Mqt the annual cost managing timber stand age and

b. Consider the case in which timber quality, and associated prices, increase with the volume of the stand. Timber prices are typically higher for larger trees used to make lumber (referred to as sawtimber) than for smaller trees used to make paper (referred to as pulpwood). Suppose that the timber price is p=6 for pulpwood and p=α6 for sawtimber, where α>1, and that the cut-off volume for sawtimber is 7000 units. That is, trees with volume less than 7000 units can be sold as pulpwood and trees with volume greater than or equal to 7000 units can be sold as sawtimber. What is the optimal rotation length for the timber stand when α=1.5 and α=2? What is the value of α that makes a manager indifferent between growing the trees for pulpwood and sawtimber?

c. In the models examined in class, we assumed that price for the resource was constant. For this problem, I want you to assume, instead, that there is downward-sloping demand given by p = α - βQ_T where Q_T is the quantity of timber sold when the trees are harvested at age T, α=18.5, and β=0.004. What is the rotation length that maximizes the present discounted value of the stream of net timber revenues from an infinite sequence of rotations? Explain how consideration of downward-sloping demand changes the optimal rotation length relative to the model in part a) that assumes a fixed price.

c. Explain the economic intuition behind the change in the price path when you go from costless to costly extraction.