the volume of hay available from a stand of grass of age T is given by V(T) = 60T - T2 - 120 for the range 6 < T < 47. Harvesting ages are constrained to be in the same range. The net price at which a unit of harvested timber may be sold is p = 1 and the interest rate is r = 0.2.

(a) Determine (mathematically) the age, TM, at which the MAI is maximized

(b) Determine (mathematically) the age, TF, at which the stand of grass should be harvested according to Fisher's Rule. Also, illustrate your answer in a diagram

(c) If the farm owner pays a rent R = 15 for this tract of land and there is no cost of replanting, determine (mathematically) the harvesting age T* at which profits are maximized by following Faustmann’s approach. Use a diagram to illustrate your answer and also explain the economic intuition for the difference between T* and TF