Notes on the Behaviour of Prices

Precis: We discuss the behaviour of prices in an n-sector, circulating capital model with no joint production, of the type considered by Sraffa in Part I of his book. Instead of following Sraffa's approach, which uses the notion of proportions of labour to means of production in the various "layers" of means of production, we base our analysis directly on the characteristic roots and vectors of the input-output matrix, A. A straightforward corollary of our main result applies to the case of uniform organic composition of capital, familiar in aggregation theory. We use two mathematical results — the Cauchy determinant and the Perron-Frobenius theorem on semi-positive indecomposable matrices.