# Capital theory ‘paradoxes’ and paradoxical results: resolved or continued?

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## Abstract

Capital theory controversies and ‘paradoxes’ showed that, due to price-feedback effects, the wage–production price–profit rate curves may display shapes inconsistent with the requirements of the neoclassical theory of value and distribution. Subsequent findings on a number of quite diverse actual single-product economies suggested that the impact of those effects is of limited empirical significance. This paper argues that, by focusing on the distributions of the eigenvalues and singular values of the system matrices, we can further study these issues and derive some meaningful theoretical results consistent with the available empirical evidence. Consequently, the real paradox, in the sense of knowledge vacuum and, thus, requiring further research, is the distributions of the characteristic values and not really the ‘paradoxes in capital theory’.

## Keywords

Capital theory Characteristic value distributions Hyper-basic industry Spectral decompositions Wage–price–profit rate curves## JEL Classification

B21 B51 C67 D57## Notes

### Acknowledgments

The material in the manuscript has been acquired according to modern ethical standards and does not contain material copied from anyone else without their written permission and there is no conflict of interest. We are indebted to two anonymous referees of this journal for helpful remarks and hints. An earlier version of this paper was presented at the 19th European Society for the History of Economic Thought Conference, 14–16 May 2015, Roma Tre University, Italy. We thank the participants of this conference and especially Heinz D. Kurz, Fabio Petri, Bertram Schefold, Persefoni Tsaliki and Stefano Zambelli for their comments, criticisms and discussions. The usual caveat applies.

## References

- Angeloussis A (2006) An empirical investigation of the reswitching of techniques phenomenon for the Greek economy, 1988–1992. Master’s Thesis, Department of Public Administration, Panteion University, Athens, Greece (in Greek)Google Scholar
- Aruka Y (1991) Generalized Goodwin’s theorems on general coordinates. Struct Change Econ Dyn 2(1):69–91. Reprinted in Aruka Y (Ed) (2011)
*Complexities of production and interacting human behaviour*(pp 39–66), Heidelberg: Physica-VerlagGoogle Scholar - Bidard C, Ehrbar HG (2007) Relative prices in the classical theory: facts and figures. Bull Polit Econ 1(2):161–211Google Scholar
- Bienenfeld M (1988) Regularity in price changes as an effect of changes in distribution. Camb J Econ 12(2):247–255Google Scholar
- Bródy A (1970) Proportions, prices and planning: a mathematical restatement of the labor theory of value. Amsterdam, North-Holland, Budapest, Akadémiai KiadóGoogle Scholar
- Garegnani P (1970) Heterogeneous capital, the production function and the theory of distribution. Rev Econ Stud 37(3):407–436CrossRefGoogle Scholar
- Han Z, Schefold B (2006) An empirical investigation of paradoxes: reswitching and reverse capital deepening in capital theory. Camb J Econ 30(5):737–765CrossRefGoogle Scholar
- Horn RA, Johnson CR (1991) Topics in matrix analysis. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Iliadi F, Mariolis T, Soklis G, Tsoulfidis L (2014) Bienenfeld’s approximation of production prices and eigenvalue distribution: further evidence from five European economies. Contrib Polit Econ 33(1):35–54CrossRefGoogle Scholar
- Krelle W (1977) Basic facts in capital theory: some lessons from the controversy in capital theory. Revue d’Économie Politique 87(2):282–329Google Scholar
- Kurz HD, Salvadori N (1995) Theory of production: a long-period analysis. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Leontief W (1953) Studies in the structure of the American economy. Oxford University Press, New YorkGoogle Scholar
- Mariolis T (2013) Applying the mean absolute eigen-deviation of labour commanded prices from labour values to actual economies. Appl Math Sci 7(104):5193–5204CrossRefGoogle Scholar
- Mariolis T (2015a) Norm bounds and a homographic approximation for the wage-profit curve. Metroeconomica 66(2):263–283CrossRefGoogle Scholar
- Mariolis T (2015b) Testing Bienenfeld’s second-order approximation for the wage-profit curve. Bull Polit Econ 9(2) (forthcoming)Google Scholar
- Mariolis T, Soklis G (2010) Additive labour values and prices of production: evidence from the supply and use tables of the French, German and Greek economies. Econ Issue 15(2):87–107Google Scholar
- Mariolis T, Tsoulfidis L (2009) Decomposing the changes in production prices into ‘capital-intensity’ and ‘price’ effects: theory and evidence from the Chinese economy. Contrib Polit Econ 28(1):1–22CrossRefGoogle Scholar
- Mariolis T, Tsoulfidis L (2011) Eigenvalue distribution and the production price-profit rate relationship: theory and empirical evidence. Evolut Inst Econ Rev 8(1):87–122CrossRefGoogle Scholar
- Mariolis T, Tsoulfidis L (2014) On Bródy’s conjecture: theory, facts and figures about instability of the US economy. Econ Syst Res 26(2):209–223CrossRefGoogle Scholar
- Mariolis T, Tsoulfidis L (2016) Modern classical economics and reality: a spectral analysis of the theory of value and distribution. Springer, TokyoCrossRefGoogle Scholar
- Mariolis T, Soklis G, Zouvela E (2013) Testing Böhm-Bawerk’s theory of capital: some evidence from the Finnish economy. Rev Aust Econ 26(2):207–220CrossRefGoogle Scholar
- Metcalfe JS, Steedman I (1981) Some long-run theory of employment, income distribution and the exchange rate. Manch School 49(1):1–20CrossRefGoogle Scholar
- Meyer CD (2001) Matrix analysis and applied linear algebra. Society for Industrial and Applied Mathematics, New YorkGoogle Scholar
- Neumann JV (1937) Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes. In: Menger K (ed) Ergebnisse eines Mathematischen Kolloquiums, 8. Deuticke, Leipzig, pp 73–83Google Scholar
- Ochoa E (1989) Value, prices and wage-profit curves in the U.S. economy. Camb J Econ 13(3):413–429Google Scholar
- Pasinetti L (1977) Lectures on the theory of production. Columbia University Press, New YorkCrossRefGoogle Scholar
- Petrović P (1991) Shape of a wage-profit curve, some methodology and empirical evidence. Metroeconomica 42(2):93–112CrossRefGoogle Scholar
- Schefold B (1971)
*Mr. Sraffa on joint production*. Ph.D. Thesis, University of Basle, Basle, SwitzerlandGoogle Scholar - Schefold B (2008) Families of strongly curved and of nearly linear wage curves: a contribution to the debate about the surrogate production function. Bull Polit Econ 2(1):1–24Google Scholar
- Sekerka B, Kyn O, Hejl L (1970) Price system computable from input–output coefficients. In: Carter AP, Bródy A (eds) Contributions to input–output analysis. North-Holland, Amsterdam, pp 183–203Google Scholar
- Shaikh AM (1998) The empirical strength of the labour theory of value. In: Bellofiore R (ed) Marxian economics: a reappraisal, vol 2. St. Martin’s Press, New York, pp 225–251Google Scholar
- Shaikh AM (2012) The empirical linearity of Sraffa’s critical output-capital ratios. In: Gehrke C, Salvadori N, Steedman I, Sturn R (eds) Classical political economy and modern theory: essays in honour of Heinz Kurz. Routledge, London, New York, pp 89–101Google Scholar
- Soklis G (2011) Shape of wage-profit curves in joint production systems: evidence from the supply and use tables of the Finnish economy. Metroeconomica 62(4):548–560CrossRefGoogle Scholar
- Soklis G (2015) Labour versus alternative value bases in actual joint production systems. Bull Polit Econ 9(1):1–31Google Scholar
- Spaventa L (1970) Rate of profit, rate of growth, and capital intensity in a simple production model. Oxf Econ Papers 22(2):129–147Google Scholar
- Sraffa P (1960) Production of commodities by means of commodities. Prelude to a critique of economic theory. Cambridge University Press, CambridgeGoogle Scholar
- Steedman I (1999) Vertical integration and ‘reduction to dated quantities of labour’. In: Mongiovi G, Petri F (eds) Value distribution and capital: essays in honour of Pierangelo Garegnani. Routledge, London, New York, pp 314–318Google Scholar
- Treitel S, Shanks JL (1971) The design of multistage separable planar filters. Inst Electr Electron Eng Trans Geosci Electron 9(1):10–27Google Scholar
- Tsoulfidis L, Mariolis T (2007) Labour values, prices of production and the effects of income distribution: evidence from the Greek economy. Econ Syst Res 19(4):425–437CrossRefGoogle Scholar