| Abstract: | The purpose of this paper is to present the theory of the multi-product firm in situations where the revenue function depends not only on the rate of output but also on changes in the rate of output, and, similarly, where the cost function depends on changes in the rate of factor utilization as well as the rate of their utilization. Since the analysis will utilize the calculus of variations, a general introduction to this technique is also presented. The model analyzed assumes perfect foresight and knowledge concerning the revenue, cost, and production functions, and the calculus of variations is used to derive the conditions for an extremum. The first section presents the mathematical model and the model of the firm, and the optimality conditions are discussed in the second section. |
