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Chapter 27

# 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.
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 ) .
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 = -
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 = = -
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
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
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
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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