Necessary and Sufficient Conditions for Constant Prices in a Sraffa’s Model

Giorgi, Giorgio

doi:10.2478/candc-2022-0020

Abstract

We give a simple and direct proof of necessary and sufficient conditions to have constant equilibrium prices in a simple Sraffa’s production model. We make some remarks on the linearity of the relation between profit rate and wage rate.

References

ABraham-Frois, G. and Berrebi, E. (1979) Theory of Value, Prices and Accumulation. A Mathematical Integration of Marx, von Neumann and Sraffa. Cambridge University Press, Cambridge.
Search in Google Scholar Back to article
Abraham-Frois, G. and Berrebi, E. (1978) Pluralité de marchandises étalons: existence et construction. Revue d’Economie Politique, 88, 688–712.
Search in Google Scholar Back to article
Abraham-Frois, G. and Berrebi, E. (1989) A la recherche de l’étalon invariable des valeurs. Revue d’Economie Politique, 99, 123-140.
Search in Google Scholar Back to article
Arena, R. (Ed.) (1990) Sraffa: Trente Ans Après. Presses Universitaires de France, Paris.
Search in Google Scholar Back to article
Baldone, S. (2006) On Sraffa’s standard commodity: is its price invariant with respect to changes in economic distribution? Cambridge Journal of Economics, 30, 313-319.
Search in Google Scholar Back to article
Bellino, E. (2004) On Sraffa’s standard commodity. Cambridge Journal of Economics, 28, 121-132.
Search in Google Scholar Back to article
Berman, A. and Plemmons, R. J. (2014) Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York.
Search in Google Scholar Back to article
Bidard, C. (1978) Sur le système étalon de Sraffa. Revue d’Economie Politique, 88, 739-745.
Search in Google Scholar Back to article
Bidard, C. (2004) Prices, Reproduction, Scarcity. Cambridge University Press, Cambridge, U. K.
Search in Google Scholar Back to article
Bidard, C. (2020) Conditions for the linearity of the wage curve. Metroeconomica, 71, 449-455.
Search in Google Scholar Back to article
Bidard, C. and Salvadori, N. (1995) Duality between prices and techniques. European Journal of Political Economy, 11, 379-389.
Search in Google Scholar Back to article
Bharadway, K. and Schefold, B. (Eds.) (1992) Essays on Piero Sraffa: Critical Perspectives on the Revival of Classical Theory. Routledge, London.
Search in Google Scholar Back to article
Blakley, G. R. and Gossling, W. F. (1967) The existence, uniqueness and stability of the standard system. The Review of Economic Studies, 34, 427-431.
Search in Google Scholar Back to article
Blaug, M. (Ed.) (1992) Piero Sraffa (1898-1983). Edward Elgar Publ. Limited, Aldershot.
Search in Google Scholar Back to article
Burmeister, E. (1968) On a theorem of Sraffa. Economica, 35, 83-87.
Search in Google Scholar Back to article
Burmeister, E. (2008) Equal organic composition of capital and regularity. Metroeconomica, 59, 323-346.
Search in Google Scholar Back to article
Debreu, G. and Herstein, I. N. (1953) Nonnegative square matrices. Econometrica, 21, 597-607.
Search in Google Scholar Back to article
Emmenegger, J. F., Chable, D. L., NOUR ELDIN, H. A. and KNOLLE, H. (2020) Sraffa and Leontief Revisited. De Gruyter, Amsterdam.
Search in Google Scholar Back to article
Gantmacher, F. R. (1959) Applications of the Theory of Matrices. Interscience, New York.
Search in Google Scholar Back to article
Giorgi, G. (1987) On the linearity of the distribution function and the fundamental Marxian theorem in simple Sraffa’s models. Economic Notes by Monte dei Paschi di Siena, 16, 2, 48-59. Reprinted in J. C. Wood (Ed.) Piero Sraffa. Critical Assessments, Vol. III. Routledge, London, 1995, 67-76.
Search in Google Scholar Back to article
Giorgi, G. and Zuccotti, C. (2012) On the linearity of the wage-profit relation in a Sraffa’s model: a mathematical summing-up. Decisions in Economics and Finance, 45, 59-73.
Search in Google Scholar Back to article
Hall, L. J. (2012) A mathematical study of the Sraffa Model. Ciencias Economicas, 30, 77-88.
Search in Google Scholar Back to article
Kurz, H. D. (Ed.) (2000) Critical Essays on Piero Sraffa’s Legacy in Economics. Cambridge Univ. Press, Cambridge, U. K.
Search in Google Scholar Back to article
Kurz, H. D. and Salvadori, N. (1995) Theory of Production. A Long-Period Analysis. Cambridge Univ. Press, Cambridge.
Search in Google Scholar Back to article
Laurent, S. (2018) The mathematical justification of the Leontief and Sraffa input-output systems. U.U.D.M. Project Report 2018:43, Uppsala Universitet.
Search in Google Scholar Back to article
Miyao, T. (1977) A generalization of Sraffa’s standard commodity and its complete characterization. International Economic Review, 18, 151-162.
Search in Google Scholar Back to article
Nikaido, H. (1968) Convex Structures and Economic Theory. Academic Press, New York.
Search in Google Scholar Back to article
Nikaido, H. (1970) Introduction to Sets and Mappings in Modern Economics. North Holland, Amsterdam.
Search in Google Scholar Back to article
Pasinetti, L. L. (1973) The notion of vertical integration in economic analysis. Metroeconomica, 25, 1-29. Reprinted in L. L. Pasinetti (Ed.), Essays in the Theory of Joint Production. Macmillan, London, 16-43.
Search in Google Scholar Back to article
Pasinetti, L. L. (1979) Lectures on the Theory of Production. Palgrave Macmillan, London.
Search in Google Scholar Back to article
Schefold, B. (1976) Relative prices as a function of the rate of profit: a mathematical note. Zeitschrift für Nationalökonomie, 36, 21-18.
Search in Google Scholar Back to article
Schefold, B. (2015) Mr Sraffa on Joint Production and Other Essays. Routledge, London.
Search in Google Scholar Back to article
Shaikh, A. (2016) Capitalism: Computation, Conflict, Crises. Oxford University Press, Oxford, U. K.
Search in Google Scholar Back to article
Sinha, A. (2010) Theories of Value from Adam Smith to Piero Sraffa. Routledge, London.
Search in Google Scholar Back to article
Sinha, A. (2016) A Revolution in Economic Theory: The Economics of Piero Sraffa. Palgrave Mac Millan, Springer International Publishing AG Switzerland.
Search in Google Scholar Back to article
Sinha, A. (Ed.) (2021) A Reflection on Sraffa’s Revolution in Economic Theory. Palgrave Macmillan, Springer Nature Switzerland AG.
Search in Google Scholar Back to article
Sinha, A. and Dupertuis, M.-S. (2009) Sraffa and the question of equilibrium. Cahiers d’Economie Politique, 56, 91-100.
Search in Google Scholar Back to article
Sraffa, P. (1960) Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory. Cambridge Univ. Press, Cambridge.
Search in Google Scholar Back to article
Takayama, A. (1985) Mathematical Economics. Cambridge Univ. Press, Cambridge.
Search in Google Scholar Back to article
Tucci, M. (1976) A mathematical formalization of a Sraffa model. Metroeconomica, 28, 16-24.
Search in Google Scholar Back to article
Wood, J. C. (Ed.) (1995) Piero Sraffa: Critical Assessments. Routledge, London.
Search in Google Scholar Back to article
Woods, J. E. (1978) Mathematical Economics. Longman, London.
Search in Google Scholar Back to article
Woods, J. E. (1985) Exercises in relative price invariance. Giornale degli Economisti e Annali di Economia, 44, 135-152.
Search in Google Scholar Back to article
Woods, J. E. (1990) The Production of Commodities: an Introduction to Sraffa. Macmillan, London.
Search in Google Scholar Back to article

Necessary and Sufficient Conditions for Constant Prices in a Sraffa’s Model

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