Consider a market for a homogenous product with n identical stores, where n is determined by free entry. Each store has a cost function C(q) = 4 + q, for q 4 and c(q) = for q > 4 (in other words, each store can sell up to 4 units and its cost of selling the first q units is 4 + q). There are 1000 consumers in the market, each of whom wishes to buy up to 1 unit and is willing to pay for it up to r = 5. Suppose that a fraction 0 1 of all the consumers is fully informed about the prices that the different stores charge. The remaining 1000(1 ) consumers are uninformed and have to pay a cost z in order to learn the prices that different stores charge. If an uninformed consumer does not pay z, she knows only the distribution of prices but not the actual prices charged by each store. Such a consumer then picks a store at random. However, once an uninformed consumer pays z, she becomes completely informed and knows all prices charged by all stores.

a. Compute the marginal and average costs of stores and illustrate it in a figure.

b. Suppose that z = 0. Solve for the long-run competitive equilibrium in the market.

c. Now suppose that z = 1. Assume that there are two prices being charged in equilibrium. What is the low price, pl? Given your answer, compute the high price, ph (hint: assume that a fraction of all stores charge pl and a fraction 1 charge ph and use the condition that ensures that uninformed consumers do not find it worthwhile to search).

d. Compute the demand faced by low and high price stores (note that uninformed consumers pick stores at random so each store gets an equal share of the 1000(1 ) uninformed consumers; informed customers are indifferent among all stores that charge low prices, so each one of these stores gets an equal share of the 1000 informed consumers).

e. Use your answers in (c) and (d) to express the zero profit conditions for high and low price stores (recall that there is a free entry so in equilibrium, each store must earn a zero profit).

f. Solve the conditions you wrote in (e) for and n.