The Inverse Optimal Problem: A Dynamic Programming Approach

Abstract

This paper solves the stochastic inverse optimal problem. Dynamic programming is used to transform the origina l problem into a differential equation. A solution exists for any pro duction function with a finite slope at the origin provided the savin gs function, starting from the origin, is steep initially and flat ev entually. Three consumption functions-linear, Keynes-ian, and Cantabr igian-are also studied with a Cobb-Douglas production technology. A w ell-known result in discrete time models-that a logarithmic utility f unction and a Cobb-Douglas production function imply a Keynesian cons umption function-does not carry through to the continuous time case. Copyright 1988 by The Econometric Society.