Abstract
This note discusses Professor Schefold’s 2016 article. It checks the mathematical treatment of transformation problem in the article. It also reviews the interpretation of Marx’s mathematical manuscripts.
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Notes
Here we call the left-hand side eigenvector of the input coefficient matrix the “standard prices.” Needless to say, we follow Sraffa (1960) in calling the right-hand side eigenvector the standard commodities.
Random matrices were first introduced into statistical theory in the 1920s. Wigner (1956) investigated these in the 1950 s for their application in nuclear physics. Random matrices have random numbers as their elements. Dyson (1962) built a Brownian movement model using random matrices. The introduction of random matrices into quantum mechanics in the 1980 s aroused mathematicians’ interest in the eigenvalues of random matrices.
Schefold (2016), p. 183, quoted Marx’s text from MEGA2 II, 9, pp. 264–5.
References
Dyson FJ (1962) A Brownian-motion model for the eigenvalues of a random matrix. J Math Phys 3:1191–1198
Leibnitz GW (1684) Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationals quantitates moratur, et singular pro illis calculi genus. Acta Eruditorum 3:467–473
Schefold B (2016) Profits equal surplus value on average and the significance of this result for the Marxian theory of accumulation. Camb J Econ 40:165–199
Sraffa P (1960) Production of commodities by means of commodities: prelude to critique of economic theory. Cambridge University Press, Cambridge
Wigner EP (1956) Results and theory of resonance absorption. In: Conference on neutron physics by time-of-flight held at Gatlinburg, Tennessee, November 1 and 2, pp 59–70
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Yamazaki, Y. Profit and value in a random system: interpretation of professor Schefold’s 2016 article. Evolut Inst Econ Rev 16, 319–325 (2019). https://doi.org/10.1007/s40844-019-00136-2
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DOI: https://doi.org/10.1007/s40844-019-00136-2