Two-Part Tax Controls for Forest Density and Rotation Time

This paper focuses on two cases, one where a logging firm does not internalize the benefits
from leaving some trees uncut and therefore chooses to clear-cut and the second where the forest
in question is unprofitable to harvest and has become over grown. A pair of taxes is presented
that, used in combination with one another, optimally control for clear-cutting rather than
banning it completely. Furthermore, the same instruments can be used to induce the optimal
behavior when it is socially optimal to harvest a forest, to prevent forest fires for example, but it
is not privately optimal.

Section 2 of this paper briefly revisits the basic Faustmann and Hartman models of optimal
forest management, then introduces a new model that allows a social planner to choose both the
optimal rotation period and the optimal amount of each acre to use commercially. Section 3 sets
up the private landowner’s problem and includes taxes aimed at controlling both rotation time
and percentage commercial use. Solutions are presented for the social and private problems, as
well as the solutions for the optimal tax instruments. Section 4 shows the results of a numerical
analysis on a simple stylized case.

2. FAUSTMANN, HARTMAN, AND BEYOND

Before jumping into a more general model, this section presents a brief overview of the
classic Faustmann and Hartman models.

The Faustmann Model

The Faustmann model solves for the optimal rotation period of a forest that will be harvested

¹ Commercial use percentage, as will be discussed in detail later in the paper, means the amount of each acre a firm
will choose strictly for its commercial value. A firm will choose this portion of each acre ex ante for all periods.

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