Logistic Growth Functions 1

Logistic growth function y= 1. Logistic function. Using Excel, for domain -3.5 PV = ($1.00 - $0.30)V/(1.02) t - $1,000. Use your spreadsheet to calculate PV at each age. At what age is the stand's PV maximized? This single-rotation model fails to consider the opportunity cost of deferring subsequent rotations: the sooner you harvest, the sooner you can start the next rotation. If commercial forestry is profitable so that replanting is justified, and if prices and costs are assumed to remain constant through time, we would expect to see harvesting and replanting every T years, providing the landowner a perpetual stream of discounted returns with present value PV*, where PV* = PV + PV/(1+r) T + PV/(1+r) 2T + PV/(1+r) 3T + . . . which collapses conveniently to PV* = PV + PV/ r T. Calculate PV* at each harvest age in your spreadsheet. At what value of T (age at harvest) is PV* maximized? Plot PV and PV* against stand age so you can clearly discern the peaks of these schedules. The Federal government offers tax incentives and subsidies to induce forest landowners to replant after harvests. Suppose the government pays $500 of the total $1,000 planting costs. If the landowner's net replanting costs are only $500, calculate the new PV and PV* schedules (r = 0.02). How does the replanting subsidy affect the optimal harvest age in the single rotation model? How does it affect optimal harvest age in the multiple-rotation model? Explain.