The location of the value theories in the complex plane and the degree of regularity-controllability of actual economies

Mariolis, Theodore (2019): The location of the value theories in the complex plane and the degree of regularity-controllability of actual economies.

Abstract

This paper expands the spectral analysis of the Sraffian value system, and shows that: (i) the hitherto alternative value theories can be conceived of as “perturbations” of the so-called pure labour value theory; (ii) these theories correspond to specific complex plane locations of the eigenvalues of the vertically integrated technical coefficients matrix; and (iii) the actual economies cannot be coherently analyzed in terms of the traditional value theories, despite the fact that their Krylov (or controllability) matrices are characterized by rather low degrees of regularity-controllability and relatively low numerical ranks. Hence, on the one hand, the Sraffian value theory is not only the most general one but also provides a sound empirical basis, while on the other hand, real-world economies constitute almost irregular-uncontrollable systems, and this explains the specific shape features of the empirical value-wage-profit rate curves.

• Item Type: MPRA Paper
• Language: English
• Keywords: Almost irregular-uncontrollable system; Characteristic value distributions; Circulant matrices; Degree of regularity-controllability; Numerical rank; Value theories
• Subjects: B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B51 - Socialist ; Marxian ; Sraffian; B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B53 - Austrian; 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

Ara, K. (1963). A note on input-output matrices. Hitotsubashi Journal of Economics, 3(2), 68-70.

Aruka, Y. (1991). Generalized Goodwin’s theorems on general coordinates. Structural Change and Economic Dynamics, 2(1), 69-91.

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

Böhm-Bawerk, E. V. ([1889] 1959). Capital and interest. South Holland: Libertarian Press.

Boley, D., & Lu, W.-S. (1986). Measuring how far a controllable system is from an uncontrollable one. Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 31(3), 249-251.

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

Cowan, N. J., Chastain, E. J., Vilhena, D. A., Freudenberg, J. S., & Bergstrom, C. T. (2012). Nodal dynamics, not degree distributions, determine the structural controllability of complex networks. PloS one, 7(6), e38398. https://doi.org/10.1371/journal.pone.0038398

Davis, P. J. (1979). Circulant matrices. New York: John Wiley & Sons.

Dmitriev, N. A., & Dynkin, E. (1946). On characteristic roots of stochastic matrices. Izvestiya Rossiiskoi Akademii Nauk SSSR Seriya Matematicheskaya, 10(2), 167-184 (in Russian; English translation in Swift, J. (1972). The location of characteristic roots of stochastic matrices (M.Sc. Thesis). McGill University, Montreal).

Ford, D. A., & Johnson, C. D. (1968). Invariant subspaces and the controllability and observability of linear dynamical systems. Society for Industrial and Applied Mathematics Journal on Control, 6(4), 553-558.

Friedland, B. (1975). Controllability index based on conditioning number. Journal of Dynamic Systems, Measurement, and Control, 97(4), 444-445.

Friedland, B. (1986). Control system design. An introduction to state-space methods. New York: McGraw-Hill.

Garegnani, P. (1970). Heterogeneous capital, the production function and the theory of distribution. The Review of Economic Studies, 37(3), 407-436.

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

Kalman, R. E. (1960). On the general theory of control systems. International Federation of Automatic Control Proceedings Volumes, 1(1), 491-502.

Kalman, R. E., Ho, Y. C., & Narendra, K. S. (1963). Controllability of linear dynamic systems. Contributions to Differential Equations, 1(2), 1963, 189-213.

Karpe1evich, F. I. (1951). On the characteristic roots of matrices with non-negative elements. Izvestiya Rossiiskoi Akademii Nauk SSSR Seriya Matematicheskaya, 15(4), 361-383 (in Russian; English translation in Swift, J. (1972). The location of characteristic roots of stochastic matrices (M.Sc. Thesis). McGill University, Montreal).

Kemp, M. C. (1973). Heterogeneous capital goods and long-run Stolper-Samuelson theorems. Australian Economic Papers, 12(21), 253-260.

Kurz, H. D., & Salvadori, N. (1995). Theory of production. A long-period analysis. Cambridge: Cambridge University Press.

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), 113-127.

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

Mariolis, T., & 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), 1-22.

Mariolis, T., & Tsoulfidis, L. (2016a). Modern classical economics and reality. A spectral analysis of the theory of value and distribution, Tokyo: Springer.

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

Mariolis, T., & Tsoulfidis, L. (2018). Less is more: Capital theory and almost irregular-uncontrollable actual economies. Contributions to Political Economy, 37(1), 65-88.

Mariolis, T., Rodousakis, N., & Katsinos, A. (2019). Wage versus currency devaluation, price pass-through and income distribution: a comparative input–output analysis of the Greek and Italian economies. Journal of Economic Structures, 8:9. https://doi.org/10.1186/s40008-019-0140-8

Marx, K. ([1894] 1959). Capital. A critique of political economy, Vol. 3. Moscow: Progress Publisher.

Meyer, C. D. (2001). Matrix analysis and applied linear algebra. New York: Society for Industrial and Applied Mathematics.

Minc, H. (1988). Nonnegative matrices. New York: John Wiley & Sons.

Miyao, T. (1977). A generalization of Sraffa’s standard commodity and its complete characterization. International Economic Review, 18(1), 151-162.

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

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.

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

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

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), 1-24.

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

Sharpe, G., & Styan, G. (1965). Circuit duality and the general network inverse. Institute of Electrical and Electronics Engineers Transactions on Circuit Theory, 12(1), 22-27.

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), 548-560.

Solow, R. (1952). On the structure of linear models. Econometrica, 20(1), 29-46.

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

Sraffa, P. (1962). Production of Commodities: a comment. The Economic Journal, 72(286), 477-479.

Stolper, W. F., & Samuelson, P. A. (1941). Protection and real wages. The Review of Economic Studies, 9(1), 58-73.

Weizsäcker, C. C. V. (1977). Organic composition of capital and average period of production. Revue d’Economie Politique, 87(2), 198-231.