V27yuan - 27 2010 W W Norton Company Inc Oligopoly Outline...

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27 Oligopoly

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2 Outline Non-collusive moves Simultaneous moves Quantity competition: Cournot model Price competition: Bertrand model Sequential moves Quantity leadership: Stackelberg model Price leadership Collusion
3 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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4 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 ).
5 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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6 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
7 Quantity Competition; An Example Π ( ; ) ( ) . y y y y y y 1 2 1 2 1 1 2 60 = - - - Then, for given y 2 , firm 1’s profit function is So, given y 2 , firm 1’s profit-maximizing output level solves Π y y y y 1 1 2 1 60 2 2 0 = - - - = . I.e., firm 1’s best response to y 2 is y R y y 1 1 2 2 15 1 4 = = - ( ) .

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8 Quantity Competition; An Example Π ( ; ) ( ) . y y y y y y y 2 1 1 2 2 2 2 2 60 15 = - - - - Similarly, given y 1 , firm 2’s profit function is 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 = - - - - = . I.e., firm 1’s best response to y 2 is y R y y 2 2 1 1 45 4 = = - ( ) .
9 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 ). ( * 1 2 * 2 y R y = and ) ( * 2 1 * 1 y R y =

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10 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 ( , ) ( , ). * * y y
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V27yuan - 27 2010 W W Norton Company Inc Oligopoly Outline...

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