Raphaële Chappe over at INET:
General equilibrium theory is presented by Mas-Colell, Whinston and Green in two rather different ways. One is entirely abstractly, as relating to the idea that “we must simultaneously determine the equilibrium values of all variables of interest” (MWG, p.511). One can hardly quarrel with this ambition, if one is adopting an equilibrium approach at all. The other, rather more specific, involves the idea that “it aims at reducing the set of variables taken as exogenous to a small number of physical realities (e.g. the set of economic agents, the available technologies, the preferences and physical endowments of goods of various agents)” (MWG, p.511). Leave aside the point that “preferences” are hardly “physical”. This particular attempt at parsimony will have to justify itself through its successes.
One of the arguments as to why it has been successful is that it helps, we are told, to establish the conditions under which “market economies” have certain desirable properties. Mas-Colell, Whinston, and Green, for instance, claim that the so-called First Fundamental Theorem of Welfare Economics presents a ‘formal expression for competitive market economies of Adam Smith’s claimed” invisible hand” property of markets’ (p.545).[1] There is, however, a critical ambiguity here: do we mean by “market economies” the theoretical objects within the universe of general equilibrium theory or the real fields of activity they claim to model? If there were no relation then presumably the former would lose some of their interest.
As is well known, Cournot, Marshall and others began to establish a mathematical framework for partial equilibrium analysis, and Edgeworth and Walras posed and to a degree addressed the problem of identifying the conditions under which a price system might enable supply to be equated to demand simultaneously in all markets for traded commodities. However, it was only in the early 1950s, with the work of Arrow and Debreu, that research in the area of study that came to be called general equilibrium theory led to a formal demonstration of conditions for such an equilibrium to exist and to have specific desirable properties.
Arguably, the importance attached to research in general equilibrium came in part from the need to address a contrary idea, which had been prominent in the late nineteenth century and the first half of the twentieth: that of the anarchy of the market — the idea that the market is not harmonious and self-adjusting, automatically making its way to equilibrium, but rather unstable and even wasteful and chaotic.
More here.