A Cross-Over Gravitation Process in Prices and Inventories

Abstract

The point of departure of the present paper is a Sraffian system of production prices, with respect to a given real wage rate. These prices are interpreted as long-run equilibrium prices, i.e., they are not only bringing about a uniform rate of profit, but at the same time they are supposed to match underlying demands and supplies of commodities. We are concerned with modelling what happens outside a long-run equilibrium and with investigating the classical problem whether, or under what circumstances, the market prices obtained will tend to the given production prices. In order to make an analytical treatment possible, we shall employ, as so many others have, a two-sector framework. Moreover, all analysis will be done in continuous time. It will be seen that, in the model specified, we have to be prepared for the phenomenon of non-convergence. In a second step, it will be studied what conditions exclude a complete divergence of trajectories. Referring to relative magnitudes, this will finally allow us to apply the famous Poincaré-Bendixson Theorem and to establish the existence of limit cycles or closed orbits. If the long-run position is unstable, they are non-degenerate and stable (or at least partly so), where relative prices and relative quantities oscillate in a more or less regular manner around their equilibrium values.

This paper is based on a part of my doctoral thesis “Production prices and dynamical processes of the gravitation of market prices”, Bremen 1985.