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The Ricardo-Lemke parametric algorithm on oddity and uniqueness

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  • Christian Bidard

Abstract

The parametric Lemke algorithm finds an odd number of solutions to the linear complementarity problem LCP (q, M), for a matrix M with zero blocks on the diagonal and vector q within a certain domain. A criterion for monotonicity and uniqueness is given. The algorithm applies to the determination of a long-run equilibrium in the presence of scarce resources, and its first description can be traced back to the nineteenth century economist David Ricardo.

Suggested Citation

  • Christian Bidard, 2012. "The Ricardo-Lemke parametric algorithm on oddity and uniqueness," EconomiX Working Papers 2012-41, University of Paris Nanterre, EconomiX.
    • Handle: RePEc:drm:wpaper:2012-41
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    File URL: http://economix.fr/pdf/dt/2012/WP_EcoX_2012-41.pdf
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    References listed on IDEAS

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    1. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    2. Christian Bidard, 2012. "The Frail Grounds of the Ricardian Dynamics," EconomiX Working Papers 2012-43, University of Paris Nanterre, EconomiX.
    3. Salvadori, Neri, 1986. "Land and Choice of Techniques within the Sraffa Framework," Australian Economic Papers, Wiley Blackwell, vol. 25(46), pages 94-105, June.
    4. Christian Bidard & Guido Erreygers, 1998. "The number and type of long-term equilibria," Journal of Economics, Springer, vol. 67(2), pages 181-205, June.
    5. 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

    Oddity; parametric Lemke algorithm; Ricardo; uniqueness;
    All these keywords.

    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
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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