The standard neoclassical (Arrow-Debreu) approach to general equilibrium has been criticised by many economists, for many reasons. Mark Blaug, for example, has written,
We may conclude that GE theory as such is a cul-de-sac: it as has no empirical content and never will have empirical content. Moreover, even as research programme in social mathematics, it must be condemned as an almost total failure.When looking at the production side of the model a common criticism made is that the model has not reason for the existence of firm. As Foss, Lando and Thomsen summarise it:
The pure analysis of the market institution leaves almost no room for the firm (Debreu 1959). Under the assumption of a perfect set of contingent markets, as well as certain other restrictive assumptions, the model describes how markets may produce efficient outcomes. The question how organizations should be structured does not arise, because market-contracting perfectly solves all incentive and coordination issues. By assumption, firm behaviour (profit maximization) is invariant to institutional form (e.g. ownership structure). The whole economy can operate efficiently as one great system of markets, in which autonomous agents enter into very elaborate contracts with each other. However, by treating the firm itself as a black box, where internal structure, contracts, etc. disappear from the picture, there are many other issues that the theory cannot address. For example, the theory does not tell us why firms exist.Nicolai Foss uses a few less words to make this point when he notes
With perfect and costless contracting, it is hard to see room for anything resembling firms (even one-person firms), since consumers could contract directly with owners of factor services and wouldn't need the services of the intermediaries known as firms.In other words the neoclassical model is DIY on steroids!!
Interestingly, in addition to the above comment on GE Mark Blaug notes that the fictional auctioneer famous from Walras's model of general equilibrium isn't in fact due to Walras.
[..] Walras never mentioned the concept of a fictional auctioneer announcing and changing prices until an equilibrium price is agreed upon - this is one of those historical myths that subsequent generations invented [..]One wonders who invented the idea.