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

  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

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.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp152.pdf
File Function: First version, 2004
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Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 152.

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Length: 21 pages
Date of creation: Mar 2004
Date of revision:
Handle: RePEc:kob:dpaper:152
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