Settlers are beginning to land on the west coast of Canada from across the Pacifc Ocean. They arrive to an empty landscape that is only suitable for agriculture or forestry. Land that is closer to the coast is ?atter and warmer, and thus, is better situated for agriculture. In contrast, land located further away from the coast has a more moderate climate and is more conducive for forestry. Let x denote the number of miles a plot of land is from the coast. The coastal mountains of Canada are rugged; thus, only 15 miles of land can be used for agriculture or forestry. For simplicity, let’s assume that plots of land are divided into parcels that are 1 mile in length (i.e., x = 1, 2, 3, …, 15). Let r = 0.05 be society’s annual discount rate.

Note that land devoted to agriculture permits a single harvest per year; thus, land devoted agriculture should be discounted using discrete time. Trees, on the other hand, grow continuously; thus, land devoted to forestry should be discounted using continuous time. Initially, all plots of land are immediately ready for agriculture; land devoted to forestry, in contrast, must incur a fxed cost of planting trees.