A multi-stage optimal control approach of durable goods pricing and the launch of new product generations

Abstract

We analyze the problem of a firm that sells durable goods. In particular, we investigate how this firm optimally combines continuous-time operational-level planning (continuously deciding on capacity investment) with discrete decision making (when to launch a new generation of the product, how to price a particular generation of the product).We find that a firm should invest most into its production capacity just after the introduction of a new product. Then there is a large number of potential customers and thus a large production capacity is needed to fulfill demand. The extent to which existing capacity can still be used in the production process for the next generation has a non-monotonic effect on the optimal timing of launching a new generation as well as on its price. We show that the optimal price declines with each new product generation.