Tasks of optimal control of per capita consumption with the equation of connection for the capital labor ratio

The optimization problem of maximizing the integral discounted utility of consumption with the equation of relation for the capital labor ratio which follows from the Solow economic growth model is considered. As you know, Solow builds his model on the basis of the Cobb-Douglas production function. However, other production functions are widely used in mathematical models. Statistical studies show that in practice both the Cobb-Douglas production function and other well-known production functions describe the dependence of national economic productivity on the capital labor ratio only approximately. Therefore, of particular interest is the formulation of optimization problems in which the equation following from the Solow model acts as a communication equation for the arbitrary nature of the dependence of the national economic productivity on capital labor ratio. It is in this form that the coupling equation, the following from the Solow model, is a convenient tool for economic research. The development and study of such productions are the goal of this paper.