Monopoly production and pricing of finitely durable goods with strategic consumers׳ fluctuating willingness to pay

Demand volatility and production lead time oblige manufacturers of made-to-stock goods to use economic forecasts in deciding on production quantities. Manufacturers of finitely durable goods face an additional complication—in making production decisions, they must consider not only the uncertainty in demand for new goods, but also how the future sales will be affected by the older goods that will become available via a secondhand market. Using a model of an infinite-horizon sequential game between a monopolistic producer of durable goods and strategic consumers, we investigate how demand volatility affects producers’ production and pricing decisions. We formulate the problem of a monopolist durable goods producer as a discrete-time Markov Decision Process and prove certain structural properties of the sales and production policy. These structural properties facilitate an efficient computational algorithm, which we use in running numerical experiments to explicate the producer׳s strategy and to conduct equilibrium comparative statics analysis. We show that a simple myopic policy is optimal when each period׳s demand is independent and identically distributed (i.i.d.). When demand is correlated across periods, the producer׳s optimal production and sales policy is not myopic, and in some states, when the economy is poor, the producer withholds some of the new goods inventory. Our numerical results suggest that in equilibrium, the producer who is dealing with myopic rather than with forward-looking consumers is more likely to sell some of these held-back goods later, as vintage goods.