RELATION OF LAND [NCOME TO LAND VALUE. 
29 
metic average annual anticipated increases in income, and r 
a % 
of interest; then V= 
rate 
r~ 
Assuming that this formula roughly describes the valuations of 
the market, it furnishes a basis for interpreting the ratios of rent to 
value for any given year, and therefore for 1920. After a little 
study of the relationships between the terms of this equation it will 
be seen that the higher the rate of interest the higher the ratio of 
rent to value, and that the larger i is, relative to a, the lower the 
ratio of rent to value, and that increases in a, while i is constant, 
bring about constantly increasing ratios of rent to value. In gem 
it may be stated that the ratio of rent to value in any given year 
depends on r and the relative size of a and i. These relationships 
are illustrated in Table 9. 
Table 9. — Effect of changes in r on ratio of rent to value (a and i constant). 
4 per cent . 
5 per cent. 
6 per cent . 
a 
i 
V 
So 
$0.20 
$250 

.20 
180 

.20 
139 
2.0 per cent. 
2.8 per cent. 
3.6 per cent. 
Effect of Changes in a (i and r Constant). 
5 per cent . 
5 per cent . 
5 per cent . 
$5 
$0.20 
$180 
6 
.20 
200 
7 
.20 
220. 
2.8 per cent. 
3.0 per cent. 
3.2 per cent. 
Effect of Changes in i (a and r Constant). 
5 per cent . 
5 per cent . 
5 per cent. 
$5 
$0.10 
$140 
5 
.20 
180 
5 
.30 
220 
3.6 per cent. 
2.8 per Dent. 
2.3 percent. 
To understand the ratios of rent to value and the variations in them 
presented in Table 1 and Figure 3, it is necessary to know the values 
of r and of a relative to i. These are given in Table 10 for those areas 
in which it was possible to get net cash rents. 
12 For this formula I am indebted to Dr. W. I. King. 
For the proof of the first part of this formula see Taylor, H. C, Agricultural Economics, p. 206. The proof 
of the latter part is as follows: 
r T (l+r) T (l^rj- T (l+r)3 
(1+r)' 
■ r + l - r + r - r +^ r x i +r x r J r + 
1+r 
1+r 
This formula does not apply when incomes arc decreasing. 
