Two-Part Tax Controls for Forest Density and Rotation Time

more concerned with reducing the amount of clear-cutting and cares less about a marginal
change in the number of trees cut if the firm harvests as low fraction.

The stylized function used for the biomass of trees in board feet, b(T), is based on data
published by Richard McArdle (1961) for the Douglas Fir.¹⁵ The estimated function shown is:

_b (T ) = ^25,000                                        (₂₈)

^b(T ) 1 + (-0.2(T-35))                                                          ⁽²⁸⁾

+e

The function is plotted in Figure I. The biomass of this particular stand peaks at 25,000
board feet per acre and reaches this peak at a stand age of 70 years.¹⁶

The price of a board foot is taken from Calish et. al. (1978) and transformed into year 2000
dollars. In the model p = 2.03.

The model is implemented in the Ox programming language developed by Doornick (1999).
T and PC are solved simultaneously based on the estimated parameters. When the real interest
rate is assumed to be 3% and γ is assumed equal to $0.02, the Faustmann optimal rotation
period, not considering the externality, is 41.6 years.¹⁷ If the externality is considered, the
optimal rotation period is 42.4 years and the optimal commercial harvest per acre is 55%. The
optimal clear-cut tax is $37,444 per square fraction of each acre for a total penalty of $11,327 per

¹⁵ The MacArdle data counts the amount of wood available from root to tip of each tree. Although a good estimate
of the wood available to a pulp and paper firm, it does not provide an estimate of the wood available to be used as
lumber. Thus, using the MacArdle data as a reference, the “stylized” biomass estimation captures roughly the
growth in mass of the wood available for lumber.

¹⁶ Obviously, trees will continue to grow past 70 years, but this model assumes that the wood useable for lumber
will reach near maximum volume by 70 years.

¹⁷ This is a point of reference only. In reality, as in the rest of the analysis, these values will vary.

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