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This is the second version of my MPRA_paper_96972.pdf (https://mpra.ub.uni-muenchen.de/96972/). The paper expands the spectral analysis of the Sraffian value system, and shows that: (i) the hitherto alternative value theories correspond to specific complex plane locations of the eigenvalues of the vertically integrated technical coefficients matrix; and (ii) the actual economies cannot be coherently analyzed in terms of the traditional value theories (classical, Marxian, Austrian, and neoclassical), 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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Using input-output data from Symmetric Input-Output Tables for the year 2010 and relevant price models, this paper provides empirical estimations of medium- and long-run effects of wage and currency devaluations on international price competitiveness and income distribution for two ‘PIIGS economies’, i.e., Greece and Italy. The findings reveal certain differentiated socio-technical production conditions in the economies under consideration casting doubt on the effectiveness of demand-switching policy measures implemented in the post-2010 Eurozone economy. At the same time, however, wage devaluation is found to be a comparatively slow and inefficient process to improve international price competitiveness in the medium-run.

Capital theory controversies and ‘paradoxes’ showed that, due to price-feedback effects, the wage-production price-profit rate curves may display shapes inconsistent with the requirements of the neoclassical theory of value and distribution. Subsequent findings on a number of quite diverse actual single-product economies suggested that the impact of those effects is of limited empirical significance. This paper argues that, by focusing on the distributions of the eigenvalues and singular values of the system matrices, we can further study these issues and derive some meaningful theoretical results consistent with the available empirical evidence. Consequently, the real paradox, in the sense of knowledge vacuum and, thus, requiring further research, is the distributions of the characteristic values and not really the ‘paradoxes in capital theory’.

This paper applies a recently proposed measure of production price-labour value deviation, i.e. the 'Mean Absolute Eigen-Deviation', to actual economies. The results suggest that that measure tends to the profit-wage ratio in the Sraffian Standard system divided by the number of produced commodities. This finding is reduced to the skew distribution of the eigenvalues of the vertically integrated technical coefficients matrices.

Capital theory and the price effects consequent upon changes in the distributive variables hold center stage when it comes to the internal consistency of both classical and neoclassical theories of value. This paper briefly reviews the literature and then focuses on the detected skew eigenvalue distribution of the vertically integrated technical coefficients matrices of actual economies. The findings prompt the use of the Schur triangularization theorem for the construction even of a single industry from the input–output structure of the entire economy. Such a hyper-basic industry, in combination with hyper-non-basic industries, embodies properties that may capture the behavior of the entire economic system. Thus, we can derive some meaningful results consistent with the available empirical evidence, which finally suggest that actual economies tend to respond as ‘irregular-uncontrollable’ systems.

This book presents an in-depth, novel, and mathematically rigorous treatment of the modern classical theory of value based on the spectral analysis of the price–profit–wage rate system. The classical theory is also subjected to empirical testing to show its logical consistency and explanatory content with respect to observed phenomena and key economic policy issues related to various multiplier processes. In this context, there is an examination of the trajectories of relative prices when the distributive variables change, both theoretically and empirically, using actual input–output data from a number of quite divers
e economies. It is suggested that the actual economies do not behave like the parable of a one-commodity world of the traditional neoclassical theory, which theorizes the relative scarcities of “goods and production factors” as the fundamental determinants of relative prices and their movement. By contrast, the results of the empirical analysis are fully consistent with the modern classical theory, which makes the intersectoral structure of production and the way in which net output is distributed amongst its claimants the fundamental determinants of price magnitudes. At the same time, however, these results indicate that only a few vertically integrated industries (“industry core” or “hyper-basic industries”) are enough to shape the behaviour of the entire economy in the case of a disturbance. This fact is reduced to the skew distribution of the eigenvalues of the matrices of vertically integrated technical coefficients and reveals that, across countries and over time, the effective dimensions of actual economies are surprisingly low.

CD-ROM contains: Searchable copy of textbook and all solutions -- Additional references -- Thumbnail sketches and photographs of mathematicians -- History of linear algebra and computing.

The Cambridge debate showed that an aggregation of capital is not possible in general. A recent investigation has found one
example for reswitching and several for reverse capital deepening, but the paradoxes appear to be infrequent. The paper provides
a theoretical justification of this result and shows how wage curves of input–output matrices with small non-dominant eigenvalues
become quasi-linear with some numéraires. Large random systems lead to the genesis of such states. Approximate surrogate production
functions then seem possible. A family of economic systems with constant capital composition allows construction of a surrogate
production function.