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Testable Restrictions og General Equilibrium Theory in Exchange Economies with Externalities

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Andrés Carvajal ()
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 unfalsifiability 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 REPÚBLICA in its series BORRADORES DE ECONOMIA with number 003556.

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Length: 70
Date of creation: 31 Jan 2003
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Handle: RePEc:col:000094:003556

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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. [Downloadable!] (restricted)
  2. Kubler, Felix, 2003. "Observable restrictions of general equilibrium models with financial markets," Journal of Economic Theory, Elsevier, vol. 110(1), pages 137-153, May. [Downloadable!] (restricted)
  3. Ghosal, S & Polemarchakis, H, 1995. "Nash - Walras Equilibria," Papers 9580, Catholique de Louvain - Center for Operations Research and Economics.
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  4. 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. [Downloadable!]
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  5. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
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  7. Diewert, W. E., 1977. "Generalized slutsky conditions for aggregate consumer demand functions," Journal of Economic Theory, Elsevier, vol. 15(2), pages 353-362, August. [Downloadable!] (restricted)
  8. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March. [Downloadable!] (restricted)
  9. Andrés Carvajal, . "Testable Restrictions of Nash Equilibrium in Games with Continuous Domains," Borradores de Economia 229, Banco de la Republica de Colombia. [Downloadable!]
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  10. Matzkin, Rosa L. & Richter, Marcel K., 1991. "Testing strictly concave rationality," Journal of Economic Theory, Elsevier, vol. 53(2), pages 287-303, April. [Downloadable!] (restricted)
  11. Geanakoplos, J D & Polemarchakis, H M, 1980. "On the Disaggregation of Excess Demand Functions," Econometrica, Econometric Society, vol. 48(2), pages 315-31, March. [Downloadable!] (restricted)
  12. Hansen, Lars Peter & Heckman, James J, 1996. "The Empirical Foundations of Calibration," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 87-104, Winter. [Downloadable!] (restricted)
  13. 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.
  14. Snyder, Susan K., 1999. "Testable restrictions of Pareto optimal public good provision," Journal of Public Economics, Elsevier, vol. 71(1), pages 97-119, January. [Downloadable!] (restricted)
  15. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November. [Downloadable!] (restricted)
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  16. 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. [Downloadable!] (restricted)
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