Two-Part Tax Controls for Forest Density and Rotation Time



P pe

C=

2γ


-rT T


b () - b ( t ) 1 e - r∙dt Г
b (T )   ) J


(25)


The first order condition for the optimal rotation period depends linearly on γ and PC, and
PC depends inversely on γ. Plugging the condition for optimal percentage commercial use into
equation (24) shows that the optimal rotation period does not depend on
γ:

1  G ( T, PC ) _ r

G (T)    T ~ 1 - e -rT


-rT T


-1 T


(b()-b(t))e-rtdt 11 (b(t) -b(T))e-rtdt (26)


J0


For any given PC, γ increases the optimal rotation period. However, γ also decreases the
optimal
PC. These effects cancel out exactly and the optimal T is left unaffected by γ. The
tax on the commercial use fraction will not affect the firm’s decision on rotation length.

From equation (25), it is apparent that an internal solution, 0 < PC < 1, will exist if:

pe


-rT


2γ


r b() - b(t) ']e -rtdt
к   b ( T )   )


(27)


This is true for a sufficiently small p or sufficiently large γ. There exists an internal
solution as long as the ratio of marginal timber value to marginal amenity value is sufficiently
small.

The clear-cut tax is equal to the square of PC: θ(PC)= PC2. This penalizes the firm relatively
more for a commercial use percentage closer to 100%. This reflects the idea that the planner is

22



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