Perturbation theory in a pure exchange non-equilibrium economy

Vazquez, Samuel E. and Severini, Simone (2009): Perturbation theory in a pure exchange non-equilibrium economy.

Abstract

We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous preferences and probabilistic interaction between agents. We are able to show that if the economic agents have static preferences, which are also homogeneous in any of the steady states, the final wealth distribution is independent of the dynamics of the non-equilibrium theory. In particular, it is completely determined in terms of the initial conditions, and it is independent of the probability, and the network of interaction between agents. We show that the main effect of the network is to determine the relaxation time via the usual eigenvalue gap as in random walks on graphs.

• Item Type: MPRA Paper
• Language: English
• Keywords: non-equilibrium economics; perturbation theory
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium

References

J. D. Farmer, J. Geanakoplos, The virtues and vices of equilibrium and the future of financial economics, Complexity 14 (2009): 11-38.

E. Smith and D. K. Foley, Journal of Economic Dynamics and Control, 2008, vol. 32, issue 1, pages 7-65.

J.-P. Bouchaud, J. D. Farmer, F. Lillo, How Markets Slowly Digest Changes in Supply and Demand. In Handbook of Financial Markets: Dynamics and Evolution, eds. Thorsten Hens and Klaus Schenk-Hoppe. Elsevier: Academic Press, 2008.

W. B. Arthur, Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics, K. Judd and L. Tesfatsion (Eds.), Elsevier/North-Holland, 2005.

L. Smolin, Time and symmetry in models of economic markets, February 2009. arXiv:0902.4274v1 [q-fin.GN]

A. Wilhite, Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics, K. Judd and L. Tesfatsion (Eds.), Elsevier/North-Holland, 2005.

J.-P. Bouchaud, M. M´ezard, Physica A , 282, 2000, p.536-545.

D. Aldous, J. Fill, Reversible Markov Chains and Random Walks on Graphs, stat.berkeley.edu/˜aldous/RWG

A. Farkas, P. R´ozsa, E. Stubnya, Linear Algebra Appl. 302–303 (1999) 423–433.

S. E. Vazquez, Scale Invariance, Bounded Rationality and Non-Equilibrium Economics, February 2009. arXiv:0902.3840v1 [q-fin.TR]