Week12 Oligopoly (6pp)

# Week12 Oligopoly (6pp) - Oligopoly Finally the last week A...

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1 Finally the last week! Oligopoly Chapter 27 2 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. 3 Oligopoly How do we analyze markets in which the supplying industry is oligopolistic? Use game theory We will typically consider the duopolistic case of two firms supplying the same product. 4 Four things Quantity/Cournot competition : Each firm noncooperatively and simultaneously choose quantities to maximize profits. Price/Bertrand competition : Firms independently and simultaneously choose prices to maximize profits. Quantity leadership : Sequential quantity choice. One firm chooses quantity first. Other firm chooses quantity next. First firm is Stackelberg leader , second firm is the Stackelberg follower . Collusion: Firms choose together to maximize the sum of profits. 5 Quantity/Cournot 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 ). 6 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? 1 1 2 1 2 1 1 1 ( ; ) ( ) ( ). y y p y y y c y

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7 Quantity Competition: an example Market inverse demand function: where y T = y 1 +y 2 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 ( ) . 8 Quantity Competition: an example ( ; ) ( ) . 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 9 Quantity Competition: an example Given y 2 , firm 1’s profit-maximizing output level solves y y y y 1 1 2 1 60 2 2 0 . 10 Quantity Competition: an example y y y y 1 1 2 1 60 2 2 0 . Thus for any given y 2 , firm 1’s best response to y 2 is y R y y 1 1 2 2 15 1 4 ( ) . 11 Quantity Competition: an example y 2 y 1 60 15 Firm 1’s “reaction curve” y R y y 1 1 2 2 15 1 4 ( ) . 12 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 2’s profit function is So, given y 1 , firm 2’s profit-maximizing output level solves y y y y 2 1 2 2 60 2 15 2 0 . I.e.,
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Week12 Oligopoly (6pp) - Oligopoly Finally the last week A...

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