Instead, economists infer the value of the asset from assumptions about intertemporal market equilibrium. Three cases have been examined.
The first is identical to the literature on nonrenewable resources, appropriately treating the exploitation of primary, old-growth forests as timber mining. Since it is generally uneconomic to replace primary forests with forests of a similarly old age, this analogy is not as odd as it might seem. Under these circumstances,
where C'[q(t)] is marginal extraction costs. This model of net accumulation (pure depreciation) is generally called the Hotelling model to emphasize the connection between mining old growth that will not be replaced and mining minerals that cannot be replaced.
While the Hotelling model may be appropriate for the case of pure depreciation, it misses several important aspects of the forest sector. An alternative approach is transition models, which account in part for these problems by recognizing that forest growth offsets harvests. Assuming constant prices and a forest inventory recognized only by total net growth, this model suggests that net accumulation is
where g(t) is the net forest growth in period t.
By recognizing forest growth, such a formulation improves on the ordinary Hotelling approach, but still suffers the defects of (1) ignoring endogenous price changes in the sector and (2) characterizing the forest only by net growth and not its more complex underlying age-class structure. Economic theory suggests that once the transition between old- and second-growth forests is complete, timber prices will stabilize and the economic return to holding forests will arise solely from forest growth. Vincent (1997) has developed the appropriate measures of net accumulation for optimally managed second-growth forests. Depreciation associated with the harvests equals
where h is values per unit area, v(τ) is the timber yield at age τ, and τ* is the economically optimal rotation age. Accumulation associated with the growth of subrotation-age forests is