L. L. Bean, among other stores, has a policy of replacing shoes that wear out with new ones. Suppose there are two types of shoe buyers. Half of them have desk jobs and only have a 20 percent chance of wearing out their shoes. The other half have active jobs (construction, nursing) and have a 60 percent chance of wearing out their shoes. A pair of shoes costs $25 to produce

a. If the store cannot distinguish between the two types, what is the lowest price it can charge for shoes and still break even on average? (This is the price that would prevail in a competitive market.)

b. What would happen to the equilibrium if the desk workers' valuation for shoes was less than the market price in part a? What is a possible source of inefficiency in this new equilibrium?

c. Compute the competitive equilibrium if shoe manufacturers can charge an extra price for shoes with a replacement guarantee, assuming that only the active workers purchase the guarantee.