Workshop Optimal Transport: Theory and Appli ations

Fourier Institute

Description

Niveau: Supérieur, Doctorat, Bac+8
Workshop Optimal Transport: Theory and Appli ations Fourier Institute (Grenoble I, Fran e) June 29th-July 3rd Titles and abstra ts of the talks F. Bollet (Paris-Dauphine) Phi-entropy inequalities and Fokker-Plan k equations The onvergen e to equilibrium for Fokker-Plan k type diusion equations an be studied by means of fun tional inequalities su h as the Poin aré and logarithmi Sobolev inequalities. We present this link and we derive and study a family of Phi- entropy inequalities: they provide an interpolation between these two fun tional inequalities and an make the onvergen e to equilibrium more pre ise. This is a joint work with I. Gentil. Y. Brenier (Ni e) Optimal transport, onve tion theory and semi-geostrophi equations There are several well known links between optimal transport and uid me han- i s. For instan e, the polar fa torization of maps is dire tly related to the time dis retization of the Euler equations (in the Arnold style). Another link has been re ently established with onve tion theory, the entral theory of geophysi al ows. The rst step is an interpretation of the Angenent-Haker-Tannenbaum model for optimal transport as a onve tion model in porous media (des ribed by the Dar y- Boussinesq equations).

• tions has


• tion


• unexpe ted


• image transfer


• optimal transport


• inequalities via lyapunov onditions


• stru ture


• inequalities


• transportation problem

Sujets

• Sobolevsky
• Institute
• Carrillo
• Salomon
• Samson
• Feldman
• Transportation theory

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 10
• Langue: English

Extrait

The Appropriate Treatment of Distribution in Economics   Nicolaus Tideman *   Abstract This paper argues that to address questions of distribution that concern economists, one must combine economics with a theory of justice. The paper traces the implications of one theory of justice that can be combined with economics, namely a theory that assumes that people have rights to themselves and that all people have equal rights to natural opportunities. This theory implies that people have the right to form the governments they choose, provided that they do not appropriate more than their shares of natural opportunities and that they allow all those who wish to do so to leave or to secede. The theory of justice also implies that there should be transfers among governments to equalize per-capita appropriations of natural opportunities. The obligation to compensate for appropriations of natural opportunities induces an incentive to make efficient decision about all appropriations of natural opportunities and all actions that benefit or harm other nations. The theory implies that in a just world the issues of distribution that concern economists become questions of morality or efficiency rather than justice, while in an unjust world these issues require tragic choices.                                                     *  Professor of Economics, Virginia Tech. I am grateful to Florenz Plassmann for helpful comments.

I. Introduction Questions of distribution arise in economics mainly in two ways: First, in the evaluation of proposed economic policies that increase total output but entail unintended redistribution, and second, in the evaluation of programs that a politically dominant coalition regards as achieving a more appropriate income distribution. A reduction in a tariff increases total output but it makes some people worse off. We could devise a program that provided compensation, but some people would be worse off because we never have enough information to know how much compensation is needed. What, if anything, permits us to say that a tariff reduction is a good thing? A program to support the poor by taxes on those who are better off need not make those who are taxed worse off, because those who are taxed may have compassion for the poor. But some of those who are taxed will lack compassion, and they will be taxed anyway. On what basis, if any, can we say that it is appropriate to tax them? There are three frameworks for addressing such questions that economists typically employ: the Paretan framework, the social welfare function framework, and the cost-benefit framework. More than 100 years ago, Vilfredo Pareto expressed the economists’ dilemma (translated from French): Consider any position and assume that we move away from it by a very small amount, consistent with the restrictions [on what is economically feasible]. If in so doing the welfare of all the individuals of the collectivity is increased, it is obvious that the new position is more advantageous to each of them; and vice versa, it is less so if the welfare of all of the individuals is decreased. Moreover, the welfare of some of them can remain the same, without changing these conclusions. But on the other hand, if this small movement increases the welfare of certain individuals and decreases that of others, we can no longer state positively that it is advantageous to the entire collectivity to carry out that movement.  1     Pareto’s ideas led to the definitions of Pareto improvement and Pareto optimality. Economists generally feel that they are on solid ground when selling the virtues of Pareto improvements; changes that are not Pareto improvements make us nervous. But we never have a solid basis for claiming that a proposed change would be a Pareto improvement. We                                                   1   Vilfredo Pareto, Manual of Political Economy (New York, 1971 [1909]), pp. 451–2.