On analysing the world distribution of income

This paper argues that consideration of world inequality should cause us to re-examine the key concepts underlying the welfare approach to the measurement of income inequality and the inter-relation between the measurement of inequality and the measurement of poverty. There are three reasons why we feel that a re-examination is necessary: (i) the extent of global income differences means that we cannot simply carry over the methods used at a national level; we need a more flexible measure; (ii) we have to reconcile measures of world inequality and world poverty; and (iii) we need to explore more fully the different ways in which measures may be relative or absolute. This leads us to propose a new measure, which (a) combines poverty and inequality, including provision for those who are concerned only with poverty, (b) incorporates different approaches to the measurement of inequality; and (c) allows the cost of inequality to be expressed in different ways. Applied to the world distribution for the period 1820-1992, the new measure provides different perspectives on the evolution of global inequality.global income inequality, absolute vs. relative inequality, poverty, world citizens

On the identification of the “middle class”

The paper examines the identification of the “middle class” using data from LIS and LWS. It first considers definitions based purely on income, examining the rationale for different approaches and illustrating the implications for changes over time. It argues that the concept of “class” requires the examination of other dimensions beyond income. The paper considers the role of property and, drawing on the sociological literature, of occupations.class structure, income distribution

Promise and Pitfalls in the Use of 'Secondary' Data-Sets: Income Inequality in OECD Countries

Secondary data-sets have come to play an increasing role in empirical economic research. This paper examines the major new secondary data-set assembled by Klaus Deininger and Lyn Squire (DS) at the World Bank. We concentrate on its coverage of the OECD countries. We have particularly in mind the user of income inequality statistics who does not wish to go back to the original data. In order to motivate the analysis, we first present two examples of the problems which may arise, showing how both cross-country comparisons and time-series analysis may depend sensitively on the choice of data. Section 3 of the paper sets the DS data-set in the historical context of earlier exercises in assembling comparative information on income inequality. In Section 4, we consider the methodological issues which arise in the use of income distribution data and their relation to the different sources of evidence. In Section 5, we discuss their implications for the comparison of income inequality across OECD countries, and the use of dummy variables to allow for definitional and data differences. Section 6 is concerned with changes in income inequality over time, and the establishment of consistent series for individual countries. The lessons to be drawn for use of secondary data-sets in the field of income distribution are summarised at the end of the paper.personal income distribution, secondary data-sets

Upper bounds for the eigenvalues of Hessian equations

We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equationsComment: 15 pages, 1 figur

Shape optimization for monge-ampére equations via domain derivative

In this note we prove that, if Ω is a smooth, strictly convex, open set in R n (n ≥ 2) with given measure, the L 1 norm of the convex solution to the Dirichlet problem detD 2u = 1 in , u = 0 on δΩ, is minimum whenever is an ellipsoid

A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains in a hemisphere

Here, we prove an isoperimetric inequality for the harmonic mean of the first N - 1 non-trivial Neumann eigenvalues of the Laplace-Beltrami operator for domains contained in a hemisphere of N

Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type

The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow

Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift

This paper deals with the eigenvalue problem for the operator L=-δ-x{dot operator}∇ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue λk of L under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any c>0 and k∈N the following minimization problemmin<>{λk(Ω):Ωquasi-openset,∫Ωe|x|2/2dx≤c} has a solution