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Intro_Cournot - Industrial Organization EC460 Spring 2009...

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Industrial Organization: EC460 Spring 2009 Instructor: Thomas D. Jeitschko Some Class Notes on Cournot Duopoly We considered the following scenario: Two firms (a duopoly) supply a market repre- sented by demand of P = 20 - Q , where Q = Q 1 + Q 2 . That is, the market price will be determined as the price that clears the market, given the output of the two firms. Both firms have costs of C i = ( Q i ) 2 , where i can be 1 or 2. The problem with solving this market is that the price is determined by both firms’ output—so each firm does not know what the price will be without knowing what the other firm is producing. We first consider a thought experiment in which each firm’s output might be a choice of three, four, or five units. Given this setting, we construct an outcome matrix: Q 2 = 3 Q 2 = 4 Q 2 = 5 P = 14 P = 13 P = 12 Rev 1 = Rev 2 = 42 Rev 1 = 39; Rev 2 = 52 Rev 1 = 36; Rev 2 = 60 Q 1 = 3 C 1 = C 2 = 9 C 1 = 9; C 2 = 16 C 1 = 9; C 2 = 25 π 1 = π 2 = 33 π 1 = 30; π 2 = 36 π 1 = 27; π 2 = 35 P = 13 P = 12 P = 11 Rev 1 = 52; Rev 2 = 39 Rev 1 = Rev 2 = 48 Rev 1 = 44; Rev 2 = 55 Q 1 = 4 C 1 = 16; C 2 = 9 C 1 = C 2 = 16 C 1
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