The general equilibrium theory that came to dominate the analysis of competitive markets in the last fifty years was a further development of the neoclassical economics of Walras and his follower, Vilfredo Pareto, which had been largely dormant in the interwar period. It came back to life in the era of the Cold War, when capitalism and communism were in combat. Here we examine the essentials of the theory, some of its limitations, and its larger significance.
Picture a closed economy (no foreign trade) with a given number of consumers who seek to maximize their satisfaction, a given number of producers who seek to maximize their profits, and a given amount of resources, which are divided among the consumers and producers. The question to be explored is whether there is a system of prices at which consumers succeed in optimally satisfying their preferences, within the limits set by their resources, and producers succeed in maximizing their profits, solely through the operations of competitive markets and without any government intervention. The theory then proves that such a price system exists. We do not go into the proof here, since it uses such mathematical exotica as vectors, convex spaces, and fixed point theorems. Two books present the analysis, using the mathematical logic developed in Whitehead and Russell's Principia Mathematica: Gerard Debreu, Theory of Value: An Axiomatic Analysis of Economic Equilibrium (1959) and General Equilibrium Analysis (1971) by Kenneth Arrow and Frank Hahn. They argued that there could exist in a perfectly competitive system of markets a general equilibrium of prices brought about solely by the voluntary action of consumers and producers.
The analysis was an improvement over the earlier theory of market price. Recall in our discussion of the beginnings of mathematical economics that Augustin Cournot pointed out that the demand for a commodity was a function of its price: D = F (p) in his terminology. That would be true if everything else in the economy remains the same. But everything else does not remain the same. As Irving Fisher showed in 1892, a change in one price reverberates throughout the price system. Thus, the demand for lox will be affected not only by the price of lox, but by the prices of bagels and cream cheese as well. Cournot's equation expands to D a = F (p a p b p c . . . p ) in algebraic notation. That is, the demand for commodity a is a function of its price, as well as the prices of commodities b, c, and all other commodities. Cournot's equation defined a partial equilibrium in a single market, while
the expanded equation defines a general equilibrium of all markets. The fundamental idea is that the system of markets is a unified whole.
The concept of a market system of interrelated parts led economists to examine some complex market relationships. Markets for complementary products such as lox, bagels, and cream cheese, for example, or products that can substitute for each other, such as tin or aluminum cans, were explored. The concepts of competition and monopoly were broadened from examining a single industry, such as steel or chemicals, to studying competition for the consumer's dollar by more than one product. The economics of general equilibrium theory enabled economists to broaden their field of analysis to include many areas of economic activity that previously had not been thought of as economics. Viewing households and families as utility maximizing units, their production and distribution decisions became items to be analyzed. Marital status, the number of children, education, and health care were all subject to the desire to optimize. Criminal activity, drug addiction, and inheritance were also topics to be analyzed. In other areas, game theory was applied to all kinds of personal relationships. Growth theory was broadened to include the complex relationship between past and present investments in human capital and research and development expenditures. The core assumption of general equilibrium theory, that individual preferences determined individual choices, was developed. These choices were subject to the constraints imposed by social norms and by existing technology, and they were qualified by human expectations.
Despite these advances, general equilibrium theory has serious limitations. Perhaps the most serious flaw is a failure to show how the equilibrium could be achieved. The theory defined the system of prices at which all consumers and all producers were able to optimize, but it failed to show how the economy could move from an initial disequilibrium to an equilibrium. Nirvana may be there, but how does one get to it? Debreu and Arrow/Hahn had no answer.
A second and perhaps more serious flaw involved the distribution of income and wealth. The theory postulated an initial distribution of income and wealth among consumers and producers. If the initial distribution gave half of all resources to 5 percent of the participants and half to the remaining 95 percent, the resulting equilibrium would provide many luxuries to the few and little subsistence to the many. Was this optimal? Indeed, for every possible initial distribution of resources there would be a unique equilibrium set of prices and a unique distribution of income. So even if a general equilibrium were achieved, the desirability of the result was still at issue.
Finally, the theory included assumptions that were clearly unrealistic. For example, it required that all producers and consumers have "perfect knowledge" of all prices, including all future prices, in order to make optimizing decisions about the use of their resources. This ruled out all uncertainty. Theorists took up the challenge. Some used the concept of "expected utility" to
convert uncertainty into risk whose probability could be determined, but this resulted in temporary equilibria only. Others built true uncertainty into general equilibrium models only to end up with a variety of disequilibria. These and other explorations on the frontiers of general equilibrium theory tended to undermine the very concept of.a general equilibrium.
The presence of unrealistic assumptions in general equilibrium theory was strongly attacked by critics. They pointed out assumptions about the rational behavior of consumers and producers that could be neither proven nor disproven, reflecting Godel's undecidability theorem in systems of mathematical logic. Other assumptions about the absence of uncertainty and the presence of full employment were clearly unrealistic. It was a static theory. Some critics argued that these aspects of general equilibrium theory placed it in the realm of metaphysics rather than reality. The problem may be that the mathematics used is not able to fully account for the great complexity of the real world market economy. Perhaps the underlying issue is whether a concept of the economy as a stable system in equilibrium, or tending toward equilibrium, is meaningful in a world that seems to be continually changing and sometimes in turmoil. Perhaps we should be thinking in terms of continuous disequilibrium and conflict instead of equilibrium and harmony.
Despite its flaws, general equilibrium theory swept through the economics profession in the 1970s in the same way that neoclassical economics displaced classical economics a century ago, and as Keynesian economics had swept the field a generation before. General equilibrium theory was studied by graduate students in every economics department in the Englishspeaking world. The books by Debreu or Arrow and Hahn, or textbooks derived from them, were required reading, and they still are. The leading journals in the field are filled with papers based on general equilibrium models of the economy, bolstered by econometric studies that support the hypotheses developed in the model.
The time was ripe for the general equilibrium revolution. The ideology and climate of opinion of the Cold War extolled the market economy and economic freedom in opposition to the economic planning and authoritarian government of the Soviet Union. As if by an invisible hand, high theory in economics responded by describing the competitive market economy as one in which every need or want of consumers, insofar as their resources would allow, would be met by the voluntary actions of producers. It also fitted the needs of political conservatives who believed in eliminating government from economic affairs. Political events and the ideological needs of the Cold War created a fertile environment for general equilibrium theory.
This is not to say that those who originated or developed general equilibrium theory were political conservatives or Cold Warriors. The political leanings of the individuals involved are not particularly relevant to the social and political processes by which ideas move to prominence. Walras was a socialist, Pareto a right-wing conservative. Debreu is reputed to be a political conservative. Arrow a political liberal; the two are close friends. The im
portant point is that the political and ideological climate of opinion is always an important factor in the development of ideas.