Two-Part Tax Controls for Forest Density and Rotation Time

forest over an infinite number of identical rotations. The value function can be written as
follows:

(   1   ï( Tr .                       ɔ

SV(T, H) = I —-T I ∫ e -^rtF(t, Pc )dt +G(T, Pc )e "^rT

<^{1 -} e A O                         )

Note the difference between this expression and equation (4). Now the forest externality is
both a function of age t and the commercial use percentage per acre Pc. ⁷ With respect to Pc,
the path of F(t, Pc), either decreases monotonically with the commercial percentage per acre, as
would be the case if the amenity were erosion control, or follows an inverted “U’ shape, as
would be the case if the amenity were fire control. The net timber value, G(T, Pc), is an
increasing function of both T and Pc. Since the forest planner must now make two choices, the
optimization problem produces two first order conditions: one describing the optimal rotation
time and the other describing the optimal percentage of commercial use per acre. These first
order conditions are:

∂G (T, Pc )  rT _ T ∂F ( t, Pc )

-----------e — — I----------e dt

∂P            ∂P

c               0c

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