Eigenvalue Distribution and the Production Price-Profit Rate Relationship: Theory and Empirical Evidence

  • Theodore Mariolis
  • Lefteris Tsoulfidis


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.


eigenvalue distribution production prices spectral analysis standard systems 


B51 C67 D46 D57 E11 


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  1. Aruka, Y. (1991) “Generalized Goodwin’ s theorems on general coordinates,” Structural Change and Economic Dynamics 2: 69–91.CrossRefGoogle Scholar
  2. Bailey, K. D. (1985) Entropy measures of inequality, Sociological Inquiry 55: 200–211.CrossRefGoogle Scholar
  3. Bidard, C. (1991) Prix, Reproduction, Rareté (in French), Dunod, Paris.Google Scholar
  4. Bidard, C. and H. G. Ehrbar (2007) “Relative prices in the classical theory: facts and figures,” Bulletin of Political Economy 1: 161–211.Google Scholar
  5. Bidard, C. and N. Salvadori (1995) “Duality between prices and techniques,” European Journal of Political Economy 11: 379–389.CrossRefGoogle Scholar
  6. Bienenfeld, M. (1988) “Regularity in price changes as an effect of changes in distribution,” Cambridge Journal of Economics 12: 247–255.Google Scholar
  7. Bródy, A. (1970) Proportions, Prices and Planning. A Mathematical Restatement of the Labor Theory of value, North Holland, Amsterdam.Google Scholar
  8. Bródy, A. (1997) “The second eigenvalue of the Leontief matrix,” Economic Systems Research 9: 253–258.CrossRefGoogle Scholar
  9. Caravale, G and D. Tosato (1980) Ricardo and the Theory of Value and Distribution, Routledge, London.Google Scholar
  10. Cekota, J. (1988) “Technological change in Canada (1961–1980): an application of the surrogate wage function,” Canadian Journal of Economics 21: 348–358.CrossRefGoogle Scholar
  11. 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.)Google Scholar
  12. Da Silva, E. A. and J.-L. Rosinger (1992) Prices, wages and profits in Brazil: an input-output Analysis, 1975, in F. Moseley and E. N. Wolff (eds) International Perspectives on Profitability and Accumulation, Edward Elgar, Aldershot, pp. 155–173.Google Scholar
  13. Finkelstein, M. O. and R. M. Friedberg (1967) “The Application of an entropy theory of concentration to the Clayton Act,” The Yale Law Journal 76: 677–717.CrossRefGoogle Scholar
  14. Garegnani, P. (1970) “Heterogeneous capital, the production function and the theory of distribution,” Review of Economic Studies 37: 407–436.CrossRefGoogle Scholar
  15. Goldberg, G., P. Okunev, M. Neumann and H. Schneider (2000) “Distribution of subdominant eigenvalues of random matrices,” Methodology and Computing in Applied Probability 2: 137–151.CrossRefGoogle Scholar
  16. 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) Advances in Input-Output Analysis, Ballinger, Cambridge, MA, pp. 581–602.Google Scholar
  17. Goodwin, R. M. (1977) “Capital theory in orthogonalised general co-ordinates,” in R. M. Goodwin (1983) Essays in Linear Economic Structures, Macmillan, London, pp. 153–172.Google Scholar
  18. Hamilton, C. (1986) “A general equilibrium model of structural change and economic growth, with application to South Korea,” Journal of Development Economics 23: 67–88.CrossRefGoogle Scholar
  19. Han, Z. and B. Schefold (2006) “An empirical investigation of paradoxes: reswitching and reverse capital deepening in capital theory,” Cambridge Journal of Economics 30: 737–765.CrossRefGoogle Scholar
  20. Jasso, G. (1982) “Measuring inequality: using the geometric mean/arithmetic mean ratio,” Sociological Methods and Research 10: 303–326.CrossRefGoogle Scholar
  21. Juillard, M. (1986) The Input-output Database for a Departmental Study of the US Economy, New York, New School for Social Research, Mimeo.Google Scholar
  22. Kaiman, R. E. (1961) “On the general theory of control systems,” in Proceedings of the First International Congress on Automatic Control, vol. 1, Butterworths, London, pp. 481–492.Google Scholar
  23. Krelle, W. (1977) “Basic facts in capital theory. Some lessons from the controversy in capital theory,” Revue d’ Eonomie Politique 87: 282–329.Google Scholar
  24. Kurz, H. D. and N. Salvadori (1995) Theory of Production. A Long-Period Analysis, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  25. 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, Oxford University Press, Oxford, pp. 392–417.Google Scholar
  26. Mainwaring, L. (1978) “The interest rate equalisation theorem with non-traded goods,” Journal of International Economics 8: 11–19 [Reprinted in I. Steedman (ed) (1979)].CrossRefGoogle Scholar
  27. 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: 113–127.Google Scholar
  28. Mariolis, T. (2004) “A Sraffian approach to the Stolper-Samuelson theorem,” Asian-African Journal of Economics and Econometrics 4: 1–11.Google Scholar
  29. Mariolis, T. (2010) “Norm bounds for a transformed price vector in Sraffian systems,” Applied Mathematical Sciences 4: 551–574.Google Scholar
  30. Mariolis, T. and L. Tsoulfidis (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: 1–22.CrossRefGoogle Scholar
  31. Mariolis, T. and L. Tsoulfidis (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, Scholar
  32. Mariolis, T., G. Soklis and F. Iliadi (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.)Google Scholar
  33. Marzi, G (1994) “Vertically integrated sectors and the empirics of structural change,” Structural Change and Economic Dynamics 5: 155–175.CrossRefGoogle Scholar
  34. 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) Structure, System and Economic Policy, Cambridge University Press, Cambridge, pp. 29–47.Google Scholar
  35. Metcalfe, J. S. and I. Steedman (1979) “Heterogeneous capital and the Heckscher-Ohlin-Samuelson theory of trade,” in I. Steedman (ed) (1979) Fundamental Issues in Trade Theory, Macmillan, London, pp. 64–76.Google Scholar
  36. 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).Google Scholar
  37. Parys, W. (1982) “The deviation of prices from labor values,” The American Economic Review 72: 1208–1212.Google Scholar
  38. Pasinetti, L. (1973) “The notion of vertical integration in economic analysis,” Metroeconomica 25: 1–29.CrossRefGoogle Scholar
  39. Pasinetti, L. (1977) Lectures on the Theory of Production, Columbia University Press, New York.Google Scholar
  40. Petrović, P. (1987) “The deviation of production prices from labour values: some methodological and empirical evidence,” Cambridge Journal of Economics 11: 197–210.Google Scholar
  41. Petrović, P. (1991) “Shape of a wage-profit curve, some methodology and empirical evidence,” Metroeconomica 42: 93–112.CrossRefGoogle Scholar
  42. Reati, A. (1986) “La transformation des valeurs en prix non concurrentiels” (in French), Économie Appliquée 39: 157–179.Google Scholar
  43. Ricardo, D. (1951) The Works and Correspondence of David Ricardo, vol. 1, ed. by P. Sraffa with the collaboration of M. H. Dobb, Cambridge University Press, Cambridge.Google Scholar
  44. Rothblum, U. G. and C. P. Tan (1985) “Upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices,” Linear Algebra and its Applications 66: 45–86.CrossRefGoogle Scholar
  45. Schefold, B. (1971) “Mr. Sraffa on joint production.” (Ph.D. thesis, University of Basle, Mimeo).Google Scholar
  46. Schefold, B. (1976) “Relative prices as a function of the rate of profit: a mathematical note,” Journal of Economics 36: 21–48.CrossRefGoogle Scholar
  47. Schefold, B. (1978) “On counting equations,” Journal of Economics 38: 253–285.CrossRefGoogle Scholar
  48. Schefold, B. (2008a) “C.E.S. production functions in the light of the Cambridge critique,” Journal of Macroeconomics 30: 783–797.CrossRefGoogle Scholar
  49. 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: 1–24.Google Scholar
  50. Schefold, B. (2008c) Approximate surrogate production functions, Institut für Volkswirtschaftslehre, Johann Wolfgang Goethe-Universität, Mimeo.Google Scholar
  51. Sekerka, B., O. Kyn and L. Hejl (1970) “Price system computable from input-output coefficients,” in A. P. Carter and A. Brödy (eds) Contributions to Input-Output Analysis, North-Holland, Amsterdam, pp. 183–203.Google Scholar
  52. Shaikh, A. M. (1998) “The empirical strength of the labour theory of value,” in R. Bellofiore (ed) Marxian Economics: A Reappraisal, vol. 2, St. Martin’ s Press, New York, pp. 225–251.Google Scholar
  53. Sraffa, P. (1960) Production of Commodities by Means of Commodities. Prelude to a Critique of Economic Theory, Cambridge University Press, Cambridge.Google Scholar
  54. Steedman, I. (1977) Marx after Sraffa, New Left Books, London.Google Scholar
  55. Steedman, I. (1999a) “Values do follow a simple rule!,” Economic Systems Research 11: 5–11.CrossRefGoogle Scholar
  56. Steedman, I. (1999b) “Vertical integration and ‘reduction to dated quantities of labour’,” in G. Mongiovi and F. Petri (eds) Value Distribution and Capital. Essays in Honour of Pierangelo Garegnani, Routledge, London and New York, pp. 314–318.Google Scholar
  57. Steenge, A. E. (1995) “Sraffa and Goodwin: a unifying framework for standards of value in the income distribution problem,” Journal of Economics 62: 55–75.CrossRefGoogle Scholar
  58. Steenge, A. E. and MJ.P.M. Thissen (2005) “A new matrix theorem: interpretation in terms of internal trade structure and implications for dynamic systems,” Journal of Economics 84: 71–94.CrossRefGoogle Scholar
  59. Sun, G.-Z. (2008) “The first two eigenvalues of large random matrices and Bródy’ s hypothesis on the stability of large input-output systems,” Economic Systems Research 20: 429–432.CrossRefGoogle Scholar
  60. Tsoulfidis, L. (2008) “Price-value deviations: further evidence from input-output data of Japan,” International Review of Applied Economics 22: 707–724.CrossRefGoogle Scholar
  61. Tsoulfidis, L. (2010) Competing Schools of Economic Thought, Springer, Heidelberg.Google Scholar
  62. Tsoulfidis, L. and Th. Maniatis (2002) “Values, prices of production and market prices: some more evidence from the Greek economy,” Cambridge Journal of Economics 26: 359–369.CrossRefGoogle Scholar
  63. Tsoulfidis, L. and D.-M. Rieu (2006) “Labour values, prices of production and wage-profit rate frontiers of the Korean economy,” Seoul Journal of Economics 19: 275–295.Google Scholar
  64. Tsoulfidis, L. and T. Mariolis (2007) “Labour values, prices of production and the effects of income distribution: evidence from the Greek economy,” Economic Systems Research 19: 425–437.CrossRefGoogle Scholar
  65. Velupillai, K. (ed) (1990) Nonlinear and Multisectoral Macrodynamics, New York University Press, New York.Google Scholar

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© Japan Association for Evolutionary Economics 2011

Authors and Affiliations

  1. 1.Department of Public AdministrationPanteion UniversityAthensGreece
  2. 2.Department of EconomicsUniversity of MacedoniaThessalonikiGreece

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