Eigenvalue distribution and the production price-profit rate relationship in linear single-product systems: theory and empirical evidence

Mariolis, Theodore and Tsoulfidis, Lefteris (2010): Eigenvalue distribution and the production price-profit rate relationship in linear single-product systems: theory and empirical evidence.

Abstract

A typical finding in many empirical studies is that the production price-profit rate relationship is, by and large, monotonic. This paper derives, in terms of the usual single-product model, the spectral conditions that make possible the appearance of such monotonicity. Furthermore, using data from input-output tables for a number of countries and years, it examines the extent to which actual economies fulfil those spectral conditions.

• Item Type: MPRA Paper
• Language: English
• Keywords: Eigenvalue Distribution; Production Prices; Spectral Analysis; Standard Systems
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D46 - Value Theory; B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B51 - Socialist ; Marxian ; Sraffian; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D57 - Input-Output Tables and Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67 - Input-Output Models; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E11 - Marxian ; Sraffian ; Kaleckian

References

Aruka, Y. (1991) Generalized Goodwin’s theorems on general coordinates, Structural Change and Economic Dynamics, 2, pp. 69-91.

Bailey, K. D. (1985) Entropy measures of inequality, Sociological Inquiry, 55, pp. 200-211.

Bidard, C. (1991) Prix, Reproduction, Rareté (Paris: Dunod).

Bidard, C. and Ehrbar, H. G. (2007) Relative prices in the Classical theory: facts and figures, Bulletin of Political Economy, 1, pp. 161-211.

Bidard, C. and Salvadori, N. (1995) Duality between prices and techniques, European Journal of Political Economy, 11, pp. 379-389.

Bienenfeld, M. (1988) Regularity in price changes as an effect of changes in distribution, Cambridge Journal of Economics, 12, pp. 247-255.

Bródy, A. (1970) Proportions, Prices and Planning. A Mathematical Restatement of the Labor Theory of Value (Amsterdam: North Holland).

Bródy, A. (1997) The second eigenvalue of the Leontief matrix, Economic Systems Research, 9, pp. 253-258.

Caravale, G. and Tosato, D. (1980) Ricardo and the Theory of Value and Distribution (London: Routledge).

Cekota, J (1988) Technological change in Canada (1961-80): an application of the surrogate wage function, Canadian Journal of Economics, 21, pp. 348-358.

Chilcote, E. B. (1997) Inter Industry Structure, Relative Prices, and Productivity: An Input-Output Study of the U.S. and O.E.C.D. Countries, Ph.D. Dissertation, New School for Social Research, Mimeo.

Da Silva, E. A. and Rosinger, J. - L. (1992) Prices, wages and profits in Brazil: an input-output Analysis, 1975, in: F. Moseley and E. N. Wolff (Eds) (1992) International Perspectives on Profitability and Accumulation, pp. 155-173 (Aldershot: Edward Elgar).

Finkelstein, Μ. Ο. and Friedberg, R. M. (1967) The Application of an entropy theory of concentration to the Clayton Act, The Yale Law Journal, 76, pp. 677-717.

Garegnani, P. (1970) Heterogeneous capital, the production function and the theory of distribution, Review of Economic Studies, 37, pp. 407-436.

Goldberg, G., Okunev, P., Neumann, M. and Schneider, H. (2000) Distribution of subdominant eigenvalues of random matrices, Methodology and Computing in Applied Probability, 2, pp. 137-151.

Goodwin, R. M. (1976) Use of normalized general co-ordinates in linear value and distribution theory, in: K. R. Polenske and J. V. Skolka (Eds) (1976) Advances in Input-Output Analysis, pp. 581-602 (Cambridge, MA: Ballinger).

Goodwin, R. M. (1977) Capital theory in orthogonalised general co-ordinates, in: R. M. Goodwin (1983) Essays in Linear Economic Structures, pp. 153-172 (London: Macmillan).

Han, Z. and Schefold, B. (2006) An empirical investigation of paradoxes: reswitching and reverse capital deepening in capital theory, Cambridge Journal of Economics, 30, pp. 737-765.

Horn, R. and Johnson, C. R. (1990) Matrix Analysis (Cambridge: Cambridge University Press).

Jasso, G. (1982) Measuring inequality: using the geometric mean/arithmetic mean ratio, Sociological Methods and Research, 10, pp. 303-326.

Juillard, M. (1986) Τhe Input-output Database for a Departmental Study of the US Economy. New York, New School for Social Research, Mimeo.

Kalman, R. E. (1961) On the general theory of control systems, in: Proceedings of the First International Congress on Automatic Control, vol. 1, pp. 481-492 (London: Butterworths).

Krelle, W. (1977) Basic facts in capital theory. Some lessons from the controversy in capital theory, Revue d’ Économie Politique, 87, pp. 282-329.

Kurz, H. D. and Salvadori, N. (1995) Theory of Production. A Long-Period Analysis (Cambridge: Cambridge University Press).

Leontief, W. (1985) Technological change, prices, wages and rates of return on capital in the U.S. economy, in: W. Leontief (1986) Input-Output Economics, pp. 392-417 (Oxford: Oxford University Press).

Mainwaring, L. (1978) The interest rate equalisation theorem with non-traded goods, Journal of International Economics, 8, pp. 11-19 (reprinted in: I. Steedman (Ed.) (1979)).

Mariolis, T. (2003) Controllability, observability, regularity, and the so-called problem of transforming values into prices of production, Asian-African Journal of Economics and Econometrics, 3, pp. 113-127.

Mariolis, T. (2004) A Sraffian approach to the Stolper-Samuelson theorem, Asian-African Journal of Economics and Econometrics, 4, pp. 1-11.

Mariolis, T. (2010) Norm bounds for a transformed price vector in Sraffian systems, Applied Mathematical Sciences, 4, pp. 551-574.

Mariolis, T. and Tsoulfidis, L. (2009) Decomposing the changes in production prices into ‘capital-intensity’ and ‘price’ effects: theory and evidence from the Chinese economy, Contributions to Political Economy, 28, pp. 1-22.

Mariolis, T. and Tsoulfidis, L. (2010) Measures of production price-labour value deviation and income distribution in actual economies: a note, Metroeconomica, 61, pp. 701-710 (enlarged version: Measures of production price-labour value deviation and income distribution in actual economies: theory and empirical evidence, Discussion Paper No. 02/2010, Discussion Paper Series, University of Macedonia, Department of Economics, http://econlab.uom.gr/~econwp/pdf/ dp0210.pdf).

Mariolis, T., Soklis, G. and Iliadi, F. (2010) Eigenvalue distribution and Bienenfeld’s quadratic formula (in Greek), Internal Report of the ‘Study Group on Sraffian Economics’, July 2010, Department of Public Administration, Panteion University.

Marzi, G. (1994) Vertically integrated sectors and the empirics of structural changes, Structural Change and Economic Dynamics, 5, pp. 155-175.

Mathur, P. N. (1977) A study of sectoral prices and their movements in the British economy in an input-output framework, in: W. Leontief (Ed.) (1977) Structure, System and Economic Policy, pp. 29-47 (Cambridge: Cambridge University Press).

Metcalfe, J. S. and Steedman, I. (1979) Heterogeneous capital and the Heckscher- Ohlin-Samuelson theory of trade, in: I. Steedman (Ed.) (1979) Fundamental Issues in Trade Theory, pp. 64-76 (London: Macmillan).

Ochoa, E. (1984) Labor values and prices of production: an interindustry study of the U.S. economy, 1947-1972. Ph.D. Dissertation, New School for Social Research, New York, Mimeo.

Parys, W. (1982) The deviation of prices from labor values, The American Economic Review, 72, 1208-1212.

Pasinetti, L. (1973) The notion of vertical integration in economic analysis, Metroeconomica, 25, pp. 1-29.

Pasinetti, L. (1977) Lectures on the Theory of Production (New York: Columbia University Press).

Petrović, P. (1987) The deviation of production prices from labour values: some methodological and empirical evidence, Cambridge Journal of Economics, 11, pp. 197-210.

Petrović, P. (1991) Shape of a wage-profit curve, some methodology and empirical evidence, Metroeconomica, 42, pp. 93-112.

Reati, A. (1986) La transformation des valeurs en prix non concurrentiels, Économie Appliquée, 39, pp. 157-179.

Ricardo, D. (1951) The Works and Correspondence of David Ricardo, vol. 1, edited by P. Sraffa with the collaboration of M. H. Dobb (Cambridge: Cambridge University Press).

Rothblum, U. G. and Tan, C. P. (1985) Upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices, Linear Algebra and its Applications, 66, pp. 45-86.

Schefold, B. (1971) Mr. Sraffa on joint production. Ph.D. thesis, University of Basle, Mimeo.

Schefold, B. (1976) Relative prices as a function of the rate of profit: a mathematical note, Journal of Economics, 36, pp. 21-48.

Schefold, B. (1978) On counting equations, Journal of Economics, 38, pp. 253-285.

Schefold, B. (2008a) C.E.S. production functions in the light of the Cambridge critique, Journal of Macroeconomics, 30, pp. 783-797.

Schefold, B. (2008b) Families of strongly curved and of nearly linear wage curves: a contribution to the debate about the surrogate production function, Bulletin of Political Economy, 2, pp. 1-24.

Schefold, B. (2008c) Approximate surrogate production functions, Institut für Volkswirtschaftslehre, Johann Wolfgang Goethe-Universität, Mimeo.

Sekerka, B., Kyn, O. and Hejl, L. (1970) Price system computable from input-output coefficients, in: A. P. Carter and A. Bródy (Eds) (1970) Contributions to Input-Output Analysis, pp. 183-203 (Amsterdam: North-Holland).

Shaikh, A. M. (1998) The empirical strength of the labour theory of value, in: R. Bellofiore (Ed.) (1998) Marxian Economics: A Reappraisal, vol. 2, pp. 225-251 (New York: St. Martin’s Press).

Sraffa, P. (1960) Production of Commodities by Means of Commodities. Prelude to a Critique of Economic Theory (Cambridge: Cambridge University Press).

Steedman, I. (1977) Marx after Sraffa (London: New Left Books).

Steedman, I. (1999a) Values do follow a simple rule!, Economic Systems Research, 11, pp. 5-11.

Steedman, I. (1999b) Vertical integration and ‘reduction to dated quantities of labour’, in: G. Mongiovi and F. Petri (Eds) (1999) Value Distribution and Capital. Essays in Honour of Pierangelo Garegnani, pp. 314-318 (London and New York: Routledge).

Steedman, I. and Tomkins, J. (1998) On measuring the deviation of prices from values, Cambridge Journal of Economics, 22, pp. 379-385.

Steenge, A. E. (1995) Sraffa and Goodwin: a unifying framework for standards of value in the income distribution problem, Journal of Economics, 62, pp. 55-75.

Steenge, A. E. and Thissen, M. J. P. M. (2005) A new matrix theorem: interpretation in terms of internal trade structure and implications for dynamic systems, Journal of Economics, 84, pp. 71-94.

Sun, G.-Z. (2008) The first two eigenvalues of large random matrices and Brody's hypothesis on the stability of large input-output systems, Economic Systems Research, 20, pp. 429-432.

Tsoulfidis, L. (2008) Price-value deviations: further evidence from input-output data of Japan, International Review of Applied Economics, 22, pp. 707-724.

Tsoulfidis, L. (2010) Competing Schools of Economic Thought (Heidelberg: Springer).

Tsoulfidis, L. and Maniatis, Th. (2002) Values, prices of production and market prices: some more evidence from the Greek economy, Cambridge Journal of Economics, 26, pp. 359-369.

Tsoulfidis, L. and Rieu, D.-M. (2006) Labour values, prices of production and wage-profit rate frontiers of the Korean economy, Seoul Journal of Economics, 19, pp. 275-295.

Tsoulfidis, L. and Mariolis, T. (2007) Labour values, prices of production and the effects of income distribution: evidence from the Greek economy, Economic Systems Research, 19, pp. 425-437.

Velupillai, K. (Ed.) (1990) Nonlinear and Multisectoral Macrodynamics (New York: New York University Press).