Assume that demand for services per period is Pt = 1000 − Qt where Qt is the stock of the durable consumed. Let the discount factor for both consumers and the firm be one. Suppose that the monopolist has a choice: she can either produce a product that is durable at zero marginal cost or she can produce a nondurable product—it provides consumption services for only one period—at marginal cost c. Assume that there are only two periods.
(a) For what values of c would a monopolist that sells its output and cannot commit to prices choose the nondurable product?
(b) For what values of c would a monopolist that leases its output introduce the nondurable product?
(c) What is the efficient solution? How is this related to planned obsolescence?