Nonstandard General Equilibrium

When writing his book Walras (1874–1877) had no mathematical tools, actually the so called fixed points theorems, to prove the existence of economically meaningful solutions to his one period competitive general equilibrium models, from now on shortly called walrasian models or abstract models. But he felt reasonably sure that (substantially) he had solved the existence problem in two ways, distinct both conceptually and practically. The first way was by counting the number of (independent) equations forming the model and the number of unknowns, to show that these numbers are equal. The second way discovered by Walras, a more practical one, was to make a conceptual experiment consisting in assuming that there is a particular agent, called by Walras auctioneer, who chooses “at randorn” one positive price vector and then records market demand and market supply of every good. In a second step, once ordered all markets in some sequence, the auctioneer rises prices in markets in which the excess demand is positive and decreases prices in those markets for which excess demand is negative. Walras felt sure that in the end all excess demands would be reduced (in absolute value) to zero, so obtaining a vector of equilibrium prices for his one-period models. During the whole process of manipulating prices no agent is allowed to produce or to consume: economic operators must only inform the auctioneer about their supplies and demands at the various prices, as if those prices where equilibrium ones; so `tâtonnements’ do not work in calendar time: time is here merely logical time. Moreover, to introduce an auctioneer means to assume that walrasian general equilibrium has a lot of structure.