Lec6-Problems-SOLUTIONS

# Lec6-Problems-SOLUTIONS - Lecture 6 Additional Problems...

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Lecture 6: – Additional Problems & Examples - SOLUTIONS 1) Predatory pricing 2) Limit pricing 4) Raising rivals’ costs Problem #1 (Cartel duopoly) Suppose there two firms making an identical product with a market demand of P = 250 – 2Q. Each firm has a constant average and marginal cost of production of \$5 a unit. A) Suppose these firms decide to form a Cartel. For each firm determine the resulting profit maximizing level of output, price and level of profits. Q Q Q AC P Q AC Q P Max Q - - = - = - = ) 5 2 250 ( ) ( π 0 5 ) 4 250 ( = - - = - = Q MC MR Q , 25 . 61 4 245 * = = Q * 2 * 1 625 . 30 2 * q Q q = = = 50 . 127 \$ 50 . 122 250 * 2 250 * = - = - = Q P * 2 * 1 56 . 751 , 3 \$ 625 . 30 ) 5 50 . 127 ( * ) * ( = = - = - = Q AC P B) Suppose both firms decide to compete as Cournot duopolists. For each firm determine the resulting profit maximizing level of output, price and profits. 1 1 2 1 1 1 1 ) 5 2 2 250 ( ) ( 1 q q q q AC P q AC q P Max q - - - = - = - = 0 5 ) 4 2 250 ( 1 2 1 1 1 1 = - - - = - = q q MC MR q , 2 2 1 1 2 1 25 . 61 2 1 4 245 : q q q BR - = - = 2 2 1 2 2 2 2 ) 5 2 2 250 ( ) ( 2 q q q q AC P q AC q P Max q - - - = - = - = 0 5 ) 4 2 250 ( 2 1 2 2 2 2 = - - - = - = q q MC MR q , 1 1 2 2 2 1 25 . 61 2 1 4 245 : q q q BR - = - = * 2 1 * 1 2 1 833 . 40 3 4 2 25 . 61 2 1 25 . 61 2 1 25 . 61 : . . q q q BR BR E N = = = - - = = 1 | P a g e

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67 . 81 * * 2 * 1 = + = q q Q , 67 . 86 \$ * 2 250 * = - = Q P * 2 * 1 * 1 72 . 334 , 3 \$ 833 . 40 ) 5 67 . 86 ( ) * ( π = = - = - = q AC P C) Suppose the two firms agree to act as a Cartel. Use math and logic to show that Firm 1 has an incentive to cheat on this agreement. That is, show that it is Firm 1’s best interest to agree to behave as a Cartel and then to turn around and cheat on the Cartel agreement. Suppose Firm 2 cooperates (i.e. produces their share of the Cartel’s optimal level of output) and Firm 1 cheats on the agreement (i.e. they agree to cooperate then they pick their level of output to maximize their own level of profit). Firm 2 produces 30.625 units of output. Firm 1 produces their profit maximizing level of output, 9375 . 45 2 625 . 30 50 . 122 2 625 . 30 25 . 61 2 1 25 . 61 2 1 = - = - = - = q q 5625 . 76 2 1 = + = q q Q , 88 . 96 \$ 2 250 = - = Q P 51 . 220 , 4 \$ 9375 . 45 ) 5 88 . 96 ( ) * ( * 1 * 1 = - = - = q AC P 67 . 813 , 2 \$ 625 . 30 ) 5 88 . 96 ( ) * ( * 2 * 2 = - = - = q AC P D) Fill in a 2x2 table with the payoffs for the choices the two firms’ face - where they could either cooperate (act as a Cartel) or cheat (cheat on the agreement). What is the Nash equilibrium solution of this game? Explain why this outcome makes sense. Firm 1
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Lec6-Problems-SOLUTIONS - Lecture 6 Additional Problems...

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