A monopolistic firm is considered that can choose between two production activities: a capital-intensive one and a labour-intensive one. The successive stages of evolution of the firm are discussed for several alternative formulations of the objective functional. The effect of a minimum employment constraint is investigated and other senstitivity results are provided.
KEY WORDS Activity analysis Employment Green's theorem Phase plane analysis Monopolistic firm
1 . INTRODUCTION
In the area of the dynamics of the firm, several models have been constructed that show the stages of the evolution of the firm mainly from a financial point of view (see e.g. References
1-8).
Lesourne4 has provided a general solution method by patching possible 'regimes' toget her to form the optimal path. In a more general context this method was formulated by van Loon'. Van Loon lo used this approach, which usually involves lengthy and cumbersome calculations, to solve a model in which a monopolistic firm can choose between two production activities: a capital-intensive one and a labour-intensive one. This model is the starting point of our model. We extend the problem in several directions and show that the problem can be solved more easily by use of a two-step approach. It is noted also that many of the above models can be solved with this approach. 11,12
The paper is organized as follows. In Section 2 we formulate the dynamic model and show that the problem can be decomposed into two steps. In Section 3 we solve the step I problem, which is the static problem of maximizing the net income for a fixed stock of equity. In Sections 4 and 5 the step I1 problem is solved in which optimal investment and dividend decisions are determined. Finally in Section 6 we conclude the paper with some remarks and extensions. Some details of the analysis can be found in Appendices I and 11.
2. THE MODEL
Let us consider a self-financing firm operating on a monopolistic output market. First, it is