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
More intriguing information
1. fMRI Investigation of Cortical and Subcortical Networks in the Learning of Abstract and Effector-Specific Representations of Motor Sequences2. Cultural Diversity and Human Rights: a propos of a minority educational reform
3. The Economic Value of Basin Protection to Improve the Quality and Reliability of Potable Water Supply: Some Evidence from Ecuador
4. 09-01 "Resources, Rules and International Political Economy: The Politics of Development in the WTO"
5. Artificial neural networks as models of stimulus control*
6. The Prohibition of the Proposed Springer-ProSiebenSat.1-Merger: How much Economics in German Merger Control?
7. What Drives the Productive Efficiency of a Firm?: The Importance of Industry, Location, R&D, and Size
8. The name is absent
9. XML PUBLISHING SOLUTIONS FOR A COMPANY
10. The name is absent