2007 Nobel Prize of Economics

Minnesota professor, Leonid Hurwicz, Princeton professor, Eric S. Maskin, and Chicago professor, Roger B. Myerson win the 2007 Nobel Prize in Economics for having laid the foundations of mechanism design theory.

To be honest, I don't know about this area at all, but I know the name of Professor Hurwicz. If you were a grad student of economics, you could learn his name in the field of demand theory in microeconomics.

Let me explain a little:

Let X(p, m) be the Marshallian (ordinary, uncompensated) demand function, where p is a price vector and m is an income. This function will be derived from the utility-maximization problem of an agent. It should be equal to the Hicksian (compensated) demand function, which will be derived from the expenditure-minimization problem of the agent, at the corresponding level of utility;

Hi(p,u)=Xi(p, E(p,u)) ......(1)

where u is the utility level to be targeted and E(p,u) is the expenditure to achieve the utility level, which you can get to put the Hicksian demand functions into the form of the expenditure, for example, px, in this problem.

According to the Shephard's lemma, which is the result of the Envelope Theorem,

dE(p,u)/dpi =Hi(p,u) .......(2)

where "d" means the partial derivative. Sorry, I can't write it correctly.

And then we have to show the equation (2) is symmetric. The reason will be clear soon.

First differentiate the both sides of the expenditure function with respect to pj, which means the j-th price, and you get the following equation:

dE(p,u)/dpj =Hj(p,u) ......(3)

again differentiate the both sides of the above function (3) with respect to pi, which means the i-th price, and you get the following equation:

dE(p,u)/dpipj =dHj(p,u)/dpi ......(4)

According to the Young Theorem, which is one of the most important properties of calculus, the above equation (4) is the same as the second-order derivative of the expenditure function with respect to pi, and pj:

dE(p,u)/dpjpi =dHi(p,u)/dpj,

The young Theorem;

dE(p,u)/dpipj = dE(p,u)/dpjpi

and the following relationship holds:

dHi(p,u)/dpj=dHj(p,u)/dpi

Here note that the Marshallian demand is not symmetric. (You can show it by using the Roy's identity, which is the property derived from the Duality between the utility-maximization and the expenditure-minimization problems by using the Envelope Theorem.)

If you have a system of the Marshallian demand curves, X(p, E(p,u)), it must satisfy a sense of differential equations from the equation (1);

dE(p,u)/dpi =Xi(p, E(p,u)) ......(3)

The relationship (3) holds if dHi(p,u)/dpj=dHj(p,u)/dpi, that is, the Slutsky matrix is symmetric, which was derived just before. This is the important result of Hurwicz and Uzawa (1971), On the Integrability of Demand Functions", with H. Uzawa, 1971, in Chipman et al, editors, Preferences, Utility and Demand.

The above article seems a little too special in economics, so if you want to know about this more precisely, needless to say, you should read the advanced textbook of microeconomics.

Here's the excerpt of the Press Release:

The design of economic institutions:
Adam Smith's classical metaphor of the invisible hand refers to how the market, under ideal conditions, ensures an efficient allocation of scarce resources. But in practice conditions are usually not ideal; for example, competition is not completely free, consumers are not perfectly informed and privately desirable production and consumption may generate social costs and benefits. Furthermore, many transactions do not take place in open markets but within firms, in bargaining between individuals or interest groups and under a host of other institutional arrangements.

How well do different such institutions, or allocation mechanisms, perform? What is the optimal mechanism to reach a certain goal, such as social welfare or private profit? Is government regulation called for, and if so, how is it best designed? These questions are difficult, particularly since information about individual preferences and available production technologies is usually dispersed among many actors who may use their private information to further their own interests.

Mechanism design theory, initiated by Leonid Hurwicz and further developed by Eric Maskin and Roger Myerson, has greatly enhanced our understanding of the properties of optimal allocation mechanisms in such situations, accounting for individuals' incentives and private information. The theory allows us to distinguish situations in which markets work well from those in which they do not. It has helped economists identify efficient trading mechanisms, regulation schemes and voting procedures. Today, mechanism design theory plays a central role in many areas of economics and parts of political science.

By the way, this is what I am wondering every year, why didn't the Nobel Prize go to Dr. Uzawa? He is a Japanese prominent economist and he achieved good results in economics. The topic I talked about just before is one of them, though it is with Dr. Hurwicz. Moreover, he taught Robert Lucas and Joseph Stiglitz, who are the US prominent economists and, as you know, have got the Nobel Prize already. Anyway, I don't know the reason for that.