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

PDF
MPRA_paper_14569.pdf Download (173kB)  Preview 
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 nonequilibrium 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 

Original Title:  Perturbation theory in a pure exchange nonequilibrium economy 
Language:  English 
Keywords:  nonequilibrium 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 
Item ID:  14569 
Depositing User:  Simone Severini 
Date Deposited:  12. Apr 2009 04:44 
Last Modified:  12. Feb 2013 00:42 
References:  J. D. Farmer, J. Geanakoplos, The virtues and vices of equilibrium and the future of financial economics, Complexity 14 (2009): 1138. E. Smith and D. K. Foley, Journal of Economic Dynamics and Control, 2008, vol. 32, issue 1, pages 765. 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 SchenkHoppe. Elsevier: Academic Press, 2008. W. B. Arthur, Handbook of Computational Economics, Vol. 2: AgentBased Computational Economics, K. Judd and L. Tesfatsion (Eds.), Elsevier/NorthHolland, 2005. L. Smolin, Time and symmetry in models of economic markets, February 2009. arXiv:0902.4274v1 [qfin.GN] A. Wilhite, Handbook of Computational Economics, Vol. 2: AgentBased Computational Economics, K. Judd and L. Tesfatsion (Eds.), Elsevier/NorthHolland, 2005. J.P. Bouchaud, M. M´ezard, Physica A , 282, 2000, p.536545. 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 NonEquilibrium Economics, February 2009. arXiv:0902.3840v1 [qfin.TR] 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/14569 