Managing Infinite Forest Rotations [3 points]

The president of your company has persuaded you that you should be considering all future forest rotations when considering whether to use the land as a forest for convert timber into forest products. Now you want to find the rotation lengthTthat maximizes theprivatenet present value of all forest rotations:

NPVp=D+er(iT)[pQ(T)D]

i=1

[pQ(T)D]=D+erT1.

Write down the first-order condition associated withTand interpret the condition, in terms of marginal benefits and opportunity costs. How does this condition differ from the condition in Problem 1? (Note: You do not need to derive the first-order conditionsimply adapt the condition from the lectures to this setting and interpret it.)

2.B. [1 point]Using Excel's Solver tool, determine the optimal rotation intervalTusing the parameter valuesp= 1,a= 15,b= 180,r= 0.05, andD= 1,000. Make sure you explain how you found your answer (a screen shot of your Excel spreadsheet is useful, but not necessary). IsTdifferent from the rotation intervalTsfrom Problem 1? Why or why not?

2.C. [1 point]Using Excel, determine what happens to the optimal rotation interval and the net present value of the forest if the discount rate is instead lower than we actually thought (say,r= 0.01). How do you expect a lower discount rate to effect the amount of land devoted to forestry?