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An algorithm for a piecewise linear model of trade and production with negative prices and bankruptcy

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Abstract

The general equilibrium model is approximated as a piecewise linear convex model and solved from the point of view of welfare economics using linear programming and fixed point methods.

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References

  1. K.J. Arrow and F.H. Hahn,General competitive analysis (Holden-Day, San Francisco, CA, 1971).

    Google Scholar 

  2. T.C. Bergstrom, “How to discard “free disposability”—at no cost”,Journal of Mathematical Economics, to appear.

  3. G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, NJ, 1963) 621 pp.

    Google Scholar 

  4. G. Debreu,Theory of value—An axiomatic analysis of economic equilibrium (John Wiley, New York, 1959) 107 pp.

    Google Scholar 

  5. C. Debreu, “New concepts and techniques for equilibrium analysis”,International Economic Review 3 (3) (1962) 257–273.

    Google Scholar 

  6. C. Debreu, “Four aspects of the mathematical theory of economic equilibrium”,Proceedings of the International Congress of Mathematicians, Vancouver, 1 (1974) 65–77.

    Google Scholar 

  7. C. Debreu, “Least concave utility functions”,Journal of Mathematical Economics 3 (2) (1976).

  8. B.C. Eaves, “Properly labeled simplexes”, in: G.B. Dantzig and B.C. Eaves, eds.,Studies in optimization, Vol. 10, MAA Studies in Mathematics (Springer, Berlin, 1974) 71–93 pp.

    Google Scholar 

  9. B.C. Eaves, “A finite algorithm for the linear exchange model”,Journal of Mathematical Economics 3 (1976) 197–203.

    Google Scholar 

  10. D. Gale, “Piecewise linear exchange equilibrium; 7 pp., undated, mimeographed.

  11. A.M. Geoffrion, “Elements of large-scale mathematical programming: Parts I and II”,Management Science 16 (1970) 652–691.

    Google Scholar 

  12. V. Ginsburgh and J. Waelbroeck, “Computational experience with a large general equilibrium model”, CORE Discussion Paper No. 7420, Belgium (1974) 21 pp.

  13. V. Ginsburgh and J. Waelbroeck, A general equilibrium model of world trade, Part I, Full format computation of economic equilibria”, Cowles Foundation Discussion Paper No. 412, Yale University (1975) 37 pp.

  14. V. Ginsburgh and J. Waelbroeck, “A general equilibrium model of world trade, Part II, The empirical specification”, Cowles Foundation Discussion Paper No. 413, Yale University (1975) 64 pp.

  15. O.D. Hart and H. Kuhn, “A proof of the existence of equilibrium without the free disposal assumption”,Journal of Mathematical Economics 2 (1975) 335–343.

    Google Scholar 

  16. Y. Kannai, “Approximation of convex preferences”,Journal of Mathematical Economics 1 (2) (1974) 101–106.

    Google Scholar 

  17. D.M. Kreps, “On the computation of economic equilibria using the simplex of households”, Dept. of Econ., Stanford University (1974), unpublished.

  18. L.S. Lasdon,Optimization theory for large systems (Macmillan, New York, 1970) 523 pp.

    Google Scholar 

  19. R. Mantel, “Toward a constructive proof of the existence of equilibrium in a competitive economy”,Yale Economic Essays 8 (1968) 155–196.

    Google Scholar 

  20. A. Mas-Colell, “Continuous and smooth consumers: Approximation theorems”,Journal of Economic Theory 8 (1974) 305–336.

    Google Scholar 

  21. T. Negishi, “Welfare economics and existence of an equilibrium for a competitive economy;Metroeconomica XII (1960) 92–97.

    Google Scholar 

  22. T. Rader,Theory of microeconomics (Academic Press, New York, 1972) 258–261 pp.

    Google Scholar 

  23. R. Saigal, “On the convergence rate of algorithms for solving equations that are based on methods of complementary pivoting”, Bell Telephone Laboratories, Holmdel, NJ (undated) 60 pp.

  24. H. Scarf,The computation of economic equilibria (Yale University Press, 1973) 249 pp.

  25. L.S. Shapley, “Utility comparison and the theory of games”, in:La decision, Colloques Int. du Centre Nat'l. de la Recherche Scientifique (1967) 251–263 pp.

  26. R.B. Wilson, “The bilinear complementarity problem and competitive equilibria of linear economic models”,Econometrica 46, 1 (1978) 87–103.

    Google Scholar 

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Authors and Affiliations

  1. Stanford University, Stanford, CA., USA

    G. B. Dantzig & B. C. Eaves

  2. University of California, Berkeley, CA., USA

    D. Gale

Authors
  1. G. B. Dantzig
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  2. B. C. Eaves
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  3. D. Gale
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Additional information

This research was supported in part by Army Research Office-Durham Contract DAAG-29-74-C-0032, NSF Grant MPS-72-04832-A03, and Energy Research and Development Administration Contract E(04-3)-326 PA#18.

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Dantzig, G.B., Eaves, B.C. & Gale, D. An algorithm for a piecewise linear model of trade and production with negative prices and bankruptcy. Mathematical Programming 16, 190–209 (1979). https://doi.org/10.1007/BF01582108

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  • DOI: https://doi.org/10.1007/BF01582108

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