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Nonrenewable Resource Practice Problems

Nonrenewable Resource Practice Problems. Andrew Foss ( andrew_foss@ksg09.harvard.edu ) Economics 1661 / API-135 Environmental and Resource Economics and Policy Harvard University March 13, 2009 Review Section. Practice Problem #1.

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Nonrenewable Resource Practice Problems

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  1. Nonrenewable Resource Practice Problems Andrew Foss (andrew_foss@ksg09.harvard.edu) Economics 1661 / API-135 Environmental and Resource Economics and Policy Harvard University March 13, 2009 Review Section

  2. Practice Problem #1 Suppose there is unlimited availability of a resource with inverse demand function p = 12 - 0.8 q and with marginal extraction cost MEC = 4. Suppose the time horizon is 2 periods. What quantity should be extracted each period? Unlimited availability makes this just a static efficiency problem. Find the efficient extraction level in the first period (MB = MEC), and the level in the second period is the same. D = MB MEC

  3. Practice Problem #2 Suppose there is a nonrenewable resource with inverse demand functionp = 12 - 0.8 q and with marginal extraction cost MEC = 4. The resource stock is S = 16. Suppose the time horizon is 2 periods and the discount rate isr = 20%. What quantity should be extracted each period? For scarce nonrenewable resources, the present value of marginal net benefits (MNB = p - MEC), also called the marginal user cost (MUC), should be equal across all periods. PV MNB1 PV MNB2 Math on next two slides q1 → ← q2 16 14 12 10 8 6 4 2 0

  4. Practice Problem #2 (continued) Suppose there is a nonrenewable resource with inverse demand functionp = 12 - 0.8 q and with marginal extraction cost MEC = 4. The resource stock is S = 16. Suppose the time horizon is 2 periods and the discount rate isr = 20%. What quantity should be extracted each period?

  5. Practice Problem #2 (continued) Suppose there is a nonrenewable resource with inverse demand functionp = 12 - 0.8 q and with marginal extraction cost MEC = 4. The resource stock is S = 16. Suppose the time horizon is 2 periods and the discount rate isr = 20%. What quantity should be extracted each period?

  6. Practice Problem #3 Suppose there is a nonrenewable resource with inverse demand functionp = 12 - 0.8 q and with marginal extraction cost MEC = 4. The resource stock is S = 16. Suppose the time horizon is 2 periods and the discount rate isr = 0%. What quantity should be extracted each period? For the special case of r = 0% and constant MEC for a scarce nonrenewable resource, the quantity extracted each period is the stock divided by the number of periods (constant extraction). PV MNB1 PV MNB2 Math on next two slides q1 → ← q2 16 14 12 10 8 6 4 2 0

  7. Practice Problem #3 (continued) Suppose there is a nonrenewable resource with inverse demand functionp = 12 - 0.8 q and with marginal extraction cost MEC = 4. The resource stock is S = 16. Suppose the time horizon is 2 periods and the discount rate isr = 0%. What quantity should be extracted each period?

  8. Practice Problem #3 (continued) Suppose there is a nonrenewable resource with inverse demand functionp = 12 - 0.8 q and with marginal extraction cost MEC = 4. The resource stock is S = 16. Suppose the time horizon is 2 periods and the discount rate isr = 0%. What quantity should be extracted each period?

  9. Practice Problem #4 Suppose r = 20% and the producer knows at the outset that marginal extraction cost increases in Period 2. How would that change the extraction quantities and marginal user costs in each period? • The producer should extract less in Period 2, when marginal costs are higher. That means the producer can extract more of the scarce nonrenewable resource in Period 1. • When marginal extraction cost increases in Period 2, there is less opportunity cost (less forgone future net revenue) associated with extraction in Period 1. So marginal user cost in Period 1 is lower. • Hotelling’s Rule still applies in this case (MUC2 = MUC1*(1+r) ) so marginal user cost in Period 2 is also lower than before.

  10. Practice Problem #5 Under what conditions would you expect the actual extraction rate of a nonrenewable resource to be slower than the dynamically efficient rate? • If a monopoly controls the resource market, it can increase its net revenues by cutting back on production, which implies slower extraction than the dynamically efficient rate. • Government intervention, such as production limits, may result in slower extraction than the dynamically efficient rate. • Producers might have incorrect information about potential substitutes in the future, which could lead them to extract the resource more slowly than the dynamically efficient rate.

  11. Excel Model of Nonrenewable Resource Extraction If you’re curious about how extraction and price paths depend on demand, marginal extraction cost, stock, periods, discount rate, and the price of a backstop technology (substitute), you might want to take a look at the Excel model online under “Slides from Fridays.” The model requires Solver and uses a macro (computer program). Instructions on running the model are on the first tab. If you can’t get it to run, don’t worry about it.

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