Optimization in age-structured dynamic economic models

Freiberger, M., Kuhn, M., Fürnkranz-Prskawetz, A., Sanchez-Romero, M., & Wrzaczek, S. (2024). Optimization in age-structured dynamic economic models. IIASA Working Paper. Laxenburg, Austria: WP-24-004

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Abstract

Age structured optimal control models experience increasing applications in various research fields including e.g., demography, economics, operations research, epidemiology 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 effects utility, fertility and mortality. We solve the model analytically and present numerical simulations. The potential of age-structure to solve non-standard optimal control models is demonstrated by considering optimal control models with random switches or time-lags and delays.

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