1. Optimal rotation age (ORA) Dynamic optimization problem Long discussed in economic literature Shorter rotation – benefit arrives earlier – earlier replanting opportunity – planting more frequent – timber yield is lower

2. Forest scientist's ORA doesn't like cutting down trees … Maximizes sustained gross yield Solution

3. "Economic" forest scientist's ORA takes into account planting cost maximizes sustained net yield Solution

4. Forest economists' ORA Maximize profit Economic Literature: – Maximizing present discounted value over one cycle (Von Thünen, Irving Fisher) – Maximizing internal rate of return (Boulding) – Maximizing present discounted value over infinite cycles

5. Max NPV over 1 Period

6. Max Internal Rate of Return

7. Max NPV over all Periods

8. Optimal Rotation Age T i < T  < T 1 < T g < T n

9. ORA - Assumptions future prices, wages, interest rates are known future technologies (yields, input requirements) are known growth rate initially increasing later decreasing (I.e. cubic growth function)

10. ORA - Example f (t) = b*t^2 + a*t^3 a = -1/800 b = 0.2 W[age] = 16 L[abor] = 25 P[rice] = 20 r = 0.06 = 6%

11. Growth Function f (t) = 0.2 t 2 - 1/800 t 3 Timber f(t) Time (t)

12. Maximization CriterionOptimal Rotation Age Gross sustainable yield80.00 Net sustainable yield81.21 Net present value of one period 29.56 Net present value of all periods 28.62 Internal rate of returns26.94 ORA Example, Results (see Mathematika output)