Optimal deforestation

Biological Rotation

V(t) = 10t + t² - 0.01t³. Divide volume of t by t to find the mean annual increment : MAI= 10 + t - 0.01t². Find its derivative to find the maximising t: Max Mai: d(MAI)/dt = 0 d(10 + t - 0.01t²)/dt = 0. Solve for t: 1-0.02t = 0, t=50 years.

Wicksell Rotation

Comparison between net return of cutting trees this year to cutting trees next year. (p-c)V(T0) = (p-c)V(T1)/ (1+r). Rearrange to r= V(T1) - V(T0)/ V(T0) where p is the price, c is the cost of harvest, and r is the discount rate

Faustmann Rule

Includes alternate uses of land where D is the cost of replanting and S is the site value. (p-c)V(T0) - D+S = (p-c)[V(T1)+ΔV] - D+S/ (1+r). Rearrange to r=  ∆V/((V(T₀₎-D+S) )

Efficient Rotation

Includes non timber benefits, species that prefer mature forests. Marginal cost of harvest is ΔV+H, where H is the forgone benefits of bird habitat.