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A multi-agent growth model based on the von Neumann-Leontief framework

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  • Li, Wu

Abstract

This paper presents a discrete-time growth model to describe the dynamics of a multi-agent economy, and the model consists of production process, exchange process, price and technology adjustment processes etc. Technologies of agents in each period are represented by a technology matrix pair, and some properties of Perron-Frobenius eigenvalues and eigenvectors of technology matrix pairs are discussed. An exchange model is also developed to serve as the exchange part of the growth model. And equilibrium paths of the growth model are proved to be balanced growth paths sharing a unique normalized price vector. Though this paper focuses mainly on the case of n agents and n goods, the growth model can also deal with the case of m agents and n goods. A numerical example with 6 agents and 4 goods is given, which describes the dynamics of a two-country economy and has endogenous price fluctuations and business cycles.

Suggested Citation

  • Li, Wu, 2008. "A multi-agent growth model based on the von Neumann-Leontief framework," MPRA Paper 11302, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:11302
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    File URL: https://mpra.ub.uni-muenchen.de/11302/1/MPRA_paper_11302.pdf
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    References listed on IDEAS

    as
    1. Lionel W. McKenzie, 2012. "turnpike theory," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    2. Evstigneev, Igor V. & Schenk-Hoppe, Klaus Reiner, 2007. "Pure and randomized equilibria in the stochastic von Neumann-Gale model," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 871-887, September.
    3. M. Dempster & I. Evstigneev & M. Taksar, 2006. "Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model," Annals of Finance, Springer, vol. 2(4), pages 327-355, October.
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    Cited by:

    1. Hladík, Milan, 2010. "Generalized linear fractional programming under interval uncertainty," European Journal of Operational Research, Elsevier, vol. 205(1), pages 42-46, August.

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    More about this item

    Keywords

    von Neumann’s expanding economic model; input-output model; dynamic general equilibrium; disequilibrium; multi-country economic model;
    All these keywords.

    JEL classification:

    • B51 - Schools of Economic Thought and Methodology - - Current Heterodox Approaches - - - Socialist; Marxian; Sraffian
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • F43 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Economic Growth of Open Economies
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • F1 - International Economics - - Trade

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