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Ricardo And Lemke

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  • Christian Bidard

Abstract

We study the economic mechanism which sustains the substitution of a marginal method for another when demand increases, in the presence of scarce resources. In those Ricardian dynamics, it is shown that the outgoing method is determined by the quantity side of the problem, the incoming method by the value side. That discrepancy explains both the possible failure of the dynamics and the possible occurrence of multiple equilibria. Conditions for existence, uniqueness and the working of the dynamics are stated. A parallel is drawn with the parametric Lemke algorithm used to solve linear complementarity problems.

Suggested Citation

  • Christian Bidard, 2012. "Ricardo And Lemke," EconomiX Working Papers 2012-48, University of Paris Nanterre, EconomiX.
  • Handle: RePEc:drm:wpaper:2012-48
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    File URL: http://economix.fr/pdf/dt/2012/WP_EcoX_2012-48.pdf
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    References listed on IDEAS

    as
    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, December.
    2. Erreygers, Guido, 1995. "On the Uniqueness of Square Cost-Minimizing Techniques," The Manchester School of Economic & Social Studies, University of Manchester, vol. 63(2), pages 145-166, June.
    3. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    4. Christian Bidard, 2012. "The Frail Grounds of the Ricardian Dynamics," EconomiX Working Papers 2012-43, University of Paris Nanterre, EconomiX.
    5. Salvadori, Neri, 1986. "Land and Choice of Techniques within the Sraffa Framework," Australian Economic Papers, Wiley Blackwell, vol. 25(46), pages 94-105, June.
    6. Christian Bidard & Guido Erreygers, 1998. "The number and type of long-term equilibria," Journal of Economics, Springer, vol. 67(2), pages 181-205, June.
    7. Dantzig, George B. & Manne, Alan S., 1974. "A complementarity algorithm for an optimal capital path with invariant proportions," Journal of Economic Theory, Elsevier, vol. 9(3), pages 312-323, November.
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    More about this item

    Keywords

    Dynamics; Lemke; rent; Ricardo; scarce resources;

    JEL classification:

    • B12 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Classical (includes Adam Smith)
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D33 - Microeconomics - - Distribution - - - Factor Income Distribution

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