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EC207_finalans

EC207_finalans - The Colorado College Department of...

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1 The Colorado College Department of Economics and Business Block 7 Econ 207 Final answers. 1. (a) The profit function for each duopolist is as follows: π 1 = PQ 1 –C 1 = [100-0.5(Q 1 +Q 2 )]Q 1 – 5Q 1 = 100Q 1 – 0.5Q 2 1 -0.5Q 1 Q 2 -5Q 1 = 95Q 1 – 0.5Q 2 1 -0.5Q 1 Q 2 π 2 = PQ 2 –C 2 = [100-0.5(Q 1 +Q 2 )]Q 2 – 0.5Q 2 2 = 100Q 2 – 0.5Q 2 2 -0.5Q 1 Q 2 -0.5Q 2 2 = 100Q 2 –Q 2 2 -0.5Q 1 Q 2 Using the profit maximization condition under Cournot assumption we have: 0 5 . 0 95 0 2 1 1 1 = - - = = Q Q dQ d π 0 5 . 0 2 100 0 2 1 2 2 = - - = = Q Q dQ d π The reaction functions are: Firm 1: Q 1 = 95 -0.5Q 2 => Q 2 = 190 – 2Q 1 (1) Firm 2: Q 2 = 50 -0.25Q 1 (2) (b) Substituting eq. (2) in (1) we get Q 1 = 95 – 0.5(50 -0.25Q 1 ) Q 1 = 80 Q 2 = 50 -0.25Q 1 = 50 - 0.25(80) Q 2 = 30. (c) The market price charged by each firm is given by P = 100 -0.5Q = 100 -0.5(Q 1 +Q 2 ) = 100 - 0.5(80+30) = 100 - 55 = 45 . (d) π 1 = PQ 1 –C 1 = (45)(80) – 5(80) = 3200 π 2 = PQ 2 –C 2 = (45)(30) – 0.5(30) 2 = 900 2. (a) With firm 1 as the leader it is able to predict firm 2’s reaction function. So firm 1 substitutes 2’s reaction function in its own profit equation.

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