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A multi-stage optimal control approach of durable goods pricing and the launch of new product generations. (English) Zbl 1429.91165

Summary: 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.

MSC:

91B24 Microeconomic theory (price theory and economic markets)
91B38 Production theory, theory of the firm
49N90 Applications of optimal control and differential games
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