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Weak Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models

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  • Alain Venditti

    () (Aix-Marseille University (Aix-Marseille School of Economics), CNRS-GREQAM, EHESS & EDHEC)

Abstract

Studies of optimal growth in a multisector framework are generally addressed in reduced form models. These are defined by an indirect utility function which summarizes the consumers’ preferences and the technologies. Weak concavity assumptions of the indirect utility function allow one to prove differentiability of optimal solutions and stability of steady state. This paper shows that if the consumption good production function is concave-gamma, and the instantaneous utility function is concave-rho, then the indirect utility function is weakly concave, and its curvature coefficients are bounded from above by a function of gamma and rho.

Suggested Citation

  • Alain Venditti, 2014. "Weak Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," AMSE Working Papers 1440, Aix-Marseille School of Economics, Marseille, France, revised Sep 2014.
  • Handle: RePEc:aim:wpaimx:1440
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    References listed on IDEAS

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    1. Maria Luisa Gota & Luigi Montrucchio, 1999. "On Lipschitz continuity of policy functions in continuous-time optimal growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 479-488.
    2. Nishimura, Kiyohiko Giichi, 1981. "On uniqueness of a steady state and convergence of optimal paths in multisector models of optimal growth with a discount rate," Journal of Economic Theory, Elsevier, vol. 24(2), pages 157-167, April.
    3. Montrucchio, Luigi, 1998. "Thompson metric, contraction property and differentiability of policy functions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 449-466, January.
    4. Montrucchio, Luigi, 1995. "A turnpike theorem for continuous-time optimal-control models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 599-619, April.
    5. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December.
    6. Montrucchio, Luigi, 1995. "A New Turnpike Theorem for Discounted Programs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 371-382, May.
    7. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
    8. Tyrrell Rockafellar, R., 1976. "Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate," Journal of Economic Theory, Elsevier, vol. 12(1), pages 71-113, February.
    9. Montrucchio, Luigi, 1994. "The neighbourhood turnpike property for continuous-time optimal growth models," Ricerche Economiche, Elsevier, vol. 48(3), pages 213-224, September.
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    Cited by:

    1. Kenji Sato & Makoto Yano, 2013. "Optimal ergodic chaos under slow capital depreciation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 57-67, March.

    More about this item

    Keywords

    indirect utility function; social production function; multisector optimal growth model; weak concavity;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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