Nonrenewable Resource Practice Problems

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Nonrenewable Resource Practice Problems
Andrew Foss (andrew_foss_at_ksg09.harvard.edu) Econo
mics 1661 / API-135 Environmental and Resource
Economics and Policy Harvard University March
13, 2009 Review Section
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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
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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?

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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?

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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
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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?

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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?

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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.
• Hotellings Rule still applies in this case
  (MUC2 MUC1(1r) ) so marginal user cost in
  Period 2 is also lower than before.

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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.

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Excel Model of Nonrenewable Resource Extraction

• If youre 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
  cant get it to run, dont worry about it.