SOME PROPERTIES OF THE VARIATIONAL PROBLEMS OF OPTIMAL CONTROL OF CONSUMPTION

Abstract

ARTICLE RETRACTEDIn this paper we study the General patterns of models based on variational methods in various problems of optimal control of consumption: decisionmaking in the management of the household, as well as models of the economic dynamics of the Harrod–Domar and Solow. The role of optimal control in these tasks is played by the consumption function: in the first task is a function of consumption of the household, the model of Harrod–Domar is the aggregate consumption, as in the Solow model is per capita consumption. The role of the equation of when the first task is the equation of the dynamic balance between income, expenses, and accumulated savings, the model of Harrod–Domar – equation dynamic balance between income and investment, with the assumption of proportionality of investment and derivative income, as in the Solow model the role of the equation of the relationship is played by the equation of dynamic balance between the capitallabor ratio, economic productivity and per capita consumption. In all considered processes, the optimal control problem is formulated as a maximization problem of the functional expressing the integrated discounted utility of consumption under the equity equation.

Keywords

• variational problem
• coupling equation
• optimal control
• consumption
• models of economic dynamics
• utility function
• integrated discounted utility of consumption