Optimization in Age-Structured Dynamic Economic Models

Abstract

Age-structured optimal control models experience increasing applications in various research fields including, e.g., demography, economics, operations research, epidemiology, and environmental economics. In this paper we present the mathematical theory and potential applications of age-structured optimal control models. We first state the general form of the problem and present the necessary optimality conditions. To illustrate the mathematical theory we introduce a toy model on air pollution, where consumption induces pollution which in turn negatively affects utility, fertility, and mortality. We solve the model analytically and present numerical simulations. The potential of an age-structure approach to solve non-standard optimal control models is demonstrated by considering optimal control models with random switches or time-lags and delays.