### Some recent developments on the explanation of the empirical relationship between prices and distribution

**CSWP 54 (April 2022)**
Author

*Jacobo Ferrer-Hernández and Luis Daniel Torres-González*
Keywords

**Sraffian price models; price-profit rate curves; capital value; spectral representation; labour vector-Perron-Frobenius eigenvector relation.**
JEL

**B51; C67; D57**
The paper complements recent contributions towards the explanation of the regularities in the behaviour of prices and capital intensities as an effect of hypothetical changes in the rate of profit in empirical production-price models. It is shown that theoretical price and capital curves, i.e. prices and capital values as a function of the rate of profits, depend on the product of the eigenvalues and what we call the eigenlabours —the representation of the labour vector in the space spanned by the eigenvectors of the input matrix. We report robust evidence that the eigenvalues by themselves cannot produce the curves regularly reported in the literature, but rather it is the joint action of the eigenvalues and the eigenlabours. It is conjectured that the tendency towards zero of the subdominant eigenlabours is driven by the statistical tendency towards the proportionality between the labour vector and the Perron-Frobenius eigenvector of the input matrix.

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