.org/education/intro.htm. Pritchard, G. (2002), “The must-run dispatch auction in an electricity market”, Energy Economics, 24, 199-216. Pollitt, M (1997), “The Impact of Liberalisation on the Performance of the Electricity Supply Industry.” Journal of Energy Literature, Vol. 3, October, 3-31. Small, J. (2002), “Hedge Markets for Electric Power in New Zealand”, Ministry of Economic Development. Retrieved: April 30th, 2004, from http://www.med.govt.nz/ers/electric/hedgemarkets/hedgemarkets.pdf. Speck, S. and M. Mulder (2003), “Competition on European Energy Markets: Between policy ambitions and practical restrictions”, CPB Document No 33, Netherlands Bureau for Economic Policy Analysis. Tirole, J (1988), The Theory of Industrial Organization, Chapter 8, MIT Press, Cambridge.
Watts, D. and R. Ariztía (2002), “The Electricity Crises of California, Brazil and Chile: Lessons to the Chilean Market. Retrieved: March 15, 2004, from http://www2.ing.puc.cl/power/paperspdf/wattsariztia.pdf. White, B. and P. Hodgson (2004), “Contact Energy Pricing in the Invercargill Area – A Case Study”, Ministry of Economic Development. Retrieved: March 17th, 2004, from http://www.med.govt.nz/ers/inf_disc/pricing-reports/invercargill/ invercargill.pdf. Wolak, F. and R. Patrick (1997), “The Impact of Market Rules and Market Structure on the Price Determination Process in the England and Wales Electricity Market”, Power Working Paper PWP-047, University of California Energy Institute.