Two-Part Tax Controls for Forest Density and Rotation Time

can be interpreted as the value of the growing trees at time T. Now it is possible to define the
firm’s profit function, net of taxes, at the time of harvest:

π(T,PC)=pPCb(T)-c-τ^LS-τ^CCθ(PC)

The actual penalty incurred from the clear-cut tax is the tax rate, τ^CC , multiplied by θ(PC),
an increasing, convex function of PC.¹² This allows the instrument to take the form of a
continuously graduated tax if desired by the planner.

The private landowner chooses T and PC to maximize the following value function:

PV(T, Pc ) = i-e-r^ π(T, Pc )e’^rT                       (10)

Notice that the private firm does not internalize the externality. The left-hand side of the
equation simply reflects the fact that the private value function depends on T and Pc.

Maximizing over the rotation period and percentage commercial use yields the following first
order conditions:

¹² Alternatively, τ^cc could be multiplied by Γ(P_c), a decreasing, concave function of P_c. If this were the case, τ^cc
could take the form of a subsidy. The subsidy would decrease in P_c and could entice a firm choose the optimal
percentage commercial use per acre. For the purposes of this paper, I analyze only the most intuitive case where τ^cc
is an increasing penalty on Pc.

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