Mariolis, Theodore (2003): Controllability, Observability, Regularity, and the socalled Problem of Transforming Values into Prices of Production. Published in: AsianAfrican Journal of Economics and Econometrics , Vol. 3, No. 2 (December 2003): pp. 113127.

PDF
MPRA_paper_24043.pdf Download (388Kb)  Preview 
Abstract
This paper specifies and interprets those direct relations which exist between the dual concepts of complete controllability/observability (Kalman, 1960), on the one hand, and the concept of the regular technique of production (Schefold, 1971), on the other. Specifically, it shows, first, that there is a certain dynamic system for determining labour values, which is connected with the usual system for determining prices of production (à la Sraffa, 1960, Part I) via the z(Laplace) transform, and, second, that the said system of values is completely controllable when and only when the system of production prices is regular. In view of the above, it could be considered that the z(Laplace) transform constitutes the solution to the – suitably reformulated – Marxian ‘problem of transforming values into prices of production’. However, on the basis of an economic interpretation of the z(Laplace) transform, this paper shows, ultimately, not only that such a consideration is erroneous, but also that the supposed ‘problem’ is devoid of economic meaning.
Item Type:  MPRA Paper 

Original Title:  Controllability, Observability, Regularity, and the socalled Problem of Transforming Values into Prices of Production 
Language:  English 
Keywords:  Control theory; controllability; observability; regular production technique; Sraffian theory; transformation problem 
Subjects:  B  History of Economic Thought, Methodology, and Heterodox Approaches > B5  Current Heterodox Approaches > B51  Socialist; Marxian; Sraffian D  Microeconomics > D4  Market Structure and Pricing > D46  Value Theory D  Microeconomics > D5  General Equilibrium and Disequilibrium > D57  InputOutput Tables and Analysis C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C67  InputOutput Models E  Macroeconomics and Monetary Economics > E1  General Aggregative Models > E11  Marxian; Sraffian; Institutional; Evolutionary 
Item ID:  24043 
Depositing User:  Theodore Mariolis 
Date Deposited:  23. Jul 2010 02:55 
Last Modified:  17. Feb 2013 19:00 
References:  Ahmad, S. 1991. Capital in Economic Theory: Neoclassical, Cambridge and Chaos, Aldershot, Edward Elgar. Aoki, M. 1976. Optimal Control and System Theory in Dynamic Economic Analysis, New York, NorthHolland. Aseltine, J.A. 1958. Transform Method in Linear System Analysis, New York, McGrawHill. Bidard, C. and Salvadori, N. 1995. Duality between prices and techniques, European Journal of Political Economy, vol. 11, 37989. Chen, C.T. and Desoer, C.A. 1968. Proof of Controllability of Jordan Form State Equations, IEEE Trans. Automatic Control, vol. 13, 1956. D’ Azzo, J.J. and Houpis, C.H. 1988. Linear Control System Analysis and Design: Conventional and Modern, New York, McGrawHill. Ford, D.A. and Johnson, C.D. 1968. Invariant Subspaces and the Controllability and Observability of Linear Dynamical Systems, Journal SIAM on Control, vol. 6, 55358. Gilbert, E.G. 1963. Controllability and Observability in Multivariable Control Systems, Journal SIAM on Control, vol. 2, 12851. Howard, M.C. 1980. Austrian Capital Theory: An Evaluation in Terms of Piero Sraffa’s Production of Commodities by Means of Commodities, Metroeconomica, vol. 32, 124. Johnson, C.D. 1966. Invariant Hyperplanes for Linear Dynamical Systems, IEEE Trans. Automatic Control, vol. 11, 11316. Kalman, R.E. 1960. On the General Theory of Control Systems, Proceedings First International Congress on Automatic Control, London, Butterworths, vol. 1, 48192. Kalman, R.R. 1963. Mathematical Description of Linear Dynamical Systems, Journal SIAM on Control, vol. 2, 15292. Kurz, H.D. and Salvadori, N. 1995. Theory of Production: A LongPeriod Analysis, Cambridge, Cambridge University Press. Kuo, B.C. 1995. Automatic Control Systems, New York, John Wiley and Sons. Luenberger, D.G. 1979. Introduction to Dynamic Systems: Theory, Models and Applications, New York, John Wiley and Sons. Mariolis, T. 1999. The socalled Problem of Transforming Values into Prices, Political Economy. Review of Political Economy and Social Sciences, Issue 5, 4558. Mariolis, T. 2002. On the Lack of Correspondence between Surplus Value and Profit, Panteion University, Athens, mimeo. Miyao, T. 1977. A Generalization of Sraffa’s Standard Commodity and its Complete Characterization, International Economic Review, vol. 18, 15162. Mussa, M. 1979. Empirical Regularities in the Behavior of Exchange Rates and Theories of the Foreign Exchange Market, in K. Brunner and A.H. Meltzer (eds.), Policies for Employment, Prices and Exchange Rates, Amsterdam, NorthHolland, 957. Okishio, N. 1993. Essays on Political Economy. Collected Papers, Frankfurt am Main, Peter Lang. Pasinetti, L. 1977. Lectures on the Theory of Production, London, MacMillan. 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, vol. 36, 2148. Sraffa, P. 1960. Production of Commodities by Means of Commodities, Cambridge, Cambridge University Press. Steedman, I. 1977. Marx after Sraffa, London, New Left Books. Steedman, I. 1985. Heterogeneous Labour, Money Wages, and Marx’s Theory, History of Political Economy, vol. 17, 55174. Steedman, I. and Tomkins, J. 1998. On Measuring the Deviation of Prices from Values, Cambridge Journal of Economics, vol. 22, 37985. Takayama, A. 1987. Mathematical Economics, Cambridge, Cambridge University Press. Willke, H. 1993. Systemtheorie, Stuttgart, Gustav Fischer Verlag. Wohltmann, H.W. 1981. Complete, Perfect, and Maximal Controllability of Discrete Economic Systems, Metroeconomica, vol. 41, 3958. Wolfstetter, E. 1973. Surplus Labour, Synchronised Labour Costs and Marx’s Labour Theory of Value, Economic Journal, vol. 83, 787809. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/24043 