Optimal Harvesting Age
Let there be a per unit regeneration cost C. The timber growth is measured by volume V(T) which is a function of the age of the timber T. Attaching a price P, the maximum present value of the stand represented by λ is,
Equation 1
The first order condition gives us
Equation 2
PV' (T) = iPV (T) + i λ
Where V’ is the first order derivative of V.
The results indicate that, the Faustmann harvest age T_{F}, is the one at which the marginal increase in value from delaying the harvest equals opportunity cost of delaying the harvest. The opportunity cost includes the potential interest income foregone on the delayed receipt of current harvest revenues plus the interest cost of delaying receipts from future harvest cycles. The second component reflects an implicit rental cost of land. The optimum T is popularly known as 'Faustmann Rotation Age'. Let us denote it by T_{F}.
The first order condition equation 2 can be rewritten to give us the Faustmann condition
Equation 3
Equation 3 can be interpreted as, 'hold timber stocks uncut until the rate of growth in the combined asset value of timber and land just equals market rate of interest'.