The concept of economic inequality necessarily encompasses a dimension of social welfare, for otherwise it is just the dispersion of values in a distribution. If we agree that inequality is a potential source of welfare loss in a society, our interest naturally turns towards measuring it and studying what causes or affects it. Dalton (1920) pointed out that underlying any measure of inequality is some concept of social welfare and as such, all measures imply a value judgment towards its very definition. The social welfare approach, however, is the only approach that makes this judgment explicit.
This thesis begins by introducing central concepts of inequality measurement. A coverall term 'income' is typically used to compress a set of personal attributes, ones that contribute to the individual's economic status in the society, into a single parameter. All individuals are thought to hold preferences towards equality, which are then aggregated into a social welfare function. To give a useful presentation of these preferences, the social welfare function needs to satisfy a number of basic properties that are discussed later in the thesis.
The inequality measurement literature takes interest, above all, in what causes inequality, how it develops in time and whether we can say that it is more prevalent in one society than in another. Two general objectives can be identified: that of ranking different distributions, and that of quantifying the degree of inequality in a given distribution. A well-known graphical representation of inequality in an income distribution, the Lorenz curve, gives a standard tool of comparing different distributions regarding their level of inequality. However, a 'one size fits all' approach to ranking distributions still does not exist.
To begin the discussion on quantifying the amount of inequality in a given distribution, the basic axioms of inequality measurement are introduced. They form the basis of the so-called axiomatic approach to inequality measurement, and arguably any measure should satisfy these axioms. In contrast the so-called ad hoc measures of inequality are often bluntly borrowed from statistics to measure the dispersion in an income distribution, without justifying their validity as tools of inequality measurement. In closer inspection their use more often than not cannot be motivated from either a welfare theoretic or an axiomatic point of view.
At last the approach of building inequality measures from 'scratch', based on social welfare theory, is introduced. The best known measures of this approach, the Dalton and Atkinson indices, are derived, followed by a discussion on their axiomatic properties.
