## Uniqueness and Stability of General Equilibrium

Alejandro Nadal writes:

Whatever happened to stability analysis?: Once upon a time, stability of the general equilibrium was considered an important element in the education of students in economics. Today it seldom receives the attention it deserves.... This crucial aspect of microeconomics is seldom covered adequately (if at all) in recent textbooks and university programs, whether at the undergraduate or post-graduate levels. Most students spend years learning how individual agents maximize, or exploring cases of oligopoly, or playing around with game theory, but when it comes to stability, their teachers skirt the main issues. As a result, a cloud of confusion persists. Students come to believe that somewhere in the sacred scriptures of the discipline there exists a theory that accurately reproduces just how the market forces of competition guide an economy through a price adjustment process that leads to the formation of equilibrium prices. In fact, if stability analysis received the attention it deserves, students would be able to see that it is the most important failure of general equilibrium theory....

In 1958-9 two papers, by Arrow and Hurwicz and Arrow, Block and Hurwicz, showed how under certain conditions an economy could converge to equilibrium. But these were extreme conditions: gross substitution (GS) for all goods or the validity of the weak axiom of revealed preferences (WARP) at the market level.... In the sixties a different tack was followed. Trading models were developed by Hahn and Negishi, Fisher and others.... The stability debate reached its climax with the papers published by Sonnenschein, Mantel and Debreu in 1973-4. These results show that the usual assumptions of GET allow the dynamics of the classic tâtonnement process to be essentially arbitrary. To avoid this, additional restrictions must be imposed on excess demand functions....

As Mundell once remarked, stability analysis is the most successful failure of general economic theory. It is also the best example of how an academic community pushes the most serious problems of mainstream theory under the rug and gets away with it...

From my perspective, the strange thing is that people kept trying to prove uniqueness and stability of general equilibrium.

Simply look at:

and try to avoid the conclusion that to first order the U.S. economy can be in at least meta-stable equilibrium with an adult employment-to-population ratio of about 63% or with an adult employment-to-population ratio of 58.5%--and probably anywhere in between as well.

Proposing that economists pursue the research program of demonstrating that the economy has a unique stable equilibrium has thus always seemed to me to be like proposing that physicists pursue the research program of demonstrating the feathers fall unusually rapidly...