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.
|Date of creation:||May 2003|
|Date of revision:|
|Contact details of provider:|| Postal: 2-1 Rokkodai, Nada, Kobe 657-8501 JAPAN|
Phone: +81-(0)78 803 7036
Fax: +81-(0)78 803 7059
Web page: http://www.rieb.kobe-u.ac.jp/index-e.html
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
- Takashi Kamihigashi, 2000.
"Necessity of Transversality Conditions for Stochastic Problems,"
Discussion Paper Series
115, Research Institute for Economics & Business Administration, Kobe University.
- Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
- Takashi Kamihigashi, 2001. "Necessity of Transversality Conditions for Stochastic Problems," Department of Economics Working Papers 01-02, Stony Brook University, Department of Economics.
- Takashi Kamihigashi, 2002. "Necessity of Transversality Conditions for Stochastic Problems," Discussion Paper Series 128, Research Institute for Economics & Business Administration, Kobe University.
- Robert G. King & Sergio T. Rebelo, 2000.
"Resuscitating Real Business Cycles,"
RCER Working Papers
467, University of Rochester - Center for Economic Research (RCER).
- Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
- W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 275-280.
- Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
- Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-72, March.
- Olson, Lars J., 1989. "Stochastic growth with irreversible investment," Journal of Economic Theory, Elsevier, vol. 47(1), pages 101-129, February.
- Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
When requesting a correction, please mention this item's handle: RePEc:kob:dpaper:137. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Office of Promoting Research Collaboration, Research Institute for Economics & Business Administration, Kobe University)
If references are entirely missing, you can add them using this form.