Incorporating Consumer Price Expectations in Diffusion Models

In this paper the sensitivity of the optimal price path of a new durable product to the price expectations of consumers is examined. Consumers enter the market every period in a diffusion type framework. During the initial periods more consumers enter the market due to word of mouth influence, but in the latter periods saturation effects set in. The entering set of cohorts form expectations about future prices; and in a stable equilibrium, these expectations are fulfilled. It is shown that the price path is cyclical with the following properties: at the beginning of the cycle, the price is at its highest level; it falls monotonically over time reaching a low price at the end of the cycle equal to the reservation price of the consumers willing to pay less; the cycle lengths are not equal. The sensitivity of the optimal price path to model parameters is explored through a numerical procedure.