Optimal capacity, product substitution, linear demand models, and uncertainty

Abstract

We study the capacity, pricing, and production decisions of a monopolist producing two substitutable products with flexible capacity. Although the capacity decision needs to be made ex ante, under demand uncertainty, pricing and production decisions can be postponed until after uncertainty is resolved. We show how key demand parameters (the nature of uncertainty, market size, and market risk) impact the optimal capacity decision under the linear demand function. In particular, we show that if the demand shock is multiplicative, then in terms of the invest or not decision, the firm will be immune to forecast errors in parameters of the underlying demand distribution. Furthermore, incorrectly modeling the demand shock as additive, when, in fact, it is multiplicative, may lead to overinvestment. On the other hand, although the concept of a growth in market size leads to similar conclusions under both additive and multiplicative demand shocks, how market risk affects the optimal capacity decision depends critically on the form of the demand shock as well as its correlation structure. Our analysis provides insights and principles on the optimal capacity investment decision under various demand settings.