Varian_Chapter27_Oligopoly

Varian_Chapter27_Oligopoly - Chapter Twenty-Seven Oligopoly...

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Unformatted text preview: Chapter Twenty-Seven Oligopoly Oligopoly A monopoly is an industry consisting a single firm. A duopoly is an industry consisting of two firms. An oligopoly is an industry consisting of a few firms. Particularly, each firms own price or output decisions affect its competitors profits. Oligopoly How do we analyze markets in which the supplying industry is oligopolistic? Consider the duopolistic case of two firms supplying the same product. Quantity Competition Assume that firms compete by choosing output levels. If firm 1 produces y 1 units and firm 2 produces y 2 units then total quantity supplied is y 1 + y 2 . The market price will be p(y 1 + y 2 ). The firms total cost functions are c 1 (y 1 ) and c 2 (y 2 ). Quantity Competition Suppose firm 1 takes firm 2s output level choice y 2 as given. Then firm 1 sees its profit function as Given y 2 , what output level y 1 maximizes firm 1s profit? 1 1 2 1 2 1 1 1 ( ; ) ( ) ( ). y y p y y y c y = +- Quantity Competition; An Example Suppose that the market inverse demand function is and that the firms total cost functions are p y y T T ( ) =- 60 c y y 1 1 1 2 ( ) = c y y y 2 2 2 2 2 15 ( ) . = + and Quantity Competition; An Example ( ; ) ( ) . y y y y y y 1 2 1 2 1 1 2 60 = - - - Then, for given y 2 , firm 1s profit function is So, given y 2 , firm 1s profit-maximizing output level solves y y y y 1 1 2 1 60 2 2 = - - - = . I.e., firm 1s best response to y 2 is y R y y 1 1 2 2 15 1 4 = = - ( ) . Quantity Competition; An Example y 2 y 1 60 15 Firm 1s reaction curve y R y y 1 1 2 2 15 1 4 = = - ( ) . Quantity Competition; An Example ( ; ) ( ) . y y y y y y y 2 1 1 2 2 2 2 2 60 15 = - - - - Similarly, given y 1 , firm 2s profit function is So, given y 1 , firm 2s profit-maximizing output level solves y y y y 2 1 2 2 60 2 15 2 0 = - - - - = . I.e., firm 1s best response to y 2 is y R y y 2 2 1 1 45 4 = =- ( ) . Quantity Competition; An Example y 2 y 1 Firm 2s reaction curve y R y y 2 2 1 1 45 4 = =- ( ) . 45/4 45 Quantity Competition; An Example An equilibrium is when each firms output level is a best response to the other firms output level, for then neither wants to deviate from its output level. A pair of output levels (y 1 *,y 2 *) is a Cournot-Nash equilibrium if y R y 2 2 1 * * ( ). = y R y 1 1 2 * * ( ) = and Quantity Competition; An Example y R y y 1 1 2 2 15 1 4 * * * ( ) = = - y R y y 2 2 1 1 45 4 * * * ( ) . = =- and Substitute for y 2 * to get y y y 1 1 1 15 1 4 45 4 13 * * * = -- = Hence y 2 45 13 4 8 * . =- = So the Cournot-Nash equilibrium is ( , ) ( , )....
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Varian_Chapter27_Oligopoly - Chapter Twenty-Seven Oligopoly...

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