Necessity of the Transversality Condition for Stochastic Models with Bounded or CRRA Utility
This paper shows that the standard transversality condition (STVC) is nec-essary for optimality in stochastic models with bounded or constant-relative-risk- aversion (CRRA) utility under fairly general conditions. We consider an infinite-horizon stochastic maximization problem that takes a general form of a multi-sector growth model with a single consumption good. We show that the STVC is necessary if utility is bounded or logarithmic. We also show that the STVC is necessary in the case of non-logarithmic CRRA utility as long as lifetime utility is finite at the optimum. These results apply to various stochastic growth models, including real business cycle models with endoge-nous labor supply. Since unbounded utility functions that do not belong to the CRRA class are rather rare in applications, our results provide a fairly complete set of solutions regarding necessity of the STVC in practice.
Keywords: Transversality condition, stochastic optimization, stochastic growth, CRRA, real business cycle.
JEL Classification Numbers: C61, D90, G12