Two-Part Tax Controls for Forest Density and Rotation Time

Case 1: Before the planner arrives, the private landowner is clear-cutting and harvesting the
trees sooner each period than is optimal. No prior restrictions are made on the magnitude of the
effects of PC and T on the externality, only on the sign. In this case, F(t,PC) is strictly
increasing over T, for all t<T, and strictly decreasing in PC. PC may have a large effect on the
externality in question, as it would be in the case of erosion control on a steep slope, or in the
preservation of a species habitat. Or the effect may be a small one, as might be the case if the
forest is used for hiking. Furthermore, no assumption is made as to the rate of growth of the
forest.

Case 2: The forest in question is unprofitable to harvest and has become over grown. In this
case, the forest planner must induce harvest to decrease an externality, such as fire risk,
associated with too many trees on each acre. Positive PC now acts a fire inhibitor. The
externality thus takes an inverse U shape in PC . Over a relatively low commercial percentage
per acre chosen, the amenity is increasing. More trees harvested lead to greater fire prevention.
However, over a relatively high PC the amenity is decreasing. So the forest planner wants to
induce some harvest, but a clear-cut still does not maximize the amenity value. This would be
the fairly general case under decreasing marginal amenity returns or where there are multiple
amenities, such as erosion control, scenery, and existence value, besides fire control, that are
increasing in PC.¹³ Further, the externality favors younger trees, that is F(t,PC) is decreasing
for some or all t such that the externalities balance is positive. As in the first case no prior
restrictions are made on the magnitude of the effects of PC and T, or the growth rate of the
forest.

Thus, the following section shows how the two-part instrument can be used to increase or

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