A Study on Dynamic General Equilibrium under the Classical Growth Framework

Li, Wu (2010): A Study on Dynamic General Equilibrium under the Classical Growth Framework.

Abstract

The equilibrium analyses under the classical growth framework mainly concern production processes so far and the utility-maximization of consumers is not considered sufficiently. Treating a consumer as a producer of labor or land-use right etc. with a utility parameter, this paper presents equilibrium formulas taking account of the utility-maximization of consumers, which may facilitate the analysis of dynamic general equilibrium involving both profit-maximizing firms and utility-maximizing consumers under the classical growth framework. For concreteness, some numerical examples with Cobb-Douglas production and utility functions are utilized to illustrate the method of the equilibrium analysis involving utility-maximizing consumers.

• Item Type: MPRA Paper
• Language: English
• Keywords: dynamic general equilibrium; utility; Sraffian system; von Neumann growth model; land rent
• Subjects: B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B51 - Socialist ; Marxian ; Sraffian; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q2 - Renewable Resources and Conservation > Q24 - Land; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D58 - Computable and Other Applied General Equilibrium Models; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67 - Input-Output Models

References

Quesnay, F. Quesnay's Tableau Economique [1759]. Edited by M. Kuczynski and R. L. Meek. London: Macmillan, 1972.

Marx, K. Capital, vol. II, English translation of Das Kapital, vol. II, edited by F. Engels (Hamburg, Meissner, 1885). Moscow: Progress Publishers, 1956.

Leontief, W. “Quantitative Input-Output Relations in the Economic System of the United States”, Review of Economics and Statistics, 18, pp. 105-125, 1936.

Leontief, W. Structure of the American Economy, 1919-1929. Cambridge, Mass.: Harvard University Press, 1941.

von Neumann, J. “A Model of General Economic Equilibrium”, Review of Economic Studies, 13, pp. 1–9, 1945.

Sraffa, P. Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press, 1960.

Kurz, H. and N. Salvadori. “‘Classical’ Roots of Input-Output Analysis: A Short Account of its Long Prehistory”, Economic Systems Research, 12(2), pp. 153-179, 2000.

Kurz, H. and N. Salvadori. “Sraffa and von Neumann”, Review of Political Economy, 13(2), pp. 161-180, 2001.

Kemeny, J. G., O. Morgenstern and G. L. Thompson. “A Generalization of the von Neumann Model of an Expanding Economy”, Econometrica, 24, pp. 115-135, 1956.

Gale, D. The Theory of Linear Economic Models. New York: McGraw-Hill, 1960.

Dorfman, R., P. A. Samuelson and R. M. Solow. Linear Programming and Economic Analysis. New York: McGraw-Hill, 1958.

McKenzie, L. W. “Turnpike Theorems for a Generalized Leontief Model”, Econometrica, 31, pp. 165-180, 1963.

McKenzie, L. W. “Turnpike Theory”, Econometrica, 44, pp. 841-865, 1976.

Dietzenbacher, E. “Perturbations of Matrices: A Theorem on the Perron Vector and its Applications to Input-output Models”, Journal of Economics, 48(4), pp. 389-412, 1988.

Hua, L. “On the Mathematical Theory of Globally Optimal Planned Economic Systems”, Proceedings of the National Academy of Sciences of the United States of America, 81, pp. 6549-6553, 1984.

Zhang, Jinshui. “A Multi-sector Nonlinear Dynamic Input-Output Model with Human Capital”, Economic Systems Research, 20(2), pp. 223-237, 2008.

Luenberger, D. Introduction to Dynamic Systems: Theory, Models, and Applications. John Wiley&Sons, 1979.

Bidard, C. Prices, Reproduction, Scarcity, Cambridge: Cambridge University Press, 2004.

Bidard, C. “General Theory of Rent”. Presented at the International Conference on Production and Distribution, Meiji University, Tokyo, Sept., 2010.

Kurz, H. “Rent Theory in a Multisectoral Model”, Oxford Economic Papers, 30(1), pp. 16-37, 1978.

Salvadori, N. “Land and Choice of Techniques within the Sraffa Framework”, Australian Economic Papers, 25, pp. 94-105, 1986.

Schefold, B. Mr. Sraffa on Joint Production and Other Essays. London: Unwin & Hyman, 1989.

Woods, J. “A Note on Rent”, Oxford Economic Papers, 39, pp. 388-411, 1987.

Li, W. “A Structural Growth Model and its Applications to Sraffa’s System”. Presented at the 18th International Input-Output Conference, Sydney, downloadable at http://www.iioa.org/Conference/18th-downable%20paper.htm, Jun., 2010.