Forestry

Settlers are beginning to land on the west coast of Canada from across the Pacic 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 xed cost of planting trees.

Part A: The agriculturalist's problem [5 points] Consider the agriculturalist's problem of allocating work-ers to a plot of land. Suppose that land devoted to agriculture has a production function of f(N) = (a x)Nt (b/2) N^, where a = 20, b = 2, and Nt is the number of workers in year t. Suppose agricultural output receives a price of pa = 1 in a perfectly competitive market, which is assumed to be constant over time. For simplicity, suppose that the supply of workers is perfectly elastic and the per-worker wage is equal to zero.

i)Find the optimal number of workers N for a plot of land that is x miles away from the coast. Hint: your answer will not be a number; it will be a function of x.

ii)Calculate the net present value (NPV) of a plot of land that is x miles from the coast and devoted to agricultural in perpetuity.

I just need an answer for ii)

Thank you