The Pontryagin maximum principle and optimal economic growth problems

This monograph is devoted to the theory of the Pontryagin maximum principle as applied to a special class of optimal control problems that arise in economics when studying economic growth processes. The main distinctive feature of such problems is that the control process is considered on an infinite time interval. In this monograph, we develop a new approximation approach to deriving necessary optimality conditions in the form of the Pontryagin maximum principle for problems with infinite time horizon. The attention is focused on the characterization of the behavior of the adjoint variable and the Hamiltonian of a problem at infinity. The approach proposed is applied to the analysis of the problem of optimal economic growth of a technological follower, a country that absorbs, in its technological sector, part of knowledge produced by a technological leader. By optimizing its growth performance, the technological follower dynamically redistributes available labor resources between the manufacturing and research and development (R&D) sectors of the economy. This problem is of independent interest in the endogenous economic growth theory. Moreover, it serves as an illustration of the approximation approach proposed. The main results presented in this monograph are new. They generalize and strengthen many previous studies in this direction