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Optimal Growth with Recursive Utility: An Existence Result without Convexity Assumptions

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  • N. SAGARA

    (Hosei University)

Abstract

This paper deals with the existence problem of optimal growth with recursive utility in a continuous-time model without convexity assumptions. We consider a general reduced model of capital accumulation and provide an existence result allowing the production technology to be nonconvex and the objective functional to be nonconcave and recursive. The program space under investigation is a weighted Sobolev space with discounting built in, as introduced by Chichilnisky. The compactness of the feasible set and the continuity of the objective are proven by the effective use of ℒ2-convergence. Existence follows from the classical Weierstrass theorem.

Suggested Citation

  • N. Sagara, 2001. "Optimal Growth with Recursive Utility: An Existence Result without Convexity Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 371-383, May.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:2:d:10.1023_a:1017518523055
    DOI: 10.1023/A:1017518523055
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    References listed on IDEAS

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    1. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
    2. Russell Davidson & Richard Harris, 1981. "Non-Convexities in Continuous Time Investment Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(2), pages 235-253.
    3. Becker, Robert A. & Boyd, John III & Sung, Bom Yong, 1989. "Recursive utility and optimal capital accumulation. I. Existence," Journal of Economic Theory, Elsevier, vol. 47(1), pages 76-100, February.
    4. Epstein, Larry G, 1987. "The Global Stability of Efficient Intertemporal Allocations," Econometrica, Econometric Society, vol. 55(2), pages 329-355, March.
    5. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    6. Romer, Paul M, 1986. "Cake Eating, Chattering, and Jumps: Existence Results for Variational Problems," Econometrica, Econometric Society, vol. 54(4), pages 897-908, July.
    7. Epstein, Larry G & Hynes, J Allan, 1983. "The Rate of Time Preference and Dynamic Economic Analysis," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 611-635, August.
    8. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
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    Cited by:

    1. Schumacher, Ingmar, 2011. "Endogenous discounting and the domain of the felicity function," Economic Modelling, Elsevier, vol. 28(1-2), pages 574-581, January.

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