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Testable Restrictions of General Equilibrium Theory in Exchange Economies with Externalities


  • Andrés Carvajal



The theory of general equilibrium was criticized for its apparent lack of testable implications,as seemingly implied by the results of Sonnenschein, Mantel and Debreu in the Seventies. This view was challenged by the results of Brown and Matzkin (1996) which showed the existence of testable restrictions on the equilibrium manifold of exchange economies. This paper studies a problem similar to the one posed by Brown and Matzkin, for the case of general equilibrium in the presence of externalities. The natural definition of equilibrium in such case is the Nash-Walras equilibrium concept. I first consider the case of strategic externalities, where I assume that each player chooses a consumption bundle, subject to some budget,and a strategy from a continuous domain, and where the utility of each individual depends on his consumption and on the strategies chosen by all the players. I also consider the case of consumption externalities, in which each individual's utility depends on his consumption of all commodities and on the consumption of some particular commodity by all individuals. The results obtained here are rather negative in that they point towards the unfalsiability of the equilibrium hypothesis. Under the assumption that one can observe individual choices for the externality, I find that there exist some extremely mild testable restrictions. This, however, is not a pure extension of the Brown-Matzkin result, since some individual decisions are assumed to be observed. If there is no information on individual choices, I find that the equilibrium concept imposes no testable restrictions. This occurs unless one imposes further assumptions, such as weak separability.

Suggested Citation

  • Andrés Carvajal, 2003. "Testable Restrictions of General Equilibrium Theory in Exchange Economies with Externalities," Borradores de Economia 231, Banco de la Republica de Colombia.
  • Handle: RePEc:bdr:borrec:231

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    References listed on IDEAS

    1. Andrés Carvajal, 2003. "A Continuous Extension that Preserves Concavity, Monotonicity and Lipschitz Continuity," Borradores de Economia 230, Banco de la Republica de Colombia.
    2. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 99-110.
    3. Andrés Carvajal, 2003. "Testable Restrictions of Nash Equilibrium in Games with Continuous Domains," BORRADORES DE ECONOMIA 003555, BANCO DE LA REPÚBLICA.
    4. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    5. Matzkin, Rosa L. & Richter, Marcel K., 1991. "Testing strictly concave rationality," Journal of Economic Theory, Elsevier, vol. 53(2), pages 287-303, April.
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    7. P. A. Chiappori & I. Ekeland, 1999. "Aggregation and Market Demand: An Exterior Differential Calculus Viewpoint," Econometrica, Econometric Society, vol. 67(6), pages 1435-1458, November.
    8. Chiappori, P. -A. & Ekeland, I. & Kubler, F. & Polemarchakis, H. M., 2004. "Testable implications of general equilibrium theory: a differentiable approach," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 105-119, February.
    9. Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
    10. Diewert, W. E., 1977. "Generalized slutsky conditions for aggregate consumer demand functions," Journal of Economic Theory, Elsevier, vol. 15(2), pages 353-362, August.
    11. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    12. Carvajal, Andres, 2004. "Testable restrictions on the equilibrium manifold under random preferences," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 121-143, February.
    13. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-1262, November.
    14. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    15. Geanakoplos, J D & Polemarchakis, H M, 1980. "On the Disaggregation of Excess Demand Functions," Econometrica, Econometric Society, vol. 48(2), pages 315-331, March.
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    17. Shafer, Wayne & Sonnenschein, Hugo, 1993. "Market demand and excess demand functions," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 14, pages 671-693 Elsevier.
    18. Kubler, Felix, 2003. "Observable restrictions of general equilibrium models with financial markets," Journal of Economic Theory, Elsevier, vol. 110(1), pages 137-153, May.
    19. repec:dau:papers:123456789/6427 is not listed on IDEAS
    20. Snyder, Susan K., 1999. "Testable restrictions of Pareto optimal public good provision," Journal of Public Economics, Elsevier, vol. 71(1), pages 97-119, January.
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    Cited by:

    1. Geanakoplos, John & Polemarchakis, H.M., 2008. "Pareto improving taxes," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 682-696, July.
    2. Jean-Marc Bonnisseau & Elena Mercato, 2010. "Externalities, consumption constraints and regular economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 123-147, July.
    3. Carvajal, Andres, 2004. "Testable restrictions on the equilibrium manifold under random preferences," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 121-143, February.

    More about this item


    Nash-Walras equilibrium; externalities; revealed preferences; testable restrictions.;

    JEL classification:

    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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