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Testable Restrictions of General Equilibrium Theory in Exchange Economies with Externalities

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  • Andrés Carvajal

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Abstract

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.

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Paper provided by Banco de la Republica de Colombia in its series Borradores de Economia with number 231.

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Handle: RePEc:bdr:borrec:231

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

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  1. 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.
  2. Diewert, W. E., 1977. "Generalized slutsky conditions for aggregate consumer demand functions," Journal of Economic Theory, Elsevier, vol. 15(2), pages 353-362, August.
  3. GHOSAL, Sayantan & POLEMARCHAKIS , Heracles, 1995. "Nash-Walras equilibria," CORE Discussion Papers 1995080, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. Kubler, Felix, 2003. "Observable restrictions of general equilibrium models with financial markets," Journal of Economic Theory, Elsevier, vol. 110(1), pages 137-153, May.
  6. Andrés Carvajal, 2004. "A Continuous Extension that preserves Concavity, Monotonicity and Lipschitz Continuity," Royal Holloway, University of London: Discussion Papers in Economics 04/27, Department of Economics, Royal Holloway University of London, revised Nov 2004.
  7. Andrés Carvajal, . "Testable Restrictions of Nash Equilibrium in Games with Continuous Domains," Borradores de Economia 229, Banco de la Republica de Colombia.
  8. Rosa L. Matzkin & Marcel K. Richter, 1987. "Testing Strictly Concave Rationality," Cowles Foundation Discussion Papers 844, Cowles Foundation for Research in Economics, Yale University.
  9. Snyder, Susan K., 1999. "Testable restrictions of Pareto optimal public good provision," Journal of Public Economics, Elsevier, vol. 71(1), pages 97-119, January.
  10. Lars Peter Hansen & James J. Heckman, 1996. "The Empirical Foundations of Calibration," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 87-104, Winter.
  11. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November.
  12. Andrés Carvajal, . "Testable Restrictions on the Equilibrium Manifold under Random Preferences," Borradores de Economia 233, Banco de la Republica de Colombia.
  13. 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.
  14. Geanakoplos, J D & Polemarchakis, H M, 1980. "On the Disaggregation of Excess Demand Functions," Econometrica, Econometric Society, vol. 48(2), pages 315-31, March.
  15. P.A. Chiappori & I. Ekeland & F. Kubler & H.M. Polemarchakis, 2002. "Testable Implications of General Equilibrium Theory: a differentiable approach," Working Papers 2002-10, Brown University, Department of Economics.
  16. Chiappori, Pierre-André & Ekeland, Ivar, 1999. "Aggregation and Market Demand: An Exterior Differential Calculus Viewpoint," Economics Papers from University Paris Dauphine 123456789/6427, Paris Dauphine University.
  17. Varian, Hal R, 1983. "Non-Parametric Tests of Consumer Behaviour," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 99-110, January.
  18. 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.
  19. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
  20. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
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Cited by:
  1. Jean-Marc Bonnisseau & Elena L. del Mercato, 2008. "Externalities, Consumption Constraints and Regular Economies," CSEF Working Papers 195, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 01 Dec 2009.
  2. J. D. Geanakoplos & H. M. Polemarchakis, 2006. "Pareto Improving Taxes," Levine's Bibliography 321307000000000350, UCLA Department of Economics.
  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.
  4. J. D. Geanakoplos & H. M. Polemarchakis, 2006. "Pareto Improving Taxes," Cowles Foundation Discussion Papers 1576, Cowles Foundation for Research in Economics, Yale University.
  5. John Geanakoplos & H. M. Polemarchakis, 2008. "Pareto Improving Taxes," Cowles Foundation Discussion Papers 1662, Cowles Foundation for Research in Economics, Yale University.

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