In the development of its long decades over the discipline of economics, general equilibrium is usually regarded as the ultimate formalization of economic theory and established as the fundamental framework for theoretical dissertation. General equilibrium theory is generally mentioned as providing the rigorous theoretical version of Adam Smith’s invisible hand and demonstrating the desirable properties of a competitive economy.
Yet there is much controversy concerning general equilibrium theory. Some authors have raised questions about its significance for economic theory, Ackerman went further and stated that general equilibrium is “not exactly alive and well any more”. The controversy on this issue seems to stem from the fact that although general equilibrium theory is valid in a highly formalized way, there is some question as to whether it possesses empirical content.
The best-known results of general equilibrium theory are the two theorems proved by Kenneth Arrow and Gerard Debreu. First, under familiar assumptions defining an idealized competitive market economy, any market equilibrium is a Pareto optimum. Second, under more restrictive assumptions, any Pareto optimum is a market equilibrium for some set of initial conditions. There is a long-lasting debate about the interpretation of such results, in light of the lack of realism of some of the assumptions made. For example, nonconvexities, such as increasing returns to scale in production, are common in reality and, if allowed into the theory then the existence of an equilibrium is no longer certain, and a Pareto optimum need not be a market equilibrium.
The second fundamental theorem is often interpreted as that any efficient allocation of resources could be achieved by market competition, after an appropriate lump-sum redistribution of initial endowments. In reality, this interpretation may be debatable, given the conditions assumed in the proofs which do not apply in real life, and even if they did, the application of the Arrow-Debreu theorems would require dynamic stability. Considering the process of redistributing initial resources and then letting the market achieve a new equilibrium suggests that the new equilibrium is both unique and stable. But if, for instance, the equilibrium is not unique, one of possible equilibrium point might be more socially desirable than another, and the market might converge toward the wrong one. If, on the other side, the equilibrium is unstable, the market may never reach it, or might not stay there long if surprised by random events.
In conclusion, the equilibrium in a general equilibrium model is not necessarily either unique or stable in real life and there are apparently no grounds for dismissing not well-behaved outcomes as implausible special cases.