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Optimal rotation age (ORA)

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. Forest scientist's ORA. doesn't like cutting down trees …

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Optimal rotation age (ORA)

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  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 Ti < T < T1 < Tg < Tn

  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 Timber f(t) f (t) = 0.2 t2- 1/800 t3 Time (t)

  12. ORA Example, Results (see Mathematika output)

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