Rational Expectations and Durable Goods Pricing

The market for a durable good sold by a monopolist is examined by using both continuous-time and discrete-time versions of the same model. The requirement that buyers' expectations must be fulfilled along the realized path of production is shown to place no restrictions on that path. Even the stronger requirement that buyers' expectations must continue to be fulfilled in the presence of any unexpected, exogenous perturbation to the stock places no restrictions, if expectations are allowed to depend discontinuously on the current stock. However, if expectations must depend continuously on the current stock, there is a unique equilibrium. This equilibrium is stationary, and the seller's strategy is the one described by Coase (1972): to keep the market saturated at all dates. Hence the path for output is the one for a competitive market and profit is zero. Stationary equilibria are then examined using the discrete-time model and it is shown that the path for output is very sensitive to the length of the period. As the period shrinks, the equilibrium approaches the one described above. But as the period grows, the path for output approaches the one chosen by a monopolist renter and profit approaches a maximum.