RELATION BETWEEN RENTS AND INCOMES 



99 



Another comparison of incomes and rents may be made from a 

 second insert on the same chart. It may be readily demonstrated 

 that the normal curve of error plots as a parabola on semi-logarithmic 

 paper and the logarithmic skew curve as a parabola on double logar- 

 ithmic paper. Two parabolas which represent extreme conditions of 

 spread and of concentration of rents in large cities are shown. If 

 the degree of dispersion remains fixed a change in the rent level 

 merely shifts the parabola on the chart without changing its shape. 

 The parabolic shape of rent curves and the hyperbolic shape of the 

 income curve indicate that rents are somewhat less concentrated 

 locally about their mode,^ but are more concentrated as an entire 

 group than are incomes. These curves can not well be superposed 

 for comparison since areas are not equivalent on different parts of 

 the chart. Those incomes which are closely grouped around the 

 mode represent wage-earners of such a type that several may come 

 from a single family. Conclusions regarding comparison of incomes 

 and rents must be made with caution since rents are on a family 

 basis and incomes on an individual basis. No satisfactory data 

 are available to show the variation in income distribution between 

 small subdivisions of the United States, as cities, but it is reasonable 

 to assume that there is some such variation for incomes as well as 

 for rents, although perhaps not of so great a range. 



s 



8 80 



O 70 

 (^60 



LORENZ CURVES 



SHOWING DISTRIBUTION OF 



RENTS AND INCOMES 



Atlanta Rents 1920 



Detroit Rents 1919 



Personal Incomes 



in the U.S. 1917 



) 20 30 40 50 60 70 80 90 100 

 Cumulative Per Cent.of Famiues or Persons 



Fig. 7 



A third comparison of incomes and rents is made possible by the 

 use of Lorenz curves illustrated in Fig. 7. On this form of chart a 

 * See Appendix. 



