The infinite horizon dynamic optimization problem revisited: A simple method to determine equilibrium states

This work addresses intertemporal decision problems in which the policy adopted at any given time affects the state of the system during later periods. The standard treatment of such problems employs dynamic optimization methods. When the planning period extends over an infinite time horizon, the identification of the optimal equilibrium states is of prime importance. In this work we introduce a method to reduce the identification task to the algebraic problem of solving for the roots of a simple function of the state variable, denoted the evolution function. An explicit expression for the evolution function is derived for a general setup that covers a large variety of economic and management models. When the evolution function possesses a unique feasible root, the steady state is readily identified and a characterization of the dynamic behavior is possible. The application of the proposed method is illustrated by considering several resource exploitation problems.