Li, Wu (2008): A multi-agent growth model based on the von Neumann-Leontief framework.
Download (264Kb) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||A multi-agent growth model based on the von Neumann-Leontief framework|
|Keywords:||von Neumann’s expanding economic model, input-output model, dynamic general equilibrium, disequilibrium, multi-country economic model|
|Subjects:||B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B51 - Socialist; Marxian; Sraffian
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C68 - Computable General Equilibrium Models
O - Economic Development, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models
D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D58 - Computable and Other Applied General Equilibrium Models
F - International Economics > F4 - Macroeconomic Aspects of International Trade and Finance > F43 - Economic Growth of Open Economies
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 > C67 - Input-Output Models
D - Microeconomics > D5 - General Equilibrium and Disequilibrium
E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations; Cycles
C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
F - International Economics > F1 - Trade
|Depositing User:||Wu LI|
|Date Deposited:||30. Oct 2008 09:20|
|Last Modified:||14. Feb 2013 19:22|
Bapat, R. B., D. D. Olesky, and P. van den Driessche (1995) Perron–Frobenius Theory for a Generalized Eigenproblem, Linear and Multilinear Algebra, 40, 141–152.
Debreu, G. and I. N. Herstein (1953) Nonnegative Square Matrices, Econometrica, 21, 597-607.
Dempster, M. A. H., I. V. Evstigneev and M. I. Taksar (2006) Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the von Neumann–Gale Model, Annals of Finance, 2, 327–355.
Dorfman, R., P. A. Samuelson and R. M. Solow (1958) Linear Programming and Economic Analysis. New York: McGraw-Hill.
Evstigneev, I. V. and K. R. Schenk-Hoppe (2007) Pure and Randomized Equilibria in the Stochastic von Neumann–Gale Model, Journal of Mathematical Economics, 43, 871–887.
Gale, D. (1956) The Closed Linear Model of Production, in Linear Inequalities and Related Systems, Ed. By H. W. Kuhn and A. W. Tucker. Princeton, N.J.: Princeton University Press, 285-303.
Gale, D. (1960) The Theory of Linear Economic Models. New York: McGraw-Hill.
Horn, R. A., and C. R. Johnson (1990) Matrix Analysis. Cambridge: Cambridge University Press.
Kemeny, J. G., O. Morgenstern and G. L. Thompson. (1956) A Generalization of the von Neumann Model of an Expanding Economy, Econometrica, 24, 115-135.
Leontief, W. (1936) Quantitative Input-Output Relations in the Economic System of the United States, Review of Economics and Statistics, 18: 105-125.
Leontief, W. (1941) Structure of the American Economy, 1919-1929. Cambridge, Mass.: Harvard University Press.
Mangasarian, O. L. (1971) Perron-Frobenius Properties of Ax-λBx, Journal of Mathematical Analysis and Application, 36, 86–102.
McKenzie, L. W. (1963) Turnpike Theorems for a Generalized Leontief Model, Econometrica, 31, 165-180.
McKenzie, L. W. (1976) Turnpike Theory, Econometrica, 44, 841-865.
Mehrmann, V., R. Nabben and E. Virnik (2008) Generalisation of the Perron–Frobenius Theory to Matrix Pencils, Linear Algebra and its Applications, 428, 20–38.
Morishima, M. (1960) Economic Expansion and the Interest Rate in Generalized von Neumann Models, Econometrica, 28, 352-363.
Morishima, M. (1964) Equilibrium, Stability and Growth: A Multi-sectoral Analysis. New York: Oxford University Press.
von Neumann, J. (1945) A Model of General Economic Equilibrium, Review of Economic Studies, 13, 1–9.
Solow, R, and P. Samuelson (1953) Balanced Growth under Constant Returns to Scale, Econometrica, 21, 412-424.
Sraffa, P. (1960) Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press.