Question

2) Consider a location model of differentiated products where the set of possible products is the line segment [0,11 and consumers are uniformly distributed along the line segment. Transportation costs in this model are equal to td, where d= |x- is the distance between the consumer's ideal variety and the variety she purchases. If a consumer with ideal variety x* purchases variety x at price p, then her utility is If the consumer does not purchase the good her utility is u -0. A consumer buys the good only if her utility from buying is at least zero. Suppose the market is served by a monopolist selling variety x = ½. For given s and t, find the demand the monopoly faces as a function of p (remember, consumers want to buy the good only if their utility is non-negative). Make sure that as part of your answer you specify (i) for which range of prices no consumer would want to buy the good so that demand is zero [hint: even the consumer located at x-0.5 does not buy]; (ii) for which range of prices all consumers would a) want to buy the good [hint: even the consumer located at x-0 wants to buy the good]i) For the range of prices such that some consumers buy, and some do not, state how demand depends on the price. [Hint: what is the location ofa consumer who is indifferent between buying and not buying? Consumers who are closer, will but] b) Explain in words why a monopolist selling variety x is better off the smaller is t. Assume now that the market is served by 2 firms located at 0 and 1. Each firm has a marginal cost of production c. Assume all the consumers buy, find the equilibrium. [Hint: This is want we did in class.] Explain in words why a duopolist selling variety x variety x c) d) 0 and facing a rival who sells 1 may be better off the bigger t.

Answer 1

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