How does the market work?

“Among all the Nobel Laureates in Economics, I have done the most abstract work,” Gérard Debreu said in 1985, two years after he’d received the Nobel Prize for his theory of economic equilibrium. Though he chose to stay a theorist all his life, and didn’t care much for real-world applications of his work, his mathematical models provided the basis for generations of economists to find out more about how individuals and companies interact, and how a market economy really works.

Gérard Debreu

The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, 1983


At a glance

Born: 1921, Calais, France

Died: 2004, Paris, France

Field: General equilibrium theory

Prize-winning work: Reformulation of the theory of economic equilibrium

Favorite spare-time activity: Hiking (and thinking while hiking)

Favorite hiking spot: The Californian coast, north of San Francisco

Neuroses: Was famous for always having a clean desk

On the run: Tended to drive a little faster than others

Changing from mathematics to economics

When France entered World War II in September 1939, Debreu was an 18-year-old boy who had just started his studies in mathematics. One year later, the French territory was divided into a northern zone under German military administration and a free zone in the south. Debreu travelled in both zones, but eventually decided to study in Paris. Despite the “dark outside world” of the country’s capital under Nazi occupation, he concentrated on digging deeper into the field he’d chosen. The university became his “microcosm”, and Debreu enjoyed the “superheated intellectual atmosphere”, as he recalled in his Nobel autobiography.

When D-Day came, the passionate student briefly served in the French occupation forces. Back at university, his interest in economics increased significantly. He read the theories of Léon Walras, who’d been a pioneer in the development of general equilibrium theory, and decided to follow in his footsteps. “I’d discovered the subject that fascinated me, in which I perceived that there was a great deal of work to do.”

A Frenchman in the United States

Luckily for Debreu, when he started his academic career mathematics was becoming immensely popular in economic theory. A fellowship enabled him to visit Harvard University, the University of California, Berkeley, Columbia University and the University of Chicago. It brought Debreu “up to date with all the scientific developments in economics from which France had been cut off” in wartime. And there was no going back. The Cowles Commission for Research in Economics, based in Chicago, was the hot spot for mathematical economics, and the offer they made to Debreu was “irresistible”. He decided to stay in the US and, in the years that followed, devoted most of his research to the subject that had led him towards economics in the first place: general equilibrium.

What determines a market price?

To understand the idea of general equilibrium, we have to look at one of the fundamental ideas of microeconomics – supply and demand. With demand referring to how much of a product is desired by its customers, and supply being the amount of a product the market is offering, the price will, in theory, vary until the point where both sides are correctly balanced. In this case, the market reaches an economic equilibrium. Economists would say: the market clears.

Sounds a little theoretical? It is indeed, and that’s why Debreu, alongside fellow Nobel Laureate Kenneth Arrow at Stanford, was the perfect candidate to provide the mathematical proof that general equilibrium actually exists. “The economic system is highly unified, what happens in any place within an economy has repercussions affecting the entire economy,” Arrow explained. “An innovation in one field may increase the demand for certain resources and, therefore, draw them away from others. One can’t understand even a single industry without reference to remote connections with other industries.”

To analyze these connections is fairly sophisticated. But, in their joint work, Debreu and Arrow were able to promote their theory, showing that prices exist that bring a market into equilibrium.

I try to make a theory as rigorous, as general, as simple as possible, to build a mathematical model of the economic system that explains the interdependence of all decision makers in a market.

Why can equilibrium never be reached in reality?

Debreu was occasionally asked to serve as a consultant, but declined every offer. It never occurred to him that his opinion outside academia should be considered important, since he focused on basic research rather than applications of economic theory. He knew, of course, that his formal theory was only a first approximation to understand economic activity. An equilibrium could only ever be reached theoretically, as prices for goods and services were constantly changing. But Debreu left it to other economists to develop and apply his theories to the real world. He felt that his mathematical modeling should provide a basic language for the work of others.

And it did. Economists following Debreu have constantly pointed towards the importance of his work as a crucial basis for their research, most notably Nobel laureates Peter Diamond, Robert Aumann and Daniel McFadden.

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Debreu became a US citizen in 1975. His collaborator and friend, Arrow recalled that Watergate and the impeachment process against US President Richard Nixon had made quite an impression on the Frenchman. “He said, ‘This is a great county. I will become a citizen.’”

Though interested in politics, Debreu refrained from commenting on it too often. But after he’d won the Nobel Prize, he realized the greater influence he could have. “Time has always been scarce,” he explained. “But I try not to waste it. I try to have purpose.” While he frequently protested against people’s belief that, being a Nobel Laureate, he could speak on every important issue with authority and wisdom, he used his popularity for his work in South America.

In the 1980s, he was sent to Chile by the Committee on Human Rights at the National Academy of Sciences. “I have felt a greater obligation to talk about human rights,” he explained. The delegation he was traveling with investigated whether scientists, engineers, and medical professionals were facing torture under the military dictatorship led by Augusto Pinochet.

Human rights activities can be very frustrating. Often one has the impression that one does not achieve much. But it’s not fully justified. There’re cases in which one obtains results.

What do students need to learn?

For Debreu, leaving his comfort zone was not an easy thing to do. Though revealing that he adored his grandchildren and enjoyed hiking together with his wife, he didn’t speak in great detail about his private life. His human rights work was one of the few things he liked to talk about outside his research, as was his commitment to university education and his students. “Perhaps the greatest service I can render to them is to communicate a sense of enthusiasm and excitement,” he said.

The young have a tremendous privilege. There are many opportunities open to them. What I think is most important is for them to find something in which they believe and then give that their full energy, of which they have so much.

He’d found that one thing he believed in, though many people had a hard time understanding it. It was his deep passion for abstract thinking and the beauty of mathematics, which would form his life’s work.

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