On the existence of markov-consistent plans under production uncertainty

Strotz (1956) and Pollak (1968) were among the first to study the behaviour of an economic agent whose preferences change over time. They suggested that such an agent would choose a "consistent plan", which they described as "the best plan that he would actually follow", A Markov-consistent plan has a particularly simple structure: current decisions are independent of past decisions, except insofar as past decisions affect the current values of state variables. Unfortunately, Markov-consistent plans do not general1y exist. In this paper, we demonstrate that the existence problem dissappears for finite horizon problems when one introduces even a small amount of smooth uncertainty into production.