Optimal resource allocation in a two-sector economic model with singular regimes

Abstract

The article considers the problem of resource allocation in a two-sector economic model with a nonlinear production function of a special type. The main mathematical apparatus is Pontryagin’s maximum principle, i.e., the theorem on necessary conditions of optimality. It is shown that in the given problem the maximum principle provides a necessary and sufficient condition of optimality. A possible singular solution of the problem is found. An extremum solution is constructed in explicit form under various assumptions about the initial values. A “sufficiently long” planning horizon is assumed. An alternative approach is described, which does not use the maximum principle and instead investigates the integral representation of the optimand functional. The detailed theoretical investigation of the problem is accompanied by numerous illustrations.