Optimal Control of a Three-Sector Economy: Maximizing Total Per Capita Consumption by Allocating Labor and Investment

Abstract

The dynamics of a three-sector economy (productions of materials, investment, consumption) is considered. The problem of optimal allocation of resources over a time interval is posed. The allocation of labor and the allocation of investment are chosen as control variables. The numerical maximization of the total per capita consumption is carried out. Per capita variables, time discretization, and equation approximations are used. An algorithm for quickly finding the optimal control is proposed. The solution for a particular case of the economy is obtained. A better result is shown with the accumulation of excess materials than with the production of only the required amount of materials.