Optimal resource allocation program in a two-sector economic model with an integral type functional for various amortization factors

We study the resource allocation problem in a two-sector economic model with a two-factor Cobb-Douglas production function for various amortization factors on a finite time horizon with a functional of the integral type. The problem is reduced to a canonical form by scaling the state variables and time. We show that the extremal solution constructed with the use of the maximum principle is optimal. For a sufficiently large planning horizon, the optimal control has two or three switching points, contains one singular segment, and is zero on the terminal part. The considered problem with different production functions admits a biological interpretation in a model of balanced growth of plants on a given finite time interval.