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The Futility of Utility: how market dynamics marginalize Adam Smith

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  • Joseph L. McCauley

Abstract

Econometrics is based on the nonempiric notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is usually treated by economists as a price potential, other times utility rates are treated as Lagrangians. Assumptions of integrability of Lagrangians and dynamics are implicitly and uncritically made. In particular, economists assume that price is the gradient of utility in equilibrium, but I show that price as the gradient of utility is an integrability condition for the Hamiltonian dynamics of an optimization problem in econometric control theory. One consequence is that, in a nonintegrable dynamical system, price cannot be expressed as a function of demand or supply variables. Another consequence is that utility maximization does not describe equiulibrium. I point out that the maximization of Gibbs entropy would describe equilibrium, if equilibrium could be achieved, but equilibrium does not describe real markets. To emphasize the inconsistency of the economists' notion of 'equilibrium', I discuss both deterministic and stochastic dynamics of excess demand and observe that Adam Smith's stabilizing hand is not to be found either in deterministic or stochastic dynamical models of markets, nor in the observed motions of asset prices. Evidence for stability of prices of assets in free markets simply has not been found.

Suggested Citation

  • Joseph L. McCauley, 1999. "The Futility of Utility: how market dynamics marginalize Adam Smith," Papers cond-mat/9911291, arXiv.org, revised Feb 2000.
  • Handle: RePEc:arx:papers:cond-mat/9911291
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    Cited by:

    1. Sara Bourhime & Mohamed Tkiouat, 2018. "Rethinking Microfinance in a Dual Financial System: An Agent-based Simulation," Scientific Annals of Economics and Business (continues Analele Stiintifice), Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, vol. 65(1), pages 13-29, March.
    2. Shi, Leilei, 2006. "Does security transaction volume–price behavior resemble a probability wave?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 419-436.
    3. Small Michael & Tse Chi K., 2003. "Determinism in Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(3), pages 1-31, October.
    4. McCauley, Joseph L, 2002. "Adam Smith's invisible hand is unstable: physics and dynamics reasoning applied to economic theorizing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 722-727.

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