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Perturbation theory in a pure exchange non-equilibrium economy

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  • Vazquez, Samuel E.
  • Severini, Simone

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.

Suggested Citation

  • Vazquez, Samuel E. & Severini, Simone, 2009. "Perturbation theory in a pure exchange non-equilibrium economy," MPRA Paper 14569, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:14569
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    References listed on IDEAS

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    1. Hashem Pesaran, M., 2007. "A pair-wise approach to testing for output and growth convergence," Journal of Econometrics, Elsevier, vol. 138(1), pages 312-355, May.
    2. Durlauf, Steven N. & Johnson, Paul A. & Temple, Jonathan R.W., 2005. "Growth Econometrics," Handbook of Economic Growth,in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 8, pages 555-677 Elsevier.
    3. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 70(1), pages 65-94.
    4. Giovanni Caggiano & Leone Leonida, 2009. "International output convergence: evidence from an autocorrelation function approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 139-162.
    5. Carvalho, Vasco M. & Harvey, Andrew C., 2005. "Growth, cycles and convergence in US regional time series," International Journal of Forecasting, Elsevier, vol. 21(4), pages 667-686.
    6. Bernard, Andrew B. & Durlauf, Steven N., 1996. "Interpreting tests of the convergence hypothesis," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 161-173.
    7. Yin-Wong Cheung & Antonio Garcia Pascual, 2004. "Testing for output convergence: a re-examination," Oxford Economic Papers, Oxford University Press, vol. 56(1), pages 45-63, January.
    8. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    9. Evans, Paul, 1998. "Using Panel Data to Evaluate Growth Theories," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(2), pages 295-306, May.
    10. Landon-Lane, John S. & Robertson, Peter E., 2009. "Long-run growth in the OECD: A test of the parallel growth paths hypothesis," Explorations in Economic History, Elsevier, vol. 46(3), pages 346-355, July.
    11. Ludlow, Jorge & Enders, Walter, 2000. "Estimating non-linear ARMA models using Fourier coefficients," International Journal of Forecasting, Elsevier, vol. 16(3), pages 333-347.
    12. Binder, M. & Pesaran, M.H., 1996. "Stochastic Growth," Cambridge Working Papers in Economics 9615, Faculty of Economics, University of Cambridge.
    13. Peter C. B. Phillips & Donggyu Sul, 2009. "Economic transition and growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(7), pages 1153-1185.
    14. Li, Qing & Papell, David, 1999. "Convergence of international output Time series evidence for 16 OECD countries," International Review of Economics & Finance, Elsevier, vol. 8(3), pages 267-280, September.
    15. Loewy, Michael B. & Papell, David H., 1996. "Are U.S. regional incomes converging? Some further evidence," Journal of Monetary Economics, Elsevier, vol. 38(3), pages 587-598, December.
    16. Datta, Anusua, 2003. "Time-series tests of convergence and transitional dynamics," Economics Letters, Elsevier, vol. 81(2), pages 233-240, November.
    17. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    18. Ralf Becker & Walter Enders & A. Stan Hurn, 2001. "Testing for Time Dependence in Parameters," Research Paper Series 58, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Camarero, Mariam, & FlĂ´res, R. & C. Tamarit, 2002. "Time series evidence of international output convergence in Mercosur," Computing in Economics and Finance 2002 87, Society for Computational Economics.
    20. Bentzen, Jan, 2005. "Testing for catching-up periods in time-series convergence," Economics Letters, Elsevier, vol. 88(3), pages 323-328, September.
    21. Ralf Becker & Walter Enders & Junsoo Lee, 2006. "A Stationarity Test in the Presence of an Unknown Number of Smooth Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 381-409, May.
    22. Binder, Michael & Pesaran, M Hashem, 1999. "Stochastic Growth Models and Their Econometric Implications," Journal of Economic Growth, Springer, vol. 4(2), pages 139-183, June.
    23. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    24. Peter Howitt, 2000. "Endogenous Growth and Cross-Country Income Differences," American Economic Review, American Economic Association, vol. 90(4), pages 829-846, September.
    25. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    26. Carlino, Gerald A. & Mills, Leonard O., 1993. "Are U.S. regional incomes converging? : A time series analysis," Journal of Monetary Economics, Elsevier, vol. 32(2), pages 335-346, November.
    27. Jochonia S Mathunjwa & Jonathan Temple, 2006. "Convergence behaviour in exogenous growth models," Bristol Economics Discussion Papers 06/590, Department of Economics, University of Bristol, UK.
    28. Rob Luginbuhl & Siem Jan Koopman, 2004. "Convergence in European GDP series: a multivariate common converging trend-cycle decomposition," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(5), pages 611-636.
    29. Peter E. Robertson & John Landon-Lane, 2004. "WWII and Long Run Convergence in the OECD," Econometric Society 2004 North American Summer Meetings 593, Econometric Society.
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    More about this item

    Keywords

    non-equilibrium economics; perturbation theory;

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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