The Economic Theory of Income Inequality, by Robert A. Becker (ed.)

Edward Elgar, 2013, 0 85793 908 1, hbk, lvii + 636 pp, £225

Ten years ago, Edward Elgar published a two volume collection of reprinted articles, The Economics of Poverty and Inequality, edited by Frank Cowell. The publication of this new volume of reprints, a few of which are also to be found in Cowell’s collection, is a symptom of the increasing importance of inequality as a political issue.

Like Cowell’s collection, this new volume is a treasure trove. It contains classics such as Lorenz’s 1905 ‘Methods of Measuring the Concentration of Wealth’ ( – strange how disconcerting it is to see the Lorenz curve, as originally drawn, on a graph with per cent of total wealth along the horizontal axis, and per cent of population along the vertical). It also contains more recent material, including Foster and Wolfson’s 2010 article ‘Polarization and the Decline of the Middle Class’.

As Becker points out in his comprehensive introduction, any intelligent discussion of inequality needs to discuss how it should be defined, how measured, and how evaluated – and particularly how it should be measured – a question addressed by a long section in the introduction and by most of the articles that Becker chooses to reprint. But as Tony Atkinson’s 1970 article ‘On the measurement of Inequality’ points out, measures of inequality that make no reference to an understanding of society’s welfare might be quite misleading: hence the importance of the Pigou-Dalton ‘transfer principle’, which states that we should only use a measure of inequality if it always decreases when a rich person transfers resources to a poorer person.

This principle is satisfied if two income distributions are represented by Lorenz curves that do not cross: and here we can legitimately say that the distribution represented by the curve closest to the straight line diagonal is more equal than the one represented by the curve more distant from the diagonal. Where the Lorenz curves cross – that is, where one distribution is more equal at one end of the income distribution, and the other more equal at the other – then deciding which distribution represents the least inequality is more problematic. A number of the articles tackle this problem. More complex still is the attempt to construct measures of inequality that take account of both income and wealth, and the four papers that discuss such multidimensional inequality measures are understandably amongst the most complex in the volume, both conceptually and mathematically.

Many of the articles require an understanding of mathematical models of the economy, and the reader who is not familiar with the mathematics of economics will find some of the papers hard going. But a number of the articles are more generally accessible, and particularly those in the fourth part of the book, which explore the relationship between inequality measurement and understandings of individual and social welfare: although here too there is often plenty of mathematical notation.

A number of the papers have an eye to the effects of inequality of income or wealth on society, although often implicitly rather than explicitly. The final two papers make an explicit connection between income inequality and the polarization of society. Becker quite correctly titles this section ‘Directions for future research on economic inequality’, for what income inequality is doing to our society is rightly a cause for concern and therefore an important field for further research.

This final section suggests that perhaps there should have been an additional concluding collection of articles on economic analysis of the effects on inequality of social policy reforms: both those reforms that have been implemented, and those that have not yet been. Tony Atkinson already has three articles in Becker’s collection, and if this additional section had been added then it would almost certainly have contained yet more of Atkinson’s output: but that would not have been a problem – merely a recognition that Atkinson has contributed substantially both to an understanding of the measurement of inequality and to our understanding of what might be done about it.

It will be of interest to readers of this Newsletter that much of the effort that Atkinson has put into the evaluation of the effects on inequality of feasible policy changes has been expended on the proposal for a Citizen’s Income.