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Optimal growth and the golden rule in a two-sector model of capital accumulation

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  • Mehdi Senouci

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

We contribute to the literature on optimal growth in two-sector models by solving a Ram- sey problem with a concave utility function. The unique possible steady-state is independent of initial conditions and of the instantaneous utility function, but not of the discount rate, and is characterized by a wage-rental ratio depending solely on the technology of the capital sector. For an initially low-capital economy, we show that the wage-rental ratio increasingly converges to its balanced value during transition. If the consumption sector is relatively capital-intensive, the relative price of capital increases during transition. If the investment sector is relatively more capital-intensive, it decreases. We also prove that a negative shock on the subjective rate of impatience, that makes the social planner more patient, leads to an immediate positive jump in asset prices.

Suggested Citation

  • Mehdi Senouci, 2011. "Optimal growth and the golden rule in a two-sector model of capital accumulation," PSE Working Papers halshs-00572510, HAL.
    • Handle: RePEc:hal:psewpa:halshs-00572510
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00572510
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    References listed on IDEAS

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    Cited by:

    1. Mehdi Senouci, 2012. "Technical change in a neoclassical two-sector model of optimal growth," Working Papers halshs-00589627, HAL.

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    Keywords

    capital accumulation; optimal growth; golden rule; two-sector models;
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