186 NATURE OF CAPITAL AND INCOME [Crar. X1 
if a house worth $10,000 yields in any given year a net rent 
of $1000, the value return is ten per cent per year. An 
important case of value return is evidently the rate of in- 
terest. 
Thus we have four ratios: — 
1. Quantity of services per unit of He, _ py ysieal productivity. 
2. Value of services per unit of time, 
quantity of capital, 
3. Quantity of services per unit of time, 
value of capital, 
4. Value of services per unit of time, 
value of capital, 
= value productivity. 
= physical return. 
= value return. 
These four magnitudes must be carefully distinguished. 
They are, as mathematicians say, of different “ dimensions.” 
This fact is suggested in the four following phrases, which 
may be taken as typical : — 
Bushels per acre per year. 
Dollars per acre per year. 
Bushels per dollarjper year. 
Dollars per dollar per year. 
§3 
The failure to keep these four magnitudes clearly dis- 
tinguished has already led to a great many confusions in 
economic science. The spurious distinction between rent as 
the income from “land” and interest as the income from 
“capital” is a case in point.” From this confusion comes 
the notion that land differs from “capital” in that there is 
a margin of cultivation for the former and none for the 
PSO 
! For a mathematical statement, see Appendix to Chap. XI. 
2 The error is fully exposed in Cannan’s “What is Capital ?”’ Eco~ 
nomic Journal, June, 1897, pp. 283-284, and in Fetter’s “The Rela-~ 
tions between Rent and Interest,” a paper presented before the 
American Economic Association, December, 1903. See also Hicks’s 
Lectures on Economics, Cincinnati, 1901, p. 228, and the present 
writer's “Role of Capital in Economic Theory,” Economic Journal, 
December, 1897, p. 524, and “Precedents for Defining Capital,” 
Quarterly Journal of Economics, May, 1904.