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On "sectoral supply functions" and some critical roles for the consumptions and leisure arbitrages in the stability properties of a competitive equilibrium with heterogeneous goods

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  • Drugeon, Jean-Pierre

Abstract

This article appraises a pareto-optimal competitive equilibrium with heterogeneous consumption goods through a new representation of competitive prices and the building of a pair of new aggregate structures labelled "sectoral supply functions" -- SSF -- that are defined over the aggregate values of the inputs and the relative price of the capital good. An alternative dual appraisal of a class of preferences that take explicit account of heterogeneous consumptions and leisure arbitrages then allows for an unrestricted class of general statements on the stability properties of an optimal accumulation environment that subsumes earlier results as special cases. These are based upon the features of Hicksian demands and it is argued that the retainment of a given sectoral configuration in factors shares and the imposition of concavity and positive income elasticities do not suffice to rule out optimal cycles if consumptions or leisure considered by pairs happen to exhibit complementaries. The SSF approach is finally argued to outshine the PPF protocole because it allows for a simple explicit derivation in the Cobb-Douglas case that have become, since the seminal contribution of Benhabib and Farmer in the nineties, the cornerstone of macroeconomic analysis.

Suggested Citation

  • Drugeon, Jean-Pierre, 2010. "On "sectoral supply functions" and some critical roles for the consumptions and leisure arbitrages in the stability properties of a competitive equilibrium with heterogeneous goods," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1030-1063, November.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1030-1063
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    References listed on IDEAS

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    1. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    2. Emanuel M. Drandakis, 1963. "Factor Substitution in the Two-Sector Growth Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 217-228.
    3. Jess Benhabib & Kazuo Nishimura, 2012. "Competitive Equilibrium Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 75-96, Springer.
    4. Akihiro Amano, 1964. "Determinants Of Comparative Costs: A Theoretical Approach," Oxford Economic Papers, Oxford University Press, vol. 16(3), pages 389-400.
    5. Hirofumi Uzawa, 1964. "Optimal Growth in a Two-Sector Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(1), pages 1-24.
    6. Emmanuel M. Drandakis, 1963. "Factor Substitution in the Two-Sector Growth Model," Cowles Foundation Discussion Papers 154R, Cowles Foundation for Research in Economics, Yale University.
    7. Becker, Robert A. & Tsyganov, Eugene N., 2002. "Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households," Journal of Economic Theory, Elsevier, vol. 105(1), pages 188-225, July.
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    Cited by:

    1. Barinci, Jean-Paul & Cho, Hye-Jin & Drugeon, Jean-Pierre, 2021. "On equilibrium elasticities of substitution in simple overlapping generations economies with heterogeneous goods," Mathematical Social Sciences, Elsevier, vol. 112(C), pages 120-137.
    2. Jean-Paul Barinci & Hye-Jin Cho & Jean-Pierre Drugeon, 2021. "On equilibrium elasticities of substitution in simple overlapping generations economies with heterogeneous goods," Post-Print halshs-03238950, HAL.

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