The Meaning Of A Word Is Its Use In The Language

The economy is never in equilibrium, or so many heterodox economists say. Being a Joan Robinson fan, I'm likely to agree. To understand the implications of the idea, and the use and abuse of equilibrium analysis, one must understand what economists mean by "equilibrium".

Tyler Cowen and Richard Fink provide an example of abuse, that is, a confusion about the implications of the economy not being in equilibrium. In the following passage, Cowen and Fink explicitly put aside income effects, false prices, strategic behavior, etc.:

"all that the Rothbard-Mises analysis implies is that there is a tendency towards equilibrium in a world with frozen data. Of course, this implies little or nothing about whether there is a tendency towards equilibrium in a world where the data are not frozen. All that [Evenly Rotating Economy] theorists are saying is that, if we freeze the disequilibrating forces, then the equilibrating forces will prevail. But on this basis we may likewise assert a tendency towards disequilibrium. By allowing the data to change just as it does in the real world, and 'freezing' all individual learning, we can demonstrate that the economy would degenerate into a series of successively less-coordinated states of disequilibrium. However, this would clearly be an illegitimate proof of a real world tendency towards disequilibrium..." -- Tyler Cowen and Richard Fink, "Inconsistent Equilibrium Constructs: The Evenly Rotating Economy of Mises and Rothbard", m V. 75, N. 4 (Sep. 1985): 866-869

(Hat tip to Matthew Mueller.) If there were a tendency, with frozen data, towards a ERE, the time path of the ERE corresponding to the data at each moment of time would show the tendency of the economy as a function of time. This is not the only point at which Cowen and Fink are confused.

What economists mean by equilibrium is not a simple question. Economists use the word "equilibrium" in many ways. The number of such ways has proliferated with the development of game theory. In this post, I compare and contrast only two uses of the word "equilibrium". And I think I don't fully explicate even these two uses.

The economy can be said to be in equilibrium when the following two conditions are met:

• The quantity supplied equals the quantity demanded of all commodities with positive prices
• The quantity supplied does not fall below the quantity demanded of all goods with zero prices.

This definition is specific to a particular neoclassical theory (or model).

Another definition comes out of the mathematical abstraction of a dynamical system. A dynamical system specifies how state variables change at any momement of time as a function of the location in state space. For example, a system of differential equations can define a dynamical system:

dx(t)/dt = f(x(t))

A limit point is a location, x, in the state space such that that location does not change with respect to time as function of the system dynamics. In other words, f(x) is zero at a limit point. Certain loci, other than the set of limit points, are of interest in dynamical systems. I am thinking specifically of limit cycles, strange attractors, and non-wandering sets. Consider a model of the economy as a dynamical system. The economy is in equilibrium, by a dynamical systems definition, when it is at a limit point.

The definition of equilibrium as equating supply and demand can be read as a special case of the definition of equilibrium as a limit point in a dynamical system. The tâtonnement process is a model of a type of dynamical system. Equilibrium, in the sense of a limit point in this system, is equilibrium in the sense of no excess demand for goods.

But Keynes can be read as suggesting the dynamical system definition of equilibrium need not equate supply and demand, particularly in the labor market. That is, Keynes' view of the possibility of the existence of an equilibrium with unemployment is more general and points to a non-neoclassical theory of prices.