100 BELL SYSTEM TECHNICAL JOURNAL 



diagonal line at 45 represents a uniform distribution and the further 

 a given curve falls to the right of and below that line the more unequal 

 the distribution represented. If incomes were plotted on a family 

 basis, the resulting curve would lie somewhat closer to the diagonal 

 line than the one shown, but it is fairly evident that incomes are 

 more unequally distributed than rents. For instance, the top 10 

 per cent of incomes are on the average about 42 per cent of the total 

 income, while the top 10 per cent of rents are from 22 to 32 per cent of 

 the aggregate rent in most cities. These three comparisons confirm 

 the idea discussed in the first part of this paper, that the proportion 

 of income spent for rent is less among the larger incomes. 



Of the extensive data on income distributions few can well be used 

 for comparison with rent data. In order that a cumulative curve 

 really mean anything, it must represent an entire group, not merely 

 items from one end or the other of the complete scale. Therefore, the 

 various tables of earnings of working class families and individuals 

 are of doubtful use here, although they do show, plotted on double 

 logarithmic or logarithmic probability paper, that the type of dis- 

 tribution of earnings about an average value is practically identical for 

 various nationalities in similar industries, or for men, women and 

 children in all industries. However, the average earnings of the 

 various classes are widely different. A few examples are shown in 

 Fig. 5. 



Income tax returns are of some interest although they are defective 

 in several respects: they only include the upper part of society, a 

 large number of persons fail to make returns and large amounts of 

 income are tax exempt. Federal income tax data, which are available 

 on a uniform basis for the years 1917-1920, may best be studied by 

 plotting on double logarithmic paper, preferably after reducing the 

 figures for the various states to a basis of returns per 1000 popula- 

 tion. There are small changes from year to year in the position of 

 the curve for any given state, which are not significant, since they 

 may be due either to changes in the average income, or to increased 

 efficiency of tax collection. Changes from year to year in the slope 

 of the curve for any one state are small, indicating that there exists 

 in each state a definite type of distribution of wealth and earning 

 power. Differences in the position and slope of the curves for dif- 

 ferent, states are conspicuous, indicating that both the per capita 

 income and the distribution of the total income among individuals 

 are different in different states. New York, for instance, shows a 

 wide spread, i.e., a relatively large number of very high incomes, and 

 Iowa shows a narrow spread, i.e., a large number of incomes around 



