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Chapter 27 - Chapter Twenty-Seven Oligopoly Oligopoly A...

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Chapter Twenty-Seven Oligopoly
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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 firm’s own price or output decisions affect its competitors’ profits.
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Oligopoly How do we analyze markets in which the supplying industry is oligopolistic? Consider the duopolistic case of two firms supplying the same product.
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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 ) .
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Quantity Competition Suppose firm 1 takes firm 2’s 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 1’s profit? Π 1 1 2 1 2 1 1 1 ( ; ) ( ) ( ). y y p y y y c y = + -
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Quantity Competition; An Example Suppose that the market demand function is and that the firms’ total cost functions are c 1 = 10y 1 and c 2 = 10y 2 ( ) 70 T T p y y = -
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Quantity Competition; An Example 1 2 1 2 1 1 (y ; y ) = (70 - y - y ) y -10 y Π Then, for given y 2 , firm 1’s profit function is So, given y 2 , firm 1’s profit-maximizing output level solves 1 2 1 70 2 10. y y y Π = - - =
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Quantity Competition; An Example I.e. firm 1’s best response to y 2 is 1 1 2 2 1 ( ) 30 . 2 y R y y = = -
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Quantity Competition; An Example y 2 y 1 60 30 Firm 1’s “reaction curve” 1 1 2 2 1 ( ) 30 . 2 y R y y = = -
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Quantity Competition; An Example Similarly, given y 1 , firm 2’s profit function is (y 1 ;y 2 ) = (70 – y 1 – y 2 ) y 2 – 10y 2
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Quantity Competition; An Example So, given y 1 , firm 2’s profit-maximizing output level solves Π y y y y 2 1 2 2 60 2 15 2 0 = - - - - = . = 70 – y 1 – 2y 2 – 10 = 0
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Quantity Competition; An Example I.e. firm 2’s best response to y 1 is y 2 = R(y 1 ) = 30 – y 1 /2
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Quantity Competition; An Example y 2 y 1 Firm 2’s “reaction curve 30 60 y 2 = R(y 1 ) = 30 – y 1 /2
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Quantity Competition; An Example An equilibrium is when each firm’s output level is a best response to the other firm’s 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
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Quantity Competition; An Example * * * 2 1 1 2 ( ) 30 2 y y R y = = - * * * 1 2 2 1 ( ) 30 2 y y R y = = -
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Example * * * 1 1 1 y 1 y =30- 30- y =20 2 2       * * * 2 1 1 2 ( ) 30 2 y y R y = = - * * 1 2 y y =30 - 2 Substitute for y 2 * to get * 2 y =30-10=20. Hence
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Chapter 27 - Chapter Twenty-Seven Oligopoly Oligopoly A...

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