Settlers are beginning to land on the west coast of Canada from across the Paciﬁc Ocean. They arrive to an empty landscape that is only suitable for agriculture or forestry. Land that is closer to the

Settlers are beginning to land on the west coast of Canada from across the Paciﬁc Ocean. They arrive to an empty landscape that is only suitable for agriculture or forestry. Land that is closer to the coast is ﬂatter 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 ﬁxed 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^2 [PLEASE LOOK AT THE IMAGE FOR THE CORRECT EQUATION], 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. In Excel plot the NPV of agricultural land with distance from the coast x on the horizontal axis (use x = 1, 2, 3, ..., 15).

Part B; The Forester’s problem. Consider now the foresters problem of choosing the optimal rotational length for a stand of trees located x miles from the coast. Suppose a plot of land at the diatnce x from the coast produces a volume of harvestable timber at time T equal to Q(T)= (a-x)T + bT2 – yT3 . let pf be the per unit price of timber harcested from the forest, which is assumed to be constant over time. For simplicity, assume the harvesting costs are equal to zero. A plot of land devoted to forestry incurs a fixed cost of D>0 at the beginning pf each roratio (e.g. converting/clearing the land, planting the trees etc.). the forest also provides important non-timber values in the form of carbon sequestration. Assume that the per-period non-timber values of the forest increase with the volume of the forest and are equal to a(t)=(w+x)evt .

For the following questions, use the parameter values a=18, b=1,y=0.01,D=50,pf=1,w=47, and v=0.01.

Suppose that a forester is only interested in the timber value of theforested land. Using t Excel, find the foesters optimal rotation length T. Do this for different distances away from the coast (i.e for x=(0,1,2,…,15). How does the optimal rotation length change as the distance from the coast x changes? Explain. Plot the NPV of th/. e land dedicated to forestry as a function of x and include it in the graph you created in part a ii. Make sure you explain how you found the answer.
Supoose that the society values both timber and non-timber values. How does the oprimal rotational length and the NPV of the forested land for socirty compare to the forester’s optimal rotation length and NPV of forested land? Similar to the abovem find the society’s optimal rotational length T for the different distances from the coast using Excel. Plot the society’s NPV of the land devoted to forestry as a function of x and include it in the graph you created in b ii. Make sure you explain how you found your answer.

Part C: Land use over the space. Let us now consider how land is allocated to the two different activities that we investigated above: agriculture and forestry.

Suppose the market for the land is perfectly competitive. Over what diatnce form the coast x would we expect land to be devoted to agriculture? What about forestry? Explain your answer. Use your graphs and and any excel tables from parts A and B to come up with an answer.
How does land use in the competitive market compare to the use of land that is optimal for society. Explain your answer.
Suppose that society and the agriculturalist have the same value for the land that is devoted to agriculture. What is the NPV of the land to society if land use is determibed by the competitive marjet? How does this compare to society’s NPV of the land if the land-use is allocated across activities to maximize social welfare?

Part D: Climate Policy. Suppose the Canadian government has decided to be proactive in the fight against climate change. In particular, the government has recognized that the non-timber values that the forest can procie for carbon sequestration are not being fully utilized within the competitive market for land. The government decides to import a climate policy advisor that has recently graduated form UC Berkeley. Based on his superb training in natural resources economics, he recommends implementing a policy that incentivizes foresters to choose a rotational length that is equal to the optimal rotation length form society’s perpective. After running some numbers, the advisor calculates that a site-use tax equal to $100 per parcel of land would incentivize foresters to vhoose a rotational length that is relatively close to the rotation length that maximizes society’s NPV of forested land.

Is the advisors policy a good recommendation? Is society better off with a site-use tax of $100 per land parcel? Explain.
The government wants to be sure that they are getting what they paid for in a climate policy advisor, so they decide to get a second opinion by hiring a graduate from UC Davis that recently took a course in natural resource economics (most likely in the Spring of 2020). The consultant instead advises the government to implement a per-unit-volume subsidy on the timber harcest equal to $2.25 si tha the per-unit-volume price of timber for the forester is pf+2.25. is the consultants policy a good recommendation? Is the society better off with a per-unit-volume subsidy on timber harvest equal to $2.25? explain.