You are the manager of a forest products company with land recently planted (t = 0)...

 

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You are the manager of a forest products company with land recently planted (t = 0) with a fast-growing species of pine. The merchantable volume of timber at instant t 0 is given by Q(t) = at + t - y t, where a = 10, = 1, and y =0.01. (a) What is the maximum volume, and when does it occur? What rotation length maximizes mean annual increment [Q(T)/T], and what is the associated volume? (b) If the net price per unit volume is p = 1 and the discount rate is 8= 0.05, what is the optimal single rotation Ts, volume at harvest Q(Ts), and present value s(Ts)? (c) If the cost of replanting is c = 150, what is the optimal Faust- mann rotation T*, volume at the Faustmann rotation Q(T*), and present value (7*)? (d) If the price increases to p = 2, what are the new values for T's and 7*? Do the new values make sense relative to their values when p = 1? You are the manager of a forest products company with land recently planted (t = 0) with a fast-growing species of pine. The merchantable volume of timber at instant t 0 is given by Q(t) = at + t - y t, where a = 10, = 1, and y =0.01. (a) What is the maximum volume, and when does it occur? What rotation length maximizes mean annual increment [Q(T)/T], and what is the associated volume? (b) If the net price per unit volume is p = 1 and the discount rate is 8= 0.05, what is the optimal single rotation Ts, volume at harvest Q(Ts), and present value s(Ts)? (c) If the cost of replanting is c = 150, what is the optimal Faust- mann rotation T*, volume at the Faustmann rotation Q(T*), and present value (7*)? (d) If the price increases to p = 2, what are the new values for T's and 7*? Do the new values make sense relative to their values when p = 1?