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Necessity of the transversality condition for stochastic models with bounded or CRRA utility

  • Kamihigashi, Takashi

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.

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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 29 (2005)
Issue (Month): 8 (August)
Pages: 1313-1329

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Handle: RePEc:eee:dyncon:v:29:y:2005:i:8:p:1313-1329
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