On a Special Optimum Control Mode at Some Perturbation of the Production Function

A. E. Trubacheva

Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 2, pp. 105-118

Résumé

In the majority of the previous works, which used the methods of optimal control, concave production functions only were considered. Production functions are exposed to various perturbations in real economics. They are caused by the objective reasons which are impossible to predict in advance. In this work we investigate the problem of a distribution of incomes of a production between the consumption and the investments, when incomes are modelled by pertubed production functions. A priori it was impossible to assume, that at the perturbation case there is a mathematical substantiation of an optimum level of the production control. We proved the turnpike theorem which determines an optimum value of the share of investments. Thus, in the case of quasi-neoclassic production functions we demonstrated the existence of the special optimum control mode.

Détail

Keywords: perturbated production function, dynamic model, admissible trajectories, special optimum control mode, turnpike theorem, quasi-neoclassic function, rule of the accumulation, investments, consumption.