Chap27 Sol - Chapter 27 NAME Oligopoly Introduction. In...

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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 . 334 OLIGOPOLY (Ch. 27) Let us denote the Cournot equilibrium quantities by q A and q C . The Cournot equilibrium conditions are that q A = R A ( q C ) and...
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This note was uploaded on 02/29/2012 for the course ECON 2101 taught by Professor Unknown during the One '11 term at University of New South Wales.

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Chap27 Sol - Chapter 27 NAME Oligopoly Introduction. In...

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