THE TRIANGULAR FORM OF LEONTIEF’S MATRIX
Resumen
This paper presents an alternative proof of the equivalence between the existence of viable solutions to Leontief’s model and the Hawkins and Simon’s condition (H-S). In addition, it exposes the peculiar
economic significance of the coefficients in the principal diagonal of the triangular form of Leontief’s matrix, which permits us – among other things – to appreciate the tight relation between the economic and the
mathematical conditions in the solution to the model. Moreover, the paper identifies some other mathematical propositions equivalent to (H-S) possessing economic interest.
Descargas
Citas
Benítez, A. (2009). “La forma triangular de la matriz de Leontief”. Economía: Teoría y Práctica, num. 30, 115-131.
Berman, A. & Plemmons, R. J. (1994). Nonnegative Matrices in the Mathematical Sciences, Philadelphia, SCIAM.
Chenery, H. B. & Clark, P. G. (1959). Interindustry Economics, New York, Wiley.
Dorfman, R., Samuelson P. & Solow R. M. (1987). Linear Programming and Economic Analysis, New York, Dover Publications, Inc.
Gantmatcher, F. R. (1960). The Theory of Matrices, New York, Chelsea Publishing Company.
Gale, D. (1960). The Theory of Linear Economic Models, Chicago, The University of Chicago Press.
Georgescu-Roegen, N. (1950). “Leontief’s system in the light of recent results”, Review of Economics and Statistics, XXXII.
Georgescu-Roegen, N. (1966). Analytical Economics, Cambridge, Harvard University Press.
Goldberg, J. L. (1991). Matrix Theory with Applications, New York, Mc- Graw Hill Inc.
Hawkins, D. (1948). “Some conditions of macroeconomics stability”, Econométrica, num. 16, 309–322.
Hawkins, D. & Simon, H. A. (1949). “Note: Some conditions of macroeconomics stability”, New York, Econometrica, num. 17, 245–248.
Leontief, W. (1941). The Structure of the American Economy 1919-1929, Cambridge, Cambridge University Press.
Leontief, W. (1966). Input-Output Economics, New York, Oxford University Press.
McKenzie, L. W. (1960). “Matrices with dominant diagonals and economic theory”. In K. J. Arrow, S. Karlin & F. Suppes eds. Mathematical Methods in the Social Sciences, Stanford, Stanford University Press.
Nikaido, H. (1970). Introduction to Sets and Mappings in Modern Economics, Amsterdam, North Holland Publishing.
Seneta, E. (1973). Non-Negative Matrices, New York, John Wiley and Sons.
Takayama, A. (1985). Mathematical Economics, Cambridge, Cambridge University Press.
ten Raa, T. (2005). The Economics of Input–Output Analysis, Cambridge, Cambridge University Press.
Uribe, P. (1977). Análisis de Actividades y Teoría del Capital, Guadalajara, Universidad de Guadalajara.
Derechos de autor 2013 Denarius
Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0.