Intertemporal Optimization Model of Entrepreneurs Behavior

Abstract

The intertemporal problem of consumer’s behavior is the basis of modern models. The interest in this kind of problems is determined by the attempt to widen the range of directions within which it is possible to conduct additional mathematical research in the theory of consumption. The article considers the problem of maximizing discounted utility derived from an entrepreneur’s consumption due to optimal allocation of monetary means which he gets as profit from his production company and interest on assets. The difference of this problem from the basic dynamic problem of consumer’s behavior lies in the fact that an entrepreneur as an individual acts in two roles: as a consumer and as a manufacturer. Furthermore, the problem is characterized by two peculiarities: a distinctive budget limitation which includes production function and reveals an irregular differential relation and also by the presence of mixed boundary conditions on the value of capital and assets. Formalization of the problem as a dynamic optimization model is given. It was studied with the use of mathematical analysis and the means of the optimal control theory. According to parameter correlations of the model, two strategies were identified which can be recommended for an entrepreneur as the most optimal ones. The model that was developed in the course of research can serve as a tool for taking decisions because it suggests optimal strategies of allocation of financial means in an enterprise which leads to maximization of consumption utility.