HW4a - Econ 419 Industrial Organization Jura Liaukonyte...

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Unformatted text preview: 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 ( 2 260 40 2 1 = = = = P Q Q 3200 ) 40 )( 20 100 ( 2 1 = = = Cournot Cournot (b) 140 ) 60 ( 2 260 60 ) 2 ( 2 20 260 = = = = Monopoly Monopoly P Q Therefore, profit of each firm in a cartel is 3600 ) 30 )( 20 140 ( 2 1 = = = Cartel Cartel (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 ( 2 20 260 4 1 2 = = Cheating Q Therefore, the market price is 260 2 (30+45) = 110. As a result, the profit of the cheating firm is: 4050 ) 45 )( 20 110 ( 2 = = Cheating If 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 + + + + + + 1 3200 4050 1 3600 ) 3200 ( ) 3200 ( 4050 ... ) 3600 ( ) 3600 ( 3600 2 2 53 . , where is the probability adjusted discount factor. Problem 4 (a) Recall that for Cournot model with n identical firms, with marginal cost c , demand intercept a and slope -b ( ) ( ) ( ) ( ) b n c a b n c a Q Q Q n n 2 2 2 1 2 1 1 ... , 1 ... + = = = = + = = = = Therefore, 68 , 1152 ... , 24 ... 2 1 4 2 1 = = = = = = = = = P Q Q Q n (b) 140 ) 60 ( 2 260 60 ) 2 ( 2 20 260 = = = = Monopoly Monopoly P Q Therefore, 15 ... 4 2 1 = = = = Q Q Q and the profit of each firm in a cartel is 1800 ) 15 )( 20 140 ( ......
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This note was uploaded on 04/30/2008 for the course ECON 419 taught by Professor Jura during the Spring '07 term at UVA.

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HW4a - Econ 419 Industrial Organization Jura Liaukonyte...

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