Another View of the Maximum Principle for Infinite-Horizon Optimal Control Problems in Economics

We present a recently developed complete version of the Pontryagin maximum principle for a class of infinite-horizon optimal control problems arising in economics. The peculiarity of the result is that the adjoint variable is explicitly specified by a formula which resembles the Cauchy formula for solutions of linear differential systems. In certain situations this formula implies the “standard” transversality conditions at infinity. Moreover, it can serve as their alternative. We provide examples demonstrating the advantage of the suggested version of the maximum principle. In particular, we consider its applications to Halkin’s example, to Ramsey’s optimal growth model and to a basic model of optimal extraction of a non-renewable resource. An economic interpretation of the developed characterization of the adjoint variable is also presented.