This work deeply touched Debrou. Debru decided to switch to aleman and study economics from scratch. Almost at the same time, Arrow, who teaches at Stanford, began to study the general equilibrium problem. Like Debru, he has almost figured out the problem, but he just needs the help of an expert who is proficient in mathematics. He turned to Alai for help, so he found his best partner-Debru. In the early 1950s, Debrou came to the United States and gradually began to publish articles in mainstream academic journals in Britain and America, such as Econometrics. His "atom" (or "axiom") research method is impressive.
1954, an important day in the history of economics has arrived. In cooperation with Arrow, Debru published a paper entitled "Existence Equilibrium of Competitive Economy" in the third issue of Econometrics. The title of this paper is amazing. They announced that the existence of general equilibrium has been proved mathematically. In other words, this 26-page article logically verifies Adam Smith's "invisible hand" conjecture, which is the basis of the whole set of neoclassical economics. From then on, economic theory can be regarded as science, and the "general equilibrium theory" is also called Arrow-Debrou system, and almost all mainstream economists still work in this system today.
In the 1950s, it was called "Golden Year 10" by Debru. Each of his articles gives axiomatic proofs related to the core of economics, and easily proves one equilibrium theorem after another. 1959, debru decided to write a book "on price", summarizing more than ten years of research. He completed this arduous task in only 1 14 pages. This booklet restates the framework of neoclassical economics with general equilibrium theory, which not only discusses the substantive significance of concepts such as commodity, price and consumption, but also includes the problem of resource allocation under the uncertain environment expanded by Luo Gang. At this point, the dust of general equilibrium theory has settled.
Soon, Debrou discovered another important problem-bargaining. In fact, Nash has proved in the 1950s that two people can also decide the allocation of resources through bargaining, and there will eventually be an equilibrium solution according to the differences in negotiating ability. On the surface, in a complex economic system, the mechanism by which everyone trades at a unified market price and everyone bargains to form a price is completely different. With different prices, the efficiency of resource allocation is naturally different.
Cordbrugh is keenly aware that this problem is equivalent to general equilibrium. The price "core" finally formed by large-scale bargaining should be the fixed point he has been studying in the past. In order to solve this problem completely, he invited the mathematician Scarf to cooperate. 1963, they published the Limit Theory of Economic Core in International Economic Review, which proved this conjecture that has puzzled economists for many years. Debru proved the existence of general equilibrium in another way. Several different ideas lead to the same goal, and Smith's prediction was perfectly proved.
1962, debru went to the university of California at Berkeley and taught there for decades. In addition to symbolically publishing a few short articles discussing the application of "atomic" mathematical methods in economics, Debru almost never published a paper again. For him, the most important problems were solved around the age of 40. Twenty years later, he won the Nobel Prize. After more than 20 years, he passed away quietly. Although he didn't study any specific economic problems, he did change the way we think about economic problems.