General Equilibrium Theory

What is general equilibrium theory? It has been called "the crown jewel of neo-classical economics," "the economist's justification of the market system," and, by Franklin Fisher of MIT, "the central set of propositions that economists have to offer the outside world — propositions that are, in a real sense, the foundations of Western capitalism…. They underlie all the looser statements about the desirability of a free-market system." But general equilibrium theory has also been used to argue that market socialism--not capitalism--is the uniquely efficient economic system. And the theory has also been called

"a grand but total failure," and "still dead after all these years." So while general equilibrium theory is obviously highly important to anyone who cares about economic thought, there is obviously lots of disagreement on what it implies and what its cognitive status is.

The Question to which GE Theory Is an Answer

To understand what general equilibrium theory is, it helps to think about the question to which it provides an answer. That question is described by Kenneth Arrow and Frank Hahn in the introduction to their book General Competitive Analysis (1971). Arrow and Hahn ask us to imagine what would happen were we to put a question to a person entirely innocent of economic theory. Suppose we asked that person: what would happen in an economy organized around individual exchange, motivated by individual greed, and controlled by a very large number of individual agents? It seems likely, say Arrow and Hahn, that the person would answer: "There will be chaos--that is, there won’t be much coordination or efficiency in that economy—let alone justice." What general equilibrium theory proves, say Arrow and Hahn, is that "a decentralized economy motivated by self-interest and guided by price signals would be compatible with a coherent disposition of economic resources that could be regarded, in a well-defined sense, as superior to a large class of possible alternative dispositions" (pp. vi-vii). What do A. & H. envision by "a coherent disposition of economic resources?" An equilibrium disposition of such resources. What is that? The general equilibrium theorist John Hicks helpfully defined it thus:

"The static economy—in which wants are unchanging, and resources unchanging—is in equilibrium when all the individuals[—firms or natural persons--]in it are choosing those quantities, which out of the alternatives available to them, they maximally prefer to produce and consume. The quantities produced and consumed will then be equilibrium quantities."*

The Five Main Theorems of GE Theory

So general equilibrium theory is above all the proof that in a decentralized market system, there exists one set of prices and allocation of resources at which the economy is in general equilibrium. This is the Existence Theorem, famously proved in the 1950s by Kenneth Arrow, Gerard Debreu, and Lionel McKenzie. Such a general equilibrium in an economy exists when there is no excess demand or supply in any market: all markets have cleared. So proofs of the existence theorem identify the conditions under which such a general equilibrium would be achieved. Such conditions include perfect information for all participants in the economy, no transactions costs, perfectly competitive markets, and other quite stringent conditions.

But the existence theorem concerns only questions of statics. It is also important to consider the dynamics of general equilibrium. Is it possible that a decentralized competitive market system could tend to remain in equilibrium, once it achieved it? Suppose that a price disruption occurred in an economy in general equilibrium. Under what conditions would that economy tend to return to general equilibrium? The proof that such a tendency is possible--that there could be a stable general equilibrium--and the identification of the conditions under which such a tendency would existence, is the task of the Stability Theorem. There is also a Uniqueness Theorem, which identifies conditions under which that general equilibrium would be unique in that economy--i.e., that there would be only one set of prices at which there would be a general equilibrium.

General equilibrium theory is also interested in the question of whether and when such an equilibrium would be efficient. It proves that such an equilibrium is Pareto-efficient: that once an economy is in general equilibrium, no one in that economy could be made better off without making someone else worse off (the First Fundamental Theorem of Welfare Economics). This is a specification of Adam Smith's idea of the invisible hand: if everyone works in a perfectly competitive market to advance her own self-interest, everyone will attain economic benefits and advancement. The overall message here is that it is in general a good idea not to interfere in highly competitive markets.

Finally, general equilibrium theory proves that every Pareto-efficient state of an entire economy would be sustained by a general equilibrium (the Second Fundamental Theorem of Welfare Economics). That is, if we decide a particular Pareto-efficient distribution of goods is desirable, and redistribute wealth to achieve it, then if we stopped intervening and allowed an economy in general equilibrium to work freely, that Pareto-efficient distribution would be sustained. The overall message here is that interference in highly competitive markets can be a good thing, if it is done once for all and then those markets are allowed to work freely.

How GE Theory Justifies the Market System

These theorems hold immense implications for the market system, whether it be capitalist or market socialist. For, if a market system is sufficiently close to meeting the conditions of perfect competition, perfect information, and no transactions costs, etc., then it will approach a stable and optimally efficient equilibrium. But stability and optimal efficiency seem to many people to be highly desirable ideals for an economy to approach. Hence, a market system that meets all the perfect- conditions seems highly desirable. For it is an economic system likely to get us very close to those ideals. It is for this reason that general equilibrium theory is often called the theoretical underpinning of the market system. It has been used by some neo-classical economists to defend capitalism against all alternative economic systems, and by other neo-classical economists to defend market socialism against all alternative systems (e.g., Oskar Lange and Abba Lerner).

GE Theory, the Crown Jewel?

We can now understand why people call the theory "the crown jewel of neo-classical economics." It is the crown jewel in three senses. First, it allows economists to lift the holy grail of neo-classical economics: the explanation of all relative prices in an economy. Using GE theory, economists can attempt to explain the statics and dynamics of the set of all prices throughout an economy. Second, it provides a justification of the market system against non-market systems like central authoritative prices setting or feudal systems of production. Neo-classical economists have generally always favored market systems over such non-market systems--though note that market socialism is a type of market system. Third, GE theory gives a how-possible explanation of one of the central principles of neo-classical economics. These principles have been helpfully specified by Daniel Hausman as:

(1) Utility theory: Individuals have complete and transitive preferences and choose that option that they most prefer.

(2) Economic Preference: Individuals prefer larger commodity bundles to smaller. Commodities possess diminishing marginal utility or diminishing marginal rates of substitution for all individuals.

(3) Production: Increasing any output (other inputs held constant) increases output at (eventually) a diminishing rate. Increasing all inputs in a certain proportion increases output in the same proportion. Entrepreneurs or firms attempt to maximize profits.

(4) Equilibrium: An equilibrium that reconciles the activities of individuals (in which there is no excess demand on any market) exists.**

GE theory explains how (4), Equilibrium, is possible, through the proof of the Existence Theorem. So there is a sense in which GE theory is a foundation of neo-classical economics itself, though of course GE theory appeals to the other three principles of neo-classical economics in order to prove its theorems.

Problems with GE Theory

There are just two problems with general equilibrium theory. The first is that the conditions it identifies are heroically unrealistic. No one has ever observed an economy with perfect competition, or perfect information, or no transactions costs. So how far it can fairly be applied to real-world economies is a difficult question. The second is that nobody has been able to come up with conditions for Uniqueness or Stability. The only conditions which have been proved to lead to Uniqueness are theoretically unattractive and highly unrealistic. As for Stability, it has been proven that so long as there are more consumers than commodities, there will always be a set of consumer preferences and endowments at which there will be price fluctuations.***

Equilibria illustrated

http://tinyurl.com/ap36toa

Click here for a remarkable article that lays out the market-justifying role of GE theory and the theory's main assumptions and theorems, and then connects those to the assumptions and theorems of Keynesian and Marxist economics. The article's opening and closing are written from a Marxian perspective, but the argument itself should be palatable to persons of all ideologies--except defenders of the sanctity of neoclassical economics!

Development of General Equilibrium Theory

"As every individual...endeavours as much as he can both to employ his capital in the support of domestic industry, and so to direct that industry that its produce may be of the greatest value; every individual necessarily labours to render the annual revenue of the society as great as he can. He generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. Nor is it always the worse for the society that it was no part of it. By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it. I have never known much good done by those who affect to trade for the public good. It is an affectation, indeed, not very common among merchants, and very few words need by employed in dissuading them from it."

--Adam Smith, The Wealth of Nations, Bk IV, Ch. II.

Leon Walras, 1834-1910 (Wikimedia Commons)

Founder of general equilibrium theory

One of three founders of neo-classical economics and of the marginalist revolution

Elements of Pure Political Economy (1874-7)

*= John Hicks, "The Concept of Equilibrium," Capital and Growth (1965), p. 15.

**= Daniel Hausman, "What Are General Equilibrium Theories?" Essays on Philosophy and Economic Methodology (Cambridge UP, 1992): 165-171, p. 166.

***= Frank Ackerman, "Still Dead after All These Years: Interpreting the Failure of General Equilibrium Theory," in The Flawed Foundations of General Equilibrium Theory, ed. Frank Ackerman, Alejandro Nadal, et al (Routledge, 2004), p. 16.