74. MISC. PUBLICATION 218, U. §. DEPT. OF AGRICULTURE 
This formula does not contain the term Z, the land value. For 
practical application it seemed necessary to set up a corresponding 
general formula for s. Assume k income cycles of n years in each 
rotation. Hence the length of the rotation is kn years, total yield, 
kY, and the total cost of regeneration, kC. Then 
Formula 23, 
, P-O-nott-+py—1-] EY -kOC + pe P| Lp 
SY””COp erp) —1— rk +p)" 1) fas 
Formula 23 may be derived from formula 21 by eliminating L, the land value. 
By definition, 
kn — 
AS file Ed 
L= @E=n =a Ce 
The total yield tax for the even-aged forest is 
kn 
Kaye bak are. 
Eliminating X in these two equations, the value of L is determined— 
kn 
kY—EO(1+p)*°—kY¥s—e CEP 
ptr (Epi 
Then substituting this value for Z in formula 21, 
L 
r r aye, tp) t=1] +7)"=1 
$= 
Simplifying and solving for s, this reduces to formula 23 above. 
(Y¥—C—ne)[(1+p)**—1)—[ kY—bC +p) FP J tp) 1] 
7 CA WICG ep)? Ul ae) 
Values for s were obtained under a wide range of conditions, and 
it was found that in cases where the income cycle is the same as the 
rotation (even-aged forests) it is impossible to pick out any factors 
which have a predominant influence, since the result is likely to vary 
materially with changes in any of the conditions. If even-aged 
forests are eliminated from consideration, the property-tax rate and 
the rotation still have a pronounced influence on the value of the 
yield-tax rate, but the other factors have relatively little effect. 
In connection with the discussion of the yield tax in part 12, there is 
a table showing, for different rotations and property-tax rates, the 
range of values for s under a number of representative assumptions 
(table 150). There is also a table giving the average values for s 
under the same assumptions when the income cycle equals one-half 
and smaller fractions of the rotation (table 151). 
ae 
— 
SPECIFIC TAX WITH YIELD TAX 
Formulas 19 and 20 apply to cases which combine a yield tax with 
the ordinary property tax on the value of the land alone. In anumber 
