Natural Resource Economics
1. Consider the Big Surf Break problem from Quiz 1. Carefully draw a graph (or two) to depict the setting. Plot the number of surfers (N) on the horizontal axis and dollars per surfer on the vertical axis. Your graph(s) should show the following
a. The willingness to pay of a surfer (this is the monetized benefit per surfer, or the average benefit)
b. The marginal willingness to pay per surfer (this the marginal benefit of an additional surfer)
c. The open access number of surfers
d. The optimal number of surfers
e. Rents from the surf break under open access
f. Rents from the surf break with the optimal number of surfers
g. The optimal fee
2. Consider the sheep grazing problem discussed in lectures 3 and 4, and worked out in problem set 1.
a. From your notes, write down the number of sheep grazed under open access (SOA), common property (SCP), anticommons (SAC), and optimal conditions (S*). (Note that “N” refers to use rights under common property and it refers to exclusion rights under anticommons).
b. Suppose a= 100 and b = 1. Building from the simulations in problem set 1, use a computer program of your choosing (MS Excel is fine), to simulate the values of SCP and SAC for N = 0, 1, 2, 3 …. 100. Create a graph that looks like the one depicted below. On the right side, show how the number of sheep changes with N when the pasture is common property. On the left side, show how the number of sheep changes with N when the pasture is owned as an anticommons. Comment on the symmetry of use and overuse of pasture under common property and anticommons.
c. Solve for the economic rent earned from the pasture under anticommons ownership. This rent should be a function of N. Label this amount RAC. Compare this value to rents earned under common property, which you can label RCP.
d. Using the same graphical setup as above, simulate the values of RCP and RAC as N changes from 1 to 100. Comment on the symmetry of rent dissipation rents under common property and anticommons.
e. Recall the rules of the SGA, which allows each owner to charge their own fee for pasture use. Can you think of alternative rules that would lessen the anticommons problem?
3. For this problem, use the “Bakken oil decline curve.xlsx” spreadsheet posted on Learn@UW. The data show well productivity for a typical well drilled into North Dakota’s Bakken shale. Note that monthly production decreases rapidly at first, but production slows as time passes. Although production from the well is expected to last for 25 years, for this problem we will assume that all of the profitable oil is extracted in 48 months.
For the questions that follow, assume the following.
· The price of oil per barrel is $75. (This was the average price over 2005 to 2015, when many of the Bakken wells were drilled).
· Royalty payments to shale owners are 18% of total oil revenue, paid at the end of each month.
a. Calculate the present value of royalty payments for a drilling project that begins now and ends in 48 months. (I recommend using a computer program such as MS Excel). How does your answer differ if:
i. The annual discount rate is 0
ii. The annual discount rate 0.05
iii. The annual discount rate is 0.10
b. Why does a non-zero discount rate make sense? What do you think should determine which discount rate is used? Explain your reasoning.
c. Under current fracking technology, a typical Bakken well requires 1280 contiguous acres. If land is subdivided into parcels smaller than 1280 acres, then an anticommons is created. For example, if parcels are 40 acres, there are 1280/40= 32 parcel exclusion right holders that must consent to the drilling project. Suppose there is drilling delay of one month per owner due to anticommons problems. What is the total delay cost, in terms of the present value of delayed royalty payments, when parcels are 40 acres instead of 1280 acres? Assume an annual discount rate of 0.10.
d. In the previous section c, you quantified the costs of subdivision in terms of delayed royalty payments from oil drilling. Yet subdivision presumably increased the value of land for agriculture, relative to common property. Suppose there are different profit streams from farming under common and private property, as given in the table below.
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Monthly farming profit from 1280 landscape
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Common property
(32 use rights on the 1280 acres, 1 exclusion right)
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$1000
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Subdivided ownership
(32 parcels of 40 acres, each with one use right and on exclusion right)
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$2000
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Suppose shale oil is discovered immediately after land is subdivided. Was the land more valuable in a commonly owned unit of 1280 acres, or in 32 separate private parcels? (Hint: For this question, you will need to calculate the discounted value of farming profits and the discounted value of oil royalty payments over time. Assume an annual discount rate of 0.10. Explain how your answer is sensitive to the price of oil and the discount rate chosen.