Two-Part Tax Controls for Forest Density and Rotation Time

record from each site of what percentage of each acre the firm leaves uncut and assurance that
trees chosen for their amenity value, that is the trees not part of the commercial use portion of the
land, remain uncut.

Private Optimization (All Taxes Included)

For clarity of presentation, it is useful to define some functions:

b(t) = n(t)g(t)                                                     (8)

where n(t) is the number of trees, g(t) is the timber volume of a tree at any given time. Thus
b(t) can be interpreted as the timber volume of the growing trees in the stand at any given time.
The timber volume is assumed to be monotonically increasing for all t. Although the number of
trees will decrease over time, each tree grows fast enough keep the volume of timber increasing.

To implement the taxes properly, the timber value of the forest, G(T,PC), must be more
clearly defined. Let it be broken down into net revenues and costs so that G(T,PC) = pPC b(T) -
c, where p is the price of timber, net of unitary harvest costs, and c is the fixed harvest and
replant cost, a weakly increasing function of PC.¹¹ The large lump sum costs of harvest that a
firm must pay each period for capital and labor are captured by c. The intuition is that firms
must rent a certain amount of equipment and labor to harvest each acre regardless of the
commercial use percentage. Incidental marginal costs are captured in p. The term pPCb(T)

¹⁰ The policy maker would have to consider the species of tree being planted. A different number of trees could be
planted per acre, depending on the species. Furthermore, different forest types will have a different optimal
percentage of uncut trees.

¹¹ This method to define G(T, PC) loosely follows Englin and Klan (1990).

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