Econ 419 – Industrial Organization Jura Liaukonyte Homework 4 - ANSWERS Submit ONE version per study group. Write legibly. I reserve a right not to grade messy or illegible answers. Include a title page, listing the homework number and the names of all members of the study group. PART I – Analytical Problems CHAPTER 14 Problem 1 (a) 100)80(22604021=−=⇒==PQQ3200)40)(20100(21=−==CournotCournotππ(b)140)60(226060)2(220260=−=⇒=−=MonopolyMonopolyPQTherefore, profit of each firm in a cartel is 3600)30)(20140(21=−==CartelCartelππ(c) Without loss of generality, suppose Firm 2 cheats, but Firm 1 maintains its cartel quantity of 30. Then, the optimal choice for Firm 2 can be found from its best response function. ()45)30(220260412=−−=CheatingQTherefore, the market price is 260 – 2 (30+45) = 110. As a result, the profit of the cheating firm is: 4050)45)(20110(2=−=CheatingπIf Firm 2 cheats, then it earns 4050 for one period, but earns its Cournot profit; 3200, for all periods afterwards. On the other hand, if Firm 2 does not cheat, it can continue earning its cartel profit for ever. Hence, the collusive outcome can be sustained if δδδδδδδ−+≥−⇒++≥+++13200405013600)3200()3200(4050...)3600()3600(36002253.0≥⇒δ, where δis the probability adjusted discount factor. Problem 4 (a) Recall that for Cournot model with nidentical firms, with marginal cost c, demand intercept aand slope -b
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