The Distribution of Incomes in the United States

Abstract

THE Pareto law of distribution of incomes is known to be fairly satisfactory for high incomes. It has been tested with good results on a variety of data. It is less satisfactory as a description of the distribution of incomes in the lower ranges. One suspects that no single simple law of distribution of incomes will serve over the whole range. In practice, the difficulty of trying different possible theoretical distributions is mainly due to the dearth of adequate data giving the complete distribution of incomes over the whole income range. There are available now, however, certain data relating to the United States. These data, which will be the subject of the present paper, relate to single incomes.1 The irregularities in these figures, due to the method of estimating the data, have been smoothed out to a certain extent and the original figures can be reasonably well reproduced by certain mathematical formulae. The notion of trying to find a single formula which will serve for the whole range of incomes has been abandoned, and it has been assumed that different laws operate for different income ranges. The original data are shown in Table III. There are, in all, 10,058,000 incomes aggregating $11,579,390,000. We have split this whole group up into three parts: (a) THE BEAK, consisting of 3,311,000 incomes aggregating $1,431,000,000, ranging from the lowest income (unspecified in the original table) to $1,000; (b) THE HEAD, consisting of 5,182,000 incomes aggregating $5,978,000,000, ranging from $259 to $7,500; (c) THE TAIL, consisting of 1,565,000 incomes aggregating $4,171,000,000, ranging from $875 to the upper limit (unspecified in the original table). The distribution of these three groups is shown in the table below (Table I).