Optimal Resource Allocation in a Two-Sector Economic Model with an Integral Functional

Abstract

We investigate the resource allocation problem in a two-sector economic model with a Cobb-Douglas production function with different depreciation rates. The problem is considered on a finite time horizon with an integral type functional. Optimality of the extremum solution constructed by the Pontryagin maximum principle is established. When the planning horizon is sufficiently long, the optimal control has two or three switching points, contains one singular section, and vanishes on the terminal section. A transitional “calibration” regime exists between the singular section, where the motion is along a singular ray, and the terminal section. The solution of the maximum-principle boundary-value problem is presented in explicit form, accompanied by graphs based on numerical results.