(8-19) Firm profit in region 2 is increasing in so assume = for that area. K1, K1 1’s Firm profit in the high pricing region is also increasing in so assume = . K1, K1 1’s Comparing the profits gives . This is defined as true for the case under study, so if firm 2 declares firm best response is to declare =. K2 D, 1’s K1 If firm 2 declares > , the analysis for the previous case comes in to play D K2 again, and firm best response is to declare =. Finally, if firm 2 declares > 0, K1 K2 1’s firm best response is to bid > (D To summarise, the best response K1 K2). 1’s – correspondence for firm 1 is: Firm best response will now be determined. If firm 1 declares D > K1 , firm 2’s best response is to declare K2 , and for > 0 its best response is to declare K1 K2 2’s (D The best response correspondence for firm 2 is: K1). – The capacity game equilibria is obtained by intersecting each best response firm’s correspondence. Appendix 3.5: Proof of Theorem 7 For , firm best response is . For > 0, firm best response is K2 K2 K1 1’s 1’s (D Firm best response correspondence is K2). – 1’s For , firm best response is K2 . For > K1 0, firm best response is K1 2’s 2’s (D Firm best response correspondence is K2 – K1). 2’s The capacity game equilibria is obtained by intersecting each best response firm’s correspondence. Bibliography Baldwin, T. (2004), to NZ Electricity The New “Government Changes Industry”, 25 September, 2003. Zealand Herald,
(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.
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