# Equilibrium in Economics

# Equilibrium in Economics

EQUILIBRIUM AS A PROBLEM FOR MATHEMATICAL ANALYSIS

EQUILIBRIUM MODELS AS A MODE OF ExPLANATION

EQUILIBRIUM ATTAINMENT VERSUS THE EQUILIBRIUM PROCESS

The concept of an economy in equilibrium is pervasive in modern economics. The modern neoclassical concept has been a central tenet of economics since the late nineteenth century when economists began importing notions from physics and mechanics. The idea imported from physics is that claiming an economy is in a state of equilibrium implies forces exist that would correct any accidental deviation from that state of equilibrium. As such, equilibrium is a dynamic concept as it involves constant corrective movement, movement that is always in the direction of restoring an equilibrium state whenever perturbed by frequent, possibly random, deviations. An equilibrium can be dynamic in another sense, such as when it represents a persistent pattern even though the objects that form the pattern may be in constant movement. The obvious physics example is the solar system with the planets in constant movement but in predictable and stable patterns. Similarly, one can think of an entire economy in a “stationary state” with constant flows of goods and services that year by year maintain a stationary equilibrium pattern (i.e., no growth or decay).

The classical school of the early nineteenth century advanced a notion of an equilibrium that was invested mostly in the static outcome of exhausting all possibilities of improvement. Typical examples were the improvements realized by an individual firm’s progressive division of labor or by a firm’s choice to switch industries to one where the rate of return on investment capital is higher. The individual firm was said to be in equilibrium only when its production process cannot be further divided. Industries in an economy were said to be in equilibrium only when all firms in all industries are earning exactly the same rate of return and hence there would be no possibility of gain by switching industries. In both cases, the state of equilibrium depends on whether the firm knows of any possibility of improvement. It is always possible that the necessary condition for equilibrium—such as the uniform rate of return—is not actually fulfilled because firms are either unaware of any possibility of improvement or are in some way constrained from moving to a more profitable industry (as would have been the case in the eighteenth century when the king granted a profitable monopoly to one producer).

For the most part, given the diverse history of the concept, economists and economics textbooks seem confused about just what equilibrium means. Is it a static balance such as when a market’s supply equals demand? Or is it a singular state of affairs in a dynamic system that explains how the balance was obtained? A balance can be static but an equilibrium is always a dynamical concept. When modern economists say that an economy is in equilibrium they seem to be saying only that the operative forces in the economy are in balance as there is rarely anything said about the explicit dynamics needed to restore or obtain the equilibrium.

In the case of a market where supply and demand are in balance, what is most important is that there can be only one going price: the one price that clears the market and thus the one price at which it is possible for every participant to be maximizing. And while the classical economists were interested in a state of affairs where there would no longer be a reason to change as there is no possibility of gain, the primary purpose for the neoclassicals’ assumption of a state of equilibrium is to obtain the state of affairs where everyone is knowingly maximizing. It is primarily the mathematics of universal maximization that characterizes modern economic theory since the late 1930s.

## EQUILIBRIUM AS A PROBLEM FOR MATHEMATICAL ANALYSIS

The beginning of neoclassical attempts to incorporate explicit equilibrium concepts in economics in the late nineteenth century was coupled with the attempts to make economics a mathematical science like physics. The main methodological question was whether one could build a mathematical model of a whole economy consisting of many independent decision makers guided by prices determined in various markets such that the model would imply the existence of a unique set of prices (one price for each good or service transacted in the economy). One of the first economists to attempt this in the nineteenth century was the French economist Léon Walras. His approach was to represent all participants in the economy (producers or consumers of goods and services) with their objective functions (i.e., their respective utility or production functions), which represent what they wish to maximize. Each individual was simply assumed to be a maximizer such that Walras could deduce the necessary calculus conditions for each individual to be maximizing. For each individual, these conditions are in the form of equations, one for each and every good or service. Obviously this involves a huge number of equations in a real economy but this is a mathematics problem so the number does not matter. Together these conditions amount to a system of simultaneous equations and the task is to find a means of specifying the objective functions to assure the logical existence of the unique set of prices that would allow all individuals to be maximizing. Walras thought that the existence of such a set of equilibrium prices was assured whenever the number of equations equaled the number of unknowns (the prices and the quantities of all good and services transacted). He was in error about this and for many decades mathematical economists would try to create more mathematically sophisticated models that would assuredly entail equilibrium prices and quantities. The first success was not obtained until the 1930s.

It was also realized that proving the existence of a set of equilibrium prices is not enough. Model builders always face two methodological problems. First, if the equilibrium model is to explain why prices are what they are, it must also explain why they are not what they are not. If the model entailed more than one set of possible equilibrium prices, one of those sets may fit the observable prices but since the other sets are also entailed, the question is begged as to why the observed set existed and not one of the other sets. In other words, a model with multiple equilibria is an incomplete explanation of observable prices. Second, even if the model entails a unique set of equilibrium prices, not only must that set be unique but it must be stable. That is, if for any reason the equilibrium is upset (i.e., one or more of the prices deviate from the equilibrium values) will the system return to a state of equilibrium? Any possibility of multiple equilibria aggravates this problem, too. Much of the mathematical work of the 1950s and 1960s was devoted to solving both the existence problem and the stability problem. From a mathematical point of view, many models were provided that were indeed logically sufficient to solve these two problems. But critics would be quick to point out that too often the assumptions made to construct these models were unrealistic.

## EQUILIBRIUM MODELS AS A MODE OF ExPLANATION

Leaving aside the mathematical economist who is more interested in the mathematics of equilibrium models than the economy those models are designed to explain, the problems of stability and existence must be dealt with if those models are ever to be a satisfactory explanation or even a useful guide for economic policy. This is particularly so if the equilibrium model is to be used to explain prices. While claiming that the observed price of a good or service is what it is because it is an equilibrium price— that is, it is at a value that allows its market to clear (i.e., allows demand to equal supply)—the explanation is not complete unless one can also explain the how or why the price was adjusted to that equilibrium value.

Any adjustment or change in the price is a decision made by an individual who is not maximizing at the current price. So, if one assumes all demand curves are negatively sloped and supply curves are positively sloped, then for someone to be motivated to change the price it must not be at the one value necessary for market equilibrium. In particular, either the price is above the value necessary for equilibrium and thus some supplier is unable to sell the amount necessary for profit maximization or it is below that equilibrium value and at least one demander is unable to buy enough to maximize utility. Kenneth Arrow raised this issue in a 1959 article “Towards a Theory of Price Adjustment,” where he recognized that textbook theory presumes that all decision makers are in effect small fish in a big pond. That is, all textbook decision makers are price takers because they are too small to have an effect on the going price. But, if the market is in disequilibrium and everyone is a price taker, who changes the price and why? Since textbook economics has maximization as the only behavioral assumption, Arrow said that how much someone changes the price is a decision that must be explained as a maximizing choice. Interestingly, textbooks have an explanation for someone who chooses the price but it is in the chapter about the monopoly producer. While this might be seen as a means of completing the explanation of the price, it creates a contradictory situation. One would have one theory for when the market clears (everyone is a price-taking maximizer) and a different theory for the disequilibrium price adjustment. As every equilibrium model must deal with the dynamics needed to assure stability, it means that both theories must be true at the same time but they are contradictory. This is a very unsatisfactory situation for anyone wishing to use an equilibrium model to explain the one going price, one that clears the market so all participants can be maximizing.

## EQUILIBRIUM ATTAINMENT VERSUS THE EQUILIBRIUM PROCESS

Critics of equilibrium model building complain that devoting so much effort to mathematically proving the existence of a possible equilibrium misses the policy point of market equilibrium theory. The primary virtue of a market system as the basis of social organization is not the mathematical properties of a state of equilibrium but the fact that a stable market will always give the correct information to would-be market participants whenever the equilibrium has not yet been reached. A rising price indicates to producers to supply more and to consumers to demand less. But critics also claim the time required to make adjustments to achieve an equilibrium may exceed the time allowed before consumer tastes or technology changes.

In order to recognize an equilibrium process, a model must include an explanation of how the equilibrium is achieved and how long it would take to reach it. Without such recognition, the notion of a market being in a state of equilibrium adds nothing beyond the behavioral assumption of universal maximization. This is so because the assumption of utility maximization is used to explain the individual consumer’s demand decision at any given price and the assumption of profit maximization for the individual producer’s supply decision at that price. Thus if everyone is maximizing at the going price, that price must be the one that clears the market (i.e., the one where demand equals supply)—no other price is logically possible.

**SEE ALSO** *General Equilibrium; Nash Equilibrium; Partial Equilibrium*

## BIBLIOGRAPHY

Arrow, Kenneth. 1959. Towards a Theory of Price Adjustment. In *Allocation of Economic Resources*, ed. Moses Abramovitz. Stanford, CA: Stanford University Press.

Boland, Lawrence. 1986. *Methodology for a New Microeconomics: The Critical Foundations*. London: Allen & Unwin. http://www.sfu.ca/~boland.

Boland, Lawrence. 1989. *The Methodology of Economic Model Building: Methodology after Samuelson*. London: Routledge. http://www.sfu.ca/~boland.

Hahn, Frank. 1973. *On the Notion of Equilibrium in Economics*. Cambridge, U.K.: Cambridge University Press.

Mirowski, Philip. 1989. *More Heat than Light: Economics as Social Physics, Physics as Nature’s Economics*. Cambridge, U.K.: Cambridge University Press.

Wald, Abraham. [1936] 1951. On Some Systems of Equations of Mathematical Economics. *Econometrica* 19: 368–403.

*Lawrence A. Boland FRSC*

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