FOREST TAXATION IN THE UNITED STATES 75 
of States, however, a yield tax is combined with a specific tax of so 
much per acre on the land. The tax ratio in such States obviously 
varies with the land value per acre, the ratio being high for a low value 
and vice versa. If ¢ is the specific tax, then the tax ratio may be 
derived as follows: 
The part of the total tax due to the yield tax is sY, while the part 
due to the specific tax with compound interest to the end of the income 
cycle is 
t{1+(1+p)+(1+p)?+- + -+(1+p)""4], or ioe 
Total taxes are then X Ea yun Cia al 
Seen Y C6 = 
sY+t 
Kero 
P 
Cle) te 
p 
Formula 24, the tax ratio= 
WO 
A common combination of rates is 10 percent on yield plus 10 cents 
an acre each year. If it be further assumed that n=50 years, that 
Cea), When Gan, ae 
cent, then the tax ratio is 35 percent. This is approximately the same 
as a l-percent tax on value throughout a 50-year income cycle (ex- 
ample under formula 3). The initial forest value, under these 
conditions, using the following formula, 
=20 percent of Y, and that p=3 per- 
i pe A) ae 
PD t 
TaN, 
Cleo) ei Pp 
is found to be $9.60. If S were $100, however, the tax ratio would be 
only 24 percent instead of 35 percent, and the inital forest value would 
be $22.50. Whether or not the combination tax is favorable to the 
owner depends, therefore, on the comparative productivity of the site. 
An owner of the best land is taxed more lightly in proportion to value 
than are other owners. 
The arbitrary and irrational nature of the fixed annual tax may be 
illustrated by two examples, the foundation data of which are drawn 
from an earlier publication (10). 
Hardwoods will yield 6,000 board feet per acre every 100 years, 
provided the timber ‘s cut clean, and 6,000 board feet every 60 years, 
provided care is used in logging to leave the small trees standing. In 
both cases, the average stumpage price is computed as $6.50 per 
thousand, or $39 for the total yield. But an annual tax of 10 cents 
an acre compounded at 5 percent for 100 years equals $261, and for 
60 years, $35. Obviously, a 10-cent annual tax is confiscatory in 
either case (10, pp. 51-56). 
The situation of jack pine may now be considered. The following 
statement occurs on page 56 of the bulletin referred to above: ‘‘ With 
Vo = 
