Optimization Analysis of a Nonlinear Integral Model with Applications to Economics

Abstract

The nonlinear optimal control problem investigated in this paper is governed by Volterra integral equations with an unknown function in the limit of integration. Problems of such type arise in vintage capital models of mathematical economics and reveal new non-linear phenomena in economic-technological development. The main result of the paper is the explicit solution of the problem in important special cases. To construct these solutions, necessary and sufficient conditions for an extremum are derived. The exact solutions show the behavior of a capital replacement process under technological change.