Capacity Expansion and Specialization

We consider a firm which is constrained to meet a growing demand for each of its two services. There are two types of equipment available to the firm: an expensive general-purpose equipment and a cheaper specialized equipment which could provide only one of the services. We assume that the ratio of the demands is independent of time and that identical scale-economies are offered in the cost of the equipments. We establish a lower bound for the present worth of the optimal policy in the case of linearly or exponentially growing demands, and determine the conditions under which the use of the specialized equipment is justified. We show that in the case of linearly growing demands the specialized equipment should eventually be used, while if the demands are growing exponentially this may not be the case.