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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, France, revised Sep 2014.
    • Handle: RePEc:aim:wpaimx:1440
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    References listed on IDEAS

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    Cited by:

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    More about this item

    Keywords

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