The Hahn Process with Firms but No Production

Abstract

1. INTIRODUCTION ANALYSES OF THE STABILITY of general competitive equilibrium2 have typically concerned themselves with the case of pure exchange. Sometimes that restriction has been inessential. In the tatonnement case, for example, if we are willing to make the assumption that all goods are gross substitutes, then it makes little difference where the excess demand functions come from.3 In less highly special cases, the restriction to pure exchange is a more serious matter. This is particularly so in the richer world of non-tatonnement processes. The difficulties raised by the abandonment of the pure exchange assumption in such models are three. First, such models, in assumptions or proofs, rest on considerations of utility maximization which are not immediately applicable to firms. Second, it is not fully natural to assume that stocks of goods are bounded, an important feature when non-tatonnement is being considered. Third, the creation and destruction of goods in the course of the adjustment process itself must be taken into account. The present paper shows how the first and, to some extent, the second of these problems can be handled in the context of the most appealing of the non-tatonnement models, that of the Hahn process.4 The third problem, that of the creation and disappearance of goods during the adjustment process is far more difficult. It is also not special to the introduction of firms, since the pure exchange models do not allow consumption to take place until equilibrium has been reached. Thus, this