Less is More: Capital Theory and Almost Irregular-Uncontrollable Actual Economies

Mariolis, Theodore and Tsoulfidis, Lefteris (2018): Less is More: Capital Theory and Almost Irregular-Uncontrollable Actual Economies.

Abstract

Capital theory and the associated with it price effects consequent upon changes in the distributive variables hold centre stage when it comes to the internal consistency of both classical and neoclassical theories of value. This paper briefly reviews the literature and then focuses on the detected skew eigenvalue distribution of the vertically integrated technical coefficients matrices of actual economies. The findings prompt the use of the Schur triangularization theorem for the construction even of a single industry from the input-output structure of the entire economy. Such a hyper-basic industry, in combination with hyper-non-basic industries, embodies properties that may capture the behaviour of the entire economic system. Thus, we can derive some meaningful results consistent with the available empirical evidence, which finally suggest that actual economies tend to respond as ‘irregular-uncontrollable’ systems.

• Item Type: MPRA Paper
• Language: English
• Keywords: Almost irregular-uncontrollable economy; Capital theory; Eigenvalue distribution; Hyper-basic industry; Effective rank
• Subjects: B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B21 - Microeconomics; B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B51 - Socialist ; Marxian ; Sraffian; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67 - Input-Output Models; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D46 - Value Theory; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D57 - Input-Output Tables and Analysis

References

Bienenfeld, M. (1988) Regularity in price changes as an effect of changes in distribution, Cambridge Journal of Economics, 12 (2), pp. 247-255.

Bidard, C. and Salvadori, N. (1995) Duality between prices and techniques, European Journal of Political Economy, 11 (2), pp. 379-389.

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

Burmeister, E. (1974) Synthesizing the Neo-Austrian and alternative approaches to capital theory: A survey, Journal of Economic Literature, 12 (2), pp. 413-456.

Dekkers, R. (2015) Applied Systems Theory, Heidelberg, Springer.

Gurgul, H. and Wójtowicz, T. (2015) On the economic interpretation of the Bródy conjecture, Economic Systems Research, 27 (1), pp. 122-131.

Han, Z. and Schefold, B. (2006) An empirical investigation of paradoxes: reswitching and reverse capital deepening in capital theory, Cambridge Journal of Economics, 30 (5), pp. 737-765.

Iliadi, F., Mariolis, T., Soklis, G. and Tsoulfidis, L. (2014) Bienenfeld’s approximation of production prices and eigenvalue distribution: Further evidence from five European economies, Contributions to Political Economy, 33 (1), pp. 35-54.

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 (2), pp. 282-329.

Leontief, W. (1953) Studies in the Structure of the American Economy, New York, Oxford 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.

Lucas, R. E. Jr (1988) On the mechanics of economic development, Journal of Monetary Economics, 22 (1), pp. 3-42.

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(2), pp. 113-127.

Mariolis, T. (2011) A simple measure of price-labour value deviation, Metroeconomica, 62 (4), pp. 605-611.

Mariolis, T. (2013) Applying the mean absolute eigen-deviation of labour commanded prices from labour values to actual economies, Applied Mathematical Sciences, 7 (104), pp. 5193-5204.

Mariolis, T. (2015a) Norm bounds and a homographic approximation for the wage-profit curve, Metroeconomica, 66 (2), pp. 263-283.

Mariolis, T. (2015b) Testing Bienenfeld’s second-order approximation for the wage-profit curve, Bulletin of Political Economy, 9 (2), pp. 161-170.

Mariolis, T., Rodousakis, N. and Christodoulaki, A. (2015) Input-output evidence on the relative price effects of total productivity shift, International Review of Applied Economics, 29 (2), pp. 150-163.

Mariolis, T. and Soklis, G. (2010) Additive labour values and prices of production: Evidence from the supply and use tables of the French, German and Greek economies, Economic Issues, 15 (2), pp. 87-107.

Mariolis, T. and Soklis, G. (2011) On constructing numeraire-free measures of price-value deviation: A note on the Steedman-Tomkins distance, Cambridge Journal of Economics, 35 (3), pp. 613-618.

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 (1), 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 (4), pp. 701-710.

Mariolis, T. and Tsoulfidis, L. (2011) Eigenvalue distribution and the production price-profit rate relationship: Theory and empirical evidence, Evolutionary and Institutional Economics Review, 8 (1), pp. 87-122.

Mariolis, T. and Tsoulfidis, L. (2014a) Measures of production price-labour value deviation and income distribution in actual economies: Theory and empirical evidence, Bulletin of Political Economy, 8 (1), pp. 77-96.

Mariolis, T., and Tsoulfidis, L. (2014b) On Bródy’s conjecture: Theory, facts and figures about instability of the US economy, Economic Systems Research, 26 (2), pp. 209-223.

Mariolis, T. and Tsoulfidis, L. (2016a) Modern Classical Economics and Reality: A Spectral Analysis of the Theory of Value and Distribution, Tokyo, Springer.

Mariolis, T. and Tsoulfidis, L. (2016b) Capital theory ‘paradoxes’ and paradoxical results: Resolved or continued?, Evolutionary and Institutional Economics Review, 13 (2), pp. 297-322.

Marx, K. ([1894] 1959) Capital, Volume 3, Moscow, Progress Publisher.

Mas-Colell, A. (1989) Capital theory paradoxes: Anything goes, in Feiwel, G. (Ed.) Joan Robinson and Modern Economic Theory, pp. 505-520, London, Macmillan.

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

Meyer, C. D. (2001) Matrix Analysis and Applied Linear Algebra, New York, Society for Industrial and Applied Mathematics.

Ochoa, E. (1989) Value, prices and wage-profit curves in the U.S. economy, Cambridge Journal of Economics, 13 (3), pp. 413-429.

Paraskevopoulou, C., Tsaliki, P. and Tsoulfidis, L. (2016) Revisiting Leontief’s paradox, International Review of Applied Economics, 30 (6), pp. 693-713.

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

Petrović, P. (1991) Shape of a wage-profit curve, some methodology and empirical evidence, Metroeconomica, 42 (2), pp. 93-112.

Pires, L. N. and Shaikh, A. M. (2015) Eigenvalue distribution, matrix size and the linearity of wage-profit curves, paper presented at the 23rd International Input-Output Association Conference in Mexico City, 21-25 June 2015.

Ricardo, D. ([1821] 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.

Robinson, J. V. (1953) The production function and the theory of capital, The Review of Economic Studies, 21 (2), pp. 81-106.

Rodousakis, N. (2012) Goodwin’s Lotka-Volterra model in disaggregative form: A correction note, Metroeconomica 63 (4), pp. 599-613.

Rodousakis, N. (2016) Testing Goodwin’s growth cycle disaggregated models: Evidence from the input-output tables of the Greek economy for the years 1988-1997, Bulletin of Political Economy, 10 (2), pp. 99-118.

Salvadori, N. and Stedman, I. (1985) Cost functions and produced means of production: Duality and capital theory, Contributions to Political Economy, 4 (1), pp. 79-90.

Samuelson, P.A. (1953-1954) Prices of factors and goods in general equilibrium, The Review of Economic Studies, 21(1), pp. 1-20.

Samuelson, P. A. (1962) Parable and realism in capital theory: The surrogate production function, The Review of Economic Studies, 29 (3), pp. 193-206.

Samuelson, P. A. (1966) A summing up, The Quarterly Journal of Economics, 80 (4), pp. 568-583.

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 profit rate: A mathematical note, Journal of Economics, 36 (1-2), pp. 21-48.

Schefold, B. (2008) 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), pp. 1-24.

Schefold, B. (2013a) Approximate surrogate production functions, Cambridge Journal of Economics, 37 (5), pp. 1161-1184.

Schefold, B. (2013b) Only a few techniques matter! On the number of curves on the wage frontier, in E. S. Levrero, A. Palumbo, A. Stirati (Eds) Sraffa and the Reconstruction of Economic Theory, Vol. I, pp. 46-69, London, Palgrave Macmillan.

Schefold, B. (2016) Marx, the production function and the old neoclassical equilibrium: Workable under the same assumptions? With an appendix on the likelihood of reswitching and of Wicksell effects, Centro Sraffa Working Papers, No. 19, April 2016. http://www.centrosraffa.org/cswp_details.aspx?id=20.

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

Shaikh, A. M. (1984) The transformation from Marx to Sraffa: Prelude to a critique of the neo-Ricardians, in E. Mandel and A. Freeman (Eds) Ricardo, Marx, Sraffa: The Langston memorial volume, pp. 43-84, London, Verso.

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

Shaikh, A. M. (2012) The empirical linearity of Sraffa’s critical output-capital ratios, in C. Gehrke, N. Salvadori, I. Steedman and R. Sturn (Eds) Classical political economy and modern theory. Essays in honour of Heinz Kurz, pp. 89-101, London and New York, Routledge.

Shaikh A. M. (2016) Capitalism: Competition, Conflict, Crises, Oxford, Oxford University Press.

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

Steedman, I. (1999) 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, 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 (3), pp. 379-385.

Timmer, M. P., Dietzenbacher, E., Los, B., Stehrer, R. and de Vries, G. J. (2015) An illustrated user guide to the World Input-Output Database: The case of global automotive production, Review of International Economics, 23 (3), pp. 575-605.

Tsoulfidis, L. (2008) Price-value deviations: Further evidence from input-output data of Japan, International Review of Applied Economics, 22 (6), pp. 707-724.

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

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 (4), pp. 425-437.