On the Role of Money in the Process of Exchange and the Existence of a Non- Walrasian Equilibrium

Abstract

In a Walrasian world, prices vary so as to balance supply and demand for each good. Arrow and Debreu proved that under some conditions there exists a set of prices which make the agents' plans compatible. In such a framework, there is really no logical need to require that a particular good plays a special role in trade. We shall prove that such a need arises if we try to set up a concept of equilibrium when the prices are not necessarily Walrasian, and for which there is only one market for each good, that is one equation that says that there is equality between resources and uses for each good. The existence of a non-Walrasian equilibrium requires that there be a good, called money, which has to appear in each transaction or which simply has to be the measuring rod of the profitability of each transaction. We assume a pure exchange economy. There are m consumers (i= 1, ..., m). There are r goods (h = 1, ..., r). Let R'+ be the consumption set of consumer i (H.1). wi his positive initial allocation (H.2). Ui his strictly concave, continuously differentiable, and monotone utility function3 (H.3). We assume that the price vectorp (strictly positive) is given. We prescribe the following condition on an allocation:

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