please show work and they're are four parts total.

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Problem 2: Managing Innite 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 length T that maximizes the private net present value of all forest rotations: NPVP = D + i e-W'T) [pQ(T) D] erTl 2.A. [1 point] Write down the rst-order condition associated with T\" and 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 rst-order conditionsimply adapt the condition from the lectures to this setting and interpret it.) 2.3. [1 point] Using Excel's Solver tool, determine the optimal rotation interval T using the parameter values p : 1, a, : 15, b : 180, 'r : 0.05, and D : 1, 000. Make sure you explain how you found your answer (a screen shot of your Excel spreadsheet is useful, but not necessary). Is T different from the rotation interval T5 from 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, 1' = 0.01). How do you expect a lower discount rate to effect the amount of land devoted to forestry? Problem 3: Socially Optimal Forest Rotations with Non-timber values [2 points] Now suppose that the forest that you are considering to plant provides a non-timber value of sequestering carbon. Assume that the perperiod value of carbon sequestration depends linearly on the volume of the forest and is equal to a(t) 2 at. The stream of discounted non-timber values from t = 0 to t = T is thus A(T) : fOT e'\"a(t)dt : (v/r2)[1 e'TTU + rT)]. This means that the net-present-value to society of all forest rotations is: NPV" = D + A(T) + i e'r'\") po(T) D + A(T)l p120) D + M) :7D+A(T)+ eTT_1 3.A. [1 point] Suppose you want to know what the optimal rotation interval is that maximizes NPV\". Denote this as T*. Write down the rst-order condition associated with T* and interpret the condition, in terms of marginal benefits and opportunity costs. How does this condition differ from the condition in Problem 2? (Note: You do not need to derive the rst-order conditionsimply adapt the condition from the lectures to this setting and interpret it.) 3.3. [1 point] Using Excel's Solver tool, determine the optimal rotation interval T* using the parameter value v = 75 and the same values for the other parameters as in 2.3. Make sure you explain how you found your answer (a screen shot of your Excel spreadsheet is useful, but not necessary). 15 T* different from the rotation interval TO from Problem 2? Why or why not? Problem 4: Forest Policy [1.5 points] Suppose the government would like to introduce a forest policy that delays the cutting of forests in order to have a larger volume of trees available for carbon sequestration. Specically, the government would like to achieve the socially-optimal rotation interval, which considers the non-timber benefits of the forest, by introducing a severance tax on timber, which imposes a per-unit volume cost of 7 on timber harvest. This means that the private net-present-value of all forest rotations is now: NPV* = 7D + i 6\"\") [(p * nr)Q(T) * D] 'il _D+(;77)Q(T)*D eTTl 4.A. [1 point] The government is considering three different values of the tax: 7 = 0.563, 7 = 0.825, or 7 : 0.987. Use Excel to determine which one gets the closest to achieving the socially-optimal rotation interval T\". 4.3. [0.5 points] Suppose the government will pick the severance tax value that gets the closest to achiev- ing the socially-optimal rotation interval T*. Do you think that implementing this severance tax will achieve the goal of having a larger volume of trees available for carbon sequestration? Why or why not