This chapter is partly based on Ferrer-i-Carbonell and Van Praag (2003) and Van Praag (1978).
Since Gini (1912) and Dalton (1920) the distribution and inequality of income has been an important subject of study for economic and social scientists. Recent surveys are offered in the handbooks edited by Atkinson and Bourguignon (1999) and Silber (1999). Let us assume a population with individualswith incomes . Inequality may be defined in various ways. We may start with the well-known statistical- spread formula, and we define the variance of the income distribution as 13.1
wherestands for average income. The problems with this measure are that it depends on the money unit chosen and that it depends on . If the money unit changes, for example because we take $100 as our new unit instead $1, all the amounts are divided by a hundred and consequently the variance is reduced by a factor . It is obvious that this effect may be easily corrected in this setting, but there are situations where correction seems difficult; for instance, if we compare inequalities of two countries with different money systems or when we compare the development of income inequality over time in a country where there is price inflation. Another point which makes the definition rather problematic can be illustrated by the following example. Consider two populations, both consisting of three persons. The first three persons have incomes 9, 000, 10, 000, and 11, 000, while in the second population the incomes are 99, 000, 100, 000, and 101, 000. It is easily seen that the income variance will be the same for both populations. Nevertheless, we feel that the second distribution is much less unequal than the first one. The absolute differences are in both cases 1,000, but in the first case the rich person gets 10 percent more than the middle one and the middle one gets 10 percent more than the poor. In the second case those relative differences are a tiny 1 percent.