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 has active jobs (construction, nursing) and has 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 price 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.