Necessity of the Transversality Condition for Stochastic Models with Bounded or CRRA Utility

Takashi Kamihigashi

No 162, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe University

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C61 D90 G12 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2004-08, Revised 2004-10
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https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp162.pdf Revised version, 2004 (application/pdf)

Related works:
Journal Article: Necessity of the transversality condition for stochastic models with bounded or CRRA utility (2005)
Working Paper: Necessity of the Transversality Condition for Stochastic Models with Bounded or CRRA Utility (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:kob:dpaper:162

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