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Unformatted text preview: Chapter 27 NAME Oligopoly Introduction. In this chapter you will solve problems for firm and indus try outcomes when the firms engage in Cournot competition, Stackelberg competition, and other sorts of oligopoly behavior. In Cournot competi tion, each firm chooses its own output to maximize its profits given the output that it expects the other firm to produce. The industry price de pends on the industry output, say, q A + q B , where A and B are the firms. To maximize profits, firm A sets its marginal revenue (which depends on the output of firm A and the expected output of firm B since the expected industry price depends on the sum of these outputs) equal to its marginal cost. Solving this equation for firm As output as a function of firm Bs expected output gives you one reaction function; analogous steps give you firm Bs reaction function. Solve these two equations simultaneously to get the Cournot equilibrium outputs of the two firms. Example: In Heifers Breath, Wisconsin, there are two bakers, Anderson and Carlson. Andersons bread tastes just like Carlsonsnobody can tell the difference. Anderson has constant marginal costs of $1 per loaf of bread. Carlson has constant marginal costs of $2 per loaf. Fixed costs are zero for both of them. The inverse demand function for bread in Heifers Breath is p ( q ) = 6 . 01 q , where q is the total number of loaves sold per day. Let us find Andersons Cournot reaction function. If Carlson bakes q C loaves, then if Anderson bakes q A loaves, total output will be q A + q C and price will be 6 . 01( q A + q C ). For Anderson, the total cost of producing q A units of bread is just q A , so his profits are pq A q A = (6 . 01 q A . 01 q C ) q A q A = 6 q A . 01 q 2 A . 01 q C q A q A . Therefore if Carlson is going to bake q C units, then Anderson will choose q A to maximize 6 q A . 01 q 2 A . 01 q C q A q A . This expression is maximized when 6 . 02 q A . 01 q C = 1. (You can find this out either by setting As marginal revenue equal to his marginal cost or directly by setting the derivative of profits with respect to q A equal to zero.) Andersons reaction function, R A ( q C ) tells us Andersons best output if he knows that Carlson is going to bake q C . We solve from the previous equation to find R A ( q C ) = (5 . 01 q C ) /. 02 = 250 . 5 q C . We can find Carlsons reaction function in the same way. If Carlson knows that Anderson is going to produce q A units, then Carlsons profits will be p ( q A + q C ) 2 q C = (6 . 01 q A . 01 q C ) q C 2 q C = 6 q C . 01 q A q C . 01 q 2 C 2 q C . Carlsons profits will be maximized if he chooses q C to satisfy the equation 6 . 01 q A . 02 q C = 2. Therefore Carlsons reaction function is R C ( q A ) = (4 . 01 q A ) /. 02 = 200 . 5 q A . 322 OLIGOPOLY (Ch. 27) Let us denote the Cournot equilibrium quantities by q A...
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This note was uploaded on 02/13/2010 for the course ECON 100B taught by Professor Kilenthong during the Spring '08 term at UCSB.
 Spring '08
 KILENTHONG
 Oligopoly

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