Gross Substitutes, Walras’ “Rareté” and the Stability of the Middle Class

The utility notion of Walras is in essence very similar to the ideas of Jevons and Gossen. The marginal utility (rareté) relations of Walras are decreasing in the quantity and are dependent on only one variable, the “own” commodity. The reproaches made by latter economists concerning the inadequacy of the formal analysis of Walras to guarantee the uniqueness, the existence and the stability of the equilibrium were never based on this simple utility concept. In this paper we attempt to preliminary analyse the extent of the (in)adequacy again but now closely based upon the essence of Walras’ “rareté” relations. Walras, in contrast with the received opinion, is aware of the uniqueness and stability problem. He maintains that in the groping process stability is a likely property. This paper shows that if, starting from Walras’ utility notion, the marginal utility elasticities are larger than minus one, gross stability holds and the stability of the groping process is guaranteed. It is also argued that the elasticity values are more probable smaller than minus one, if the commodity quantities are closer to the existence minimum or closer to the points of satiation. From this observation it seems likely that in the area between minimum and bliss marginal utility elasticity behaves quiet (>-1) and, hence, stability is obtained. So, evenly distributed endowments or a large group of “middle class” agents increase the likelihood of stable groping processes.