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General Equilibrium as a Topological Field Theory

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  • Eric Kemp-Benedict

Abstract

General equilibrium is the dominant theoretical framework for economic policy analysis at the level of the whole economy. In practice, general equilibrium treats economies as being always in equilibrium, albeit in a sequence of equilibria as driven by external changes in parameters. This view is sometimes defended on the grounds that internal dynamics are fast, while external changes are slow, so that the economy can be viewed as adjusting instantaneously to any changed conditions. However, the argument has not been presented in a rigorous way. In this paper we show that when conditions are such that: a) economies do respond essentially instantaneously to external influences; b) the external changes are small compared to the values that characterize the economy; and c) the economy's dynamics are continuous and first-order in time (as for Walrasian tatonnement), the resulting economic theory is equivalent to a topological field theory. Because it is a topological theory it has no dynamics in a strict sense, and so perturbatively---that is, when examining dynamics in the region of a critical point---the field theory behaves as general equilibrium posits. However, the field-theoretic form of the theory admits non-perturbative instanton solutions that link different critical points. Thus, in this theory, and in contrast to general equilibrium, the internal dynamics of the model occasionally make an appearance in the form of abrupt, noise-driven transitions between critical points.

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Paper provided by arXiv.org in its series Papers with number 1209.1705.

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Date of creation: Sep 2012
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Handle: RePEc:arx:papers:1209.1705

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Web page: http://arxiv.org/

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  1. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-31, September.
  2. Victor Ginsburgh & Michiel Keyzer, 2002. "The structure of applied general equilibrium models," ULB Institutional Repository 2013/3313, ULB -- Universite Libre de Bruxelles.
  3. Alan S. Blinder, 1994. "On Sticky Prices: Academic Theories Meet the Real World," NBER Chapters, in: Monetary Policy, pages 117-154 National Bureau of Economic Research, Inc.
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  6. Jeffrey J. Reimer, 2007. "Assessing Global Computable General Equilibrium Model Validity Using Agricultural Price Volatility," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 89(2), pages 383-397.
  7. Herbert Gintis, 2007. "The Dynamics of General Equilibrium," Economic Journal, Royal Economic Society, vol. 117(523), pages 1280-1309, October.
  8. Stiglitz, Joseph E, 1987. "The Causes and Consequences of the Dependence of Quality on Price," Journal of Economic Literature, American Economic Association, vol. 25(1), pages 1-48, March.
  9. Frank Ackerman, 2001. "Still dead after all these years: interpreting the failure of general equilibrium theory," Journal of Economic Methodology, Taylor & Francis Journals, vol. 9(2), pages 119-139.
  10. Eric Kemp-Benedict, 2012. "Price and Quantity Trajectories: Second-order Dynamics," Papers 1204.3156, arXiv.org.
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