08 Jun Question Two firms compete by choosing pri
Question
Two firms compete by choosing price. Their demand functions are Q1=20-P1+P2 and Q2 = 20 + P1 – P2 where Pi and P2 are the prices charged by each firm, respectively, and QI and Q2 are the resulting demands. (Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they want, and earn infinite profits.) Marginal costs are zero. a. Suppose the two firms set their prices at the snnze time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) b. Suppose Firm 1 sets its price first, and then Firm 2 sets its price. Whatprice will eachfirrn charge, how much will it sell, and what will its profit be? c. Suppose you are one of these firms, and there are three ways you could play the game: (i) Both firms set price at the same time. (ii) You set price first, (iii) Your competitor
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