12 MISC. PUBLICATION 218, U. 8. DEPT. OF AGRICULTURE 
the reduction factor is determined by the simple relationship, 
= 1—*. 
Values for w were obtained under a wide range of conditions, and 
it was found that the variable which had the predominant influence 
in determining these values was the length of the income cycle. The 
longer the income cycle, the greater was the true exemption rate. 
Accordingly, these values were averaged by means of a curve based 
on length of income cycle. Using this curve as a guide, approxima- 
tions of the values of w were then made for various ranges of income 
cycles for practical application. They will be given in part 12 in 
connection with the discussion of the plan. For practical reasons, 
which will also be explained in connection with the plan, the reduc- 
tion factor is hmited to a maximum of 50 percent. 
YIELD TAX 
YIELD TAX, WITH AND WITHOUT LAND TAX 
In the agitation for the yield tax, which has been going on now since 
the beginning of the century, the yield-tax rate was intended to be 
so adjusted that the tax ratio 7 
obtained. That is, the yield tax was to be an equivalent of the 
property tax on an annual sustained-yield forest. It has been found 
impossible to obtain this result without assuming, contrary to the 
fact, a constant ratio of net to gross income in forest investments. 
This is due to the fact that the yield tax is based on gross income, 
while the tax ratio is based on net income. 
If the yield tax rate is s, there are no intermediate thinnings, and 
the only expenses connected with the forest are the annual expenses, 
e, of administration and protection and the cost of regeneration, C, 
GD) Saal 
P 
would be as nearly as possible 
the net income is Y)—C—e » and the tax ratio under the 
pure yield tax is 
x side tae 
Ss VG aie 
Formula 18, 
If s=20 percent, for instance, and e orp +¢ is 20 percent of 
leek Vs 
SY , 
Y, then the tax ratio is 0 80Y = 2° Percent. 
Suppose that, in addition to a yield tax, a land tax were imposed 
at the property-tax rate, the trees being exempt. The part of the 
total tax due to the yield tax is sY, while that due to the land tax is 
riot Pr—. Hence 
A=sY4rL AC Sroe 2 see and 
sYtrL Oren 
Formula 19, S y_o_, Geert 
1: Awd ei elieca diane ~ 
