Problem 3: Socially Optimal Forest Rotations with Non-timber values [2points]

Now suppose that the forest that you are considering to plant provides a non-timber value of sequestering carbon.Assume that the per-period value of carbon sequestration depends linearly on the volume of the forest and is equal to a(t) =vt.The stream of discounted non-timber values fro mt= 0 to t=T is thus A(T) =^T₀ e^rta(t)dt= (v/r²)[1e^rT(1 +rT)]. This means that the net-present-value to society of all forest rotations is:

NPV= D+A(T) +_i=1 e^r(iT)[pQ(T)D+A(T)]

=D+A(T) + (pQ(T)D+A(T)/(e^rT1))

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 first-order condition associated with T and interpret the condition, in terms of marginal benefits and opportunity costs.

3.B. [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.B. Make sure you explain how you found your answer (a screen shot of your Excel spreadsheet is useful, but not necessary).