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Homework 1 APEC 7140: Microeconomic Theory II Consider a linear city, where consumers are continuously and uniformly dis- tributed with density function 1. There are two firms (stores) that are trying to locate themselves along this linear city such that their sales would be maximized. Consumers choose a firm that is closest to them. 1. Formally represent this game in strategic form. (20 point) 2. Formally prove by negation that at (pure) strategy Nash equilibrium we have ci = 1/2;i = 1,2; where xi denotes a strategy for firm i = 1, 2. (60 point) 3. Find the Nash equilibrium if there are three firms instead. (20 points)