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

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  • Alain Venditti

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, EDHEC Business School - Département Comptabilité, Droit, Finance et Economie)

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.

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  • Alain Venditti, 2011. "Weak Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," Working Papers halshs-01059589, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01059589
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01059589
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    Cited by:

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    2. 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.

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    More about this item

    Keywords

    weak concavity; indirect utility function; social production function; multisector optimal growth model;
    All these keywords.

    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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