Necessity of the Transversality Condition for@Stochastic Models with CRRA Utility


This paper shows that the standard transversality condition (STVC) is necessary for optimality for stochastic models with constant-relative-risk-aversion (CRRA) utility under general conditions.  We consider an infinite-horizon stochastic maximization problem that takes a general form of multi-sector growth model with a single consumption good and CRRA utility.  We establish two results.  The first result is that the STVC is necessary in the case of logarithmic utility.  The second result is 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 (RBC) models with endogenous labor supply.  Our results make it clear that there is practically no issue about necessity of the STVC for stochastic models with CRRA utility.

Keywords: Transversality condition, stochastic optimization, stochastic growth, CRRA, real business cycle.

JEL Classification: C61, D90, G12

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