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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
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
Forest scientist's ORA
  • doesn't like cutting down trees …
  • Maximizes sustained gross yield
  • Solution
economic forest scientist s ora
"Economic" forest scientist's ORA
  • takes into account planting cost
  • maximizes sustained net yield
  • Solution
forest economists ora
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
optimal rotation age
Optimal Rotation Age

Ti < T < T1 < Tg < Tn

ora assumptions
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)
ora example
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%

growth function
Growth Function

Timber f(t)

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

Time (t)