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Economic Newton. In memory of Kenneth Arrow.

Economics is one of the youngest “exact sciences”. It uses models as complex as modern physics (not to be confused with mathematical physics) and works. With data like no other science – in fact, it is from economists that everyone learns data analysis.

Because of this youth and because of the speed with which it has developed in the last hundred years. like physics and chemistry two hundred years ago, like biomedicine in the same hundred years – unexpected things happen.

Kenneth Arrow is dead

Kenneth Arrow is dead – and economics should experience the same thing that physics did when Newton died. Or mathematics when Hilbert died. Arrow stood as much at the foundations of modern economics as Hilbert at the foundations of modern mathematics. Without it, it is impossible to imagine.

A great economist

Arrow was 95 years old, he lived a long life. His fundamental work was recognized very early and he spent the last forty years as a “living classic” … I remember very well how he finished his dessert and got up from the table. During the summer school in Jerusalem in 1998.

All the other professors – Milgrom and Plott, legends of their time and “youth” like Wolak. Got up and followed him without finishing what they had on their spoons; to students, Arrow was just a great economist, but to eminent economists, he was just a living God.

Impossibility of democracy

Everyone knows “Arrow’s theorem on the impossibility of democracy”. The statement that no matter what method of aggregation of citizens’ preferences we take, if this method satisfies several completely natural criteria, then it turns out that it is necessarily a dictatorship.

(That is, the society’s choice completely coincides with the preferences of one of its members.) Arrow’s proof took more than 100 pages. Modern proofs are an elementary exercise per page. (I like the second proof in John Genkoplos’ Three Short Proofs of Arrow’s Theorem the most.) The theorem has some very practical implications for building electoral systems, but Arrow’s theorem has given economics much more.

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Human behavior

It would seem that such a formal result? However, he completely changed the paradigm in economic theory. After that, it became impossible to look at issues related to incentives and human behavior in a different way.

The very idea of ​​”the set of all possible preferences” proposed by Arrow. When formulating the theorem is a whole world. From it came the fundamental results of Gibbard-Sutherwhite. On the impossibility of non-manipulative voting schemes, and the Vickrey-Clark-Groves mechanism, the basis of all theory – and practice! – auctions and mechanism design.

And the Myerson-Sutherwhite theorem on the impossibility of a mechanism that always ensures efficiency in the task of bargaining. (For those who are interested, there is a wonderful little book in Russian. By Danilov and Sotskov, Mechanisms of Group Choice.) One might say.

General equilibrium

But the theorem on the impossibility of democracy is a Ph.D. thesis. Arrow received the Nobel Prize for “the theory of general equilibrium”. Which we now teach entirely within the framework of his approach.

This approach (“general Arrow-Debré equilibrium”) is so basic that now. When microeconomics courses sometimes skip the topic altogether – partly because of the complexity, partly because of the complexity of “comparative statics” (that is, obtaining specific hypotheses).

some students even do not realize that, for example, financial mathematics is built on the concept of “general equilibrium”. You study, there is CAPM, you discuss “betas”, but, you have to understand. These “betas” are still the same general Arrow-Debreu equilibrium with imperfect financial markets. Same with computable general equilibrium models,

Economic science

As befits Newton and Gilbert, even Arrow’s individual touches on some areas of economic science became masterpieces. The 1962 article “The Economic Implications of Learning by Doing” was the forerunner of the theory of endogenous growth. Economic growth cannot be explained by population growth or fixed capital investment.

The 1963 article “Uncertainty and the Welfare Economics of Medical Care” replaces – and now, fifty years later! – an introductory course in health economics. It is also written exemplary – without a single formula, but using all the achievements of the then economic science. (I remember with what interest, not at all interested in health economics. I read this article at NES while attending a course on public sector economics.)

Death of a brilliant scientist

The death of a brilliant scientist who gained recognition during his lifetime, who left dozens of outstanding students (Harsagny! Spence! Laffon! Maskin! Myerson!) and his name, scattered over a variety of concepts and theorems of economic science, naturally does not cause a feeling of deep sorrow.

The reason to give references to his work is not for economists who deal with the terms and objects introduced by him every day, but for everyone. Moreover, some of the articles – the same economics of health care – are perfectly readable even without first listening to a course in microeconomics.

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