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

Takashi Kamihigashi

No 152, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe University

Abstract: This paper shows that the standard transversality condition (STVC) is necessary for optimality for 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 multi-sector growth model with a single consumption good. We establish three results: (i) the STVC is necessary if utility is bounded; (ii) the STVC is necessary if utility is logarithmic; and (iii) 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 endogenous 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: 21 pages
Date: 2004-03
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp152.pdf First 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:152

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