Controllability, Observability, Regularity, and the so-called Problem of Transforming Values into Prices of Production

Mariolis, Theodore (2003): Controllability, Observability, Regularity, and the so-called Problem of Transforming Values into Prices of Production. Published in: Asian-African Journal of Economics and Econometrics , Vol. 3, No. 2 (December 2003): pp. 113-127.

Abstract

This paper specifies and interprets those direct relations which exist between the dual concepts of complete controllabil-ity/observability (Kalman, 1960), on the one hand, and the con-cept 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
• 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, Pricing, and Design > D46 - Value Theory; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D57 - Input-Output 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 - Input-Output Models; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E11 - Marxian ; Sraffian ; Kaleckian

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