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Optimal rotation age (ORA)

The Optimal Rotation Age (ORA) concept is fundamental in forestry economics, exploring the dynamic optimization of tree cutting intervals. While shorter rotations can provide faster benefits and allow for earlier replanting, they often lead to reduced timber yields. Forest scientists aim to optimize sustained gross and net yields while considering planting costs. Economic principles, such as maximizing present discounted value and internal rate of return, guide decision-making in selecting the ideal rotation age. Understanding future price trends and growth rates is crucial for effective forest management.

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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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