Trees, wine, and cattle become more valuable over time and then possibly decrease in value. Draw a figure with present value on the vertical axis and years (age) on the horizontal axis and show this relationship. Show in what year the owner should “harvest” such a good assuming that there is no cost to harvesting. [If the good’s present value is P0 and we take that money and invest it at interest rate i (a small number such as 0.02 or 0.04), then its value in year t is P₀(1 + i)^t; or if we allow continuous compounding, P₀e^it. Such a curve increases exponentially over time and looks like the curve labeled “Price” in Figure 15.5. Draw curves with different possible present values. Use those curves to choose the optimal harvest time.] How would your answer change if the interest rate were zero? Show in a figure.

Figure 15.5 Price of an Exhaustible Resource