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

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  • Mariolis, Theodore

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.

Suggested Citation

  • Mariolis, Theodore, 2003. "Controllability, Observability, Regularity, and the so-called Problem of Transforming Values into Prices of Production," MPRA Paper 24043, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:24043
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    File URL: https://mpra.ub.uni-muenchen.de/24043/1/MPRA_paper_24043.pdf
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    References listed on IDEAS

    as
    1. Kurz,Heinz D. & Salvadori,Neri, 1997. "Theory of Production," Cambridge Books, Cambridge University Press, number 9780521588676, January.
    2. Steedman, Ian & Tomkins, Judith, 1998. "On Measuring the Deviation of Prices from Values," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 22(3), pages 379-385, May.
    3. Bidard, Christian & Salvadori, Neri, 1995. "Duality between prices and techniques," European Journal of Political Economy, Elsevier, vol. 11(2), pages 379-389, June.
    4. Wolfstetter, E, 1973. "Surplus Labour, Synchronised Labor Costs and Marx's Labour Theory of Value," Economic Journal, Royal Economic Society, vol. 83(331), pages 787-809, September.
    5. Mussa, Michael, 1979. "Empirical regularities in the behavior of exchange rates and theories of the foreign exchange market," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 11(1), pages 9-57, January.
    6. Syed Ahmad, 1991. "Capital in Economic Theory," Books, Edward Elgar Publishing, number 5.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Mariolis, Theodore, 2019. "The location of the value theories in the complex plane and the degree of regularity-controllability of actual economies," MPRA Paper 96972, University Library of Munich, Germany.
    2. Theodore Mariolis & Nikolaos Rodousakis & Apostolis Katsinos, 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, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-23, December.
    3. Theodore Mariolis & Lefteris Tsoulfidis, 2018. "Less Is More: Capital Theory And Almost Irregular-Uncontrollable Actual Economies," Contributions to Political Economy, Cambridge Political Economy Society, vol. 37(1), pages 65-88.
    4. Mariolis, Theodore & Tsoulfidis, Lefteris, 2010. "Eigenvalue distribution and the production price-profit rate relationship in linear single-product systems: theory and empirical evidence," MPRA Paper 43716, University Library of Munich, Germany.

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    More about this item

    Keywords

    Control theory; controllability; observability; regular production technique; Sraffian theory; transformation problem;
    All these keywords.

    JEL classification:

    • B51 - Schools of Economic Thought and Methodology - - Current Heterodox Approaches - - - Socialist; Marxian; Sraffian
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D57 - Microeconomics - - General Equilibrium and Disequilibrium - - - Input-Output Tables and Analysis
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • E11 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Marxian; Sraffian; Kaleckian

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