Consider a competitive market for equipment that lasts two periods. Consumers can purchase new equipment at price E in either period. In the second period, all old equipment requires servicing in order to work. At this time, consumers who own equipment can either service it at the price p or purchase new equipment. The utility from new equipment is u, while the utility derived from old (serviced) equipment is v u. The discount factor is given by δ. Hence, consumers with equipment service their equipment if and only if v - c ≥ u - K.

The marginal cost of producing a unit of equipment is K while the marginal cost of providing service is c K . Assume that v - c > u - K > 0 so that at competitive prices, E = K and p = c, all consumers strictly prefer to buy new equipment in period 1 and then service it in period 2.

Now, although the market for equipment is competitive, the market for service is proprietary because the equipment manufacturer ties the availability of parts to the purchase of service from the manufacturer. Hence, the equipment manufacturer is able to exercise monopoly power in its aftermarket for service.

(a) Given equipment price, E , what is the price of service in terms of E ?

(b) Competition in the equipment market, however, drives the equipment manufacturer's long-run profit to zero. What is the price of equipment?