D.  Resource Allocation Over Time

• How should nonrenewable resources be allocated over time?

- Renewable resources - resources that are regenerated over time through ecological processes

Ex. - Farms, forests, fisheries

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- Nonrenewable resources - resources that do not regenerate through ecological processes, at least on a human time scale

Ex. - Oil, coal, minerals

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1.  Allocation of nonrenewable resources

• Assumptions

- Known, limited quantity of a resource

- Two different time periods

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• Need to balance benefits of current consumption with future consumption

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a.  Equilibrium in current period

• Marginal net benefit - the net benefit of the consumption or production of an additional unit of a resource

• Marginal net benefit = marginal benefits - marginal costs

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• Marginal net benefit function

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• Total net benefit - total benefit minus total cost

• Maximized when marginal net benefit = 0

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b.  Dynamic equilibrium for two periods

• Assume supply and demand are the same in the second period

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(1)  Present value

• Current value of a stream of future costs and benefits

• Money in the future is worth less than money in the present

• Due to inflation and foregone returns

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(2)  Algebraic solution

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(3)  Total net benefit

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c.  User costs

• Opportunity costs associated with the loss of future potential uses of a resource, resulting from consumption of the resource in the present

• Equals the present value of marginal net benefits for the second period

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• Consumption in the present is justified if marginal net benefit in the present is greater than the user cost

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d.  Resource depletion tax

• User cost is the cost of a negative externality

• Use a Pigouvian tax to deal with negative externalities

• Resource depletion tax - a tax on the extraction or sale of a natural resource

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e.  Other policies

(1) Direct government control

(2)  Set aside resource deposits

(3)  Maintaining stockpiles

(4)  Private solution can be achieved if future shortages can be foreseen

• Scarcity rent - payments to resource owners in excess of the amount necessary to keep those resources in production

• Equal to the vertical difference between the supply and demand curves

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2.  Hotelling's Rule

a.  Impact of fluctuations in the discount rate

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b.  Hotelling's Rule

• In equilibrium, the net price (price minus production costs, or the scarcity rent) of a resource must rise at a rate equal to the rate of interest

- If net price + interest > expected future price => extract now

- If net price + interest < expected future price => extract in future

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c.  Issues

(1)  Ethically, should something be left for future generations?

• Hartwick Rule - resource rents should be invested rather than consumed

• Replace natural resources with produced capital

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(2) Discounting puts low weight on well-being of future generations, particularly far in the future

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(3)  Environmental externalities from extraction may make social cost higher than private cost

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