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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.

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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.

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