ps3_ProblemSet - AEM 4240 Problem Set #3 1. Rad and Bug...

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AEM 4240 Problem Set #3 1. Rad and Bug (Bertrand competition with differentiated products) Firms RAD and BUG are the only two firms in a market. They make slightly different products, but each produces with a constant marginal cost of MC=10. The demand that RAD faces is: q R = 1000-10 P R -(10000/P B ), (or P R = 100-{q R / 10}-{1000/ P B }), which implies that MR R =100- (q R / 5)-(1000/ P B ). Likewise, the demand the BUG faces is q B =1000-10 P B - (10000/ P R ). a) What is RAD's best response price as a function of the price that BUG charges? b) Show that at the Nash equilibrium, both firms charge PR = PB = 43.51. c) If BUG found a way to produce its product (exactly the same product) with a MC=0, would it change the demand that either firm faced? Would it change either firm's reaction function? Would it change the Nash equilibrium? 2. BLUE and AXE (Bertrand competition with fixed capacities) In a market with annual demand Q = 100 - P, there are two firms, BLUE and AXE, that make identical products. The firms compete on prices. Because their products are identical, if one charges a lower price than the other, all consumers will want to buy from the lower-priced firm. If both firms charge the same price, consumers will be indifferent and end up splitting their purchases about evenly between the firms. In order to produce output, a firm must have capacity. One unit of capacity can produce one unit of output per year. Once it has built a unit of capacity, each firm can produce a unit of output from that capacity at a marginal cost of 20. The cost of building one unit of capacity is 200.
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ps3_ProblemSet - AEM 4240 Problem Set #3 1. Rad and Bug...

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