# Capital theory ‘paradoxes’ and paradoxical results: resolved or continued?

## Abstract

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’.

### Keywords

Capital theory Characteristic value distributions Hyper-basic industry Spectral decompositions Wage–price–profit rate curves### JEL Classification

B21 B51 C67 D57## Notes

### Acknowledgments

The material in the manuscript has been acquired according to modern ethical standards and does not contain material copied from anyone else without their written permission and there is no conflict of interest. We are indebted to two anonymous referees of this journal for helpful remarks and hints. An earlier version of this paper was presented at the 19th European Society for the History of Economic Thought Conference, 14–16 May 2015, Roma Tre University, Italy. We thank the participants of this conference and especially Heinz D. Kurz, Fabio Petri, Bertram Schefold, Persefoni Tsaliki and Stefano Zambelli for their comments, criticisms and discussions. The usual caveat applies.

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