Chapter 12
Answers to Problem for Review
1. According to Hotelling’s valuation principle, the value of mineral reserves can be
estimated as the current net price multiplied by the estimated volume of extractable
reserves. The value of 1 million dry long ton units of iron ore in this case is thus 1
million x ($0.40 - $0.25) = $150,000.
2. a) Hotelling’s rule states that in competitive equilibrium, the marginal rent from a
resource (price – MCextraction) will increase at a rate equal to the discount rate. A
decrease in price could be consistent with this rule if the marginal extraction cost
decreased by even more than the price, leading to an increase in marginal rent at the
discount rate.
b) The known supplies of oil change over time, violating Hotelling’s assumption of a
fixed supply. The capital intensive nature of the oil industry makes it difficult for
producers to react quickly to anticipated price changes, and unexpected demand
shocks can alter prices and prevent firms from equating the present value of rents.
3. True. If the marginal cost of extraction increases over time and the marginal benefit
curve stays the same, the undiscounted NMB must fall over time, being the difference
between the constant marginal benefit and the growing marginal extraction cost. With
an increasing marginal extraction cost, rents can only rise if the price rises.
4. Under the assumptions of the depletable resource model in the text, resource extraction
must fall over time as illustrated in the graph to allow prices and rents to increase.
Actual extraction levels may deviate from this relationship as the result of new
resource discoveries or changes in marginal benefits, marginal extraction costs,
marginal opportunity costs, or discount rates, among other influences.
Copper
Resource Extraction
Time
5. Uncertain. Neither riparian rights nor prior appropriation rights entail a mechanism to
allocate water efficiently. The relative efficiency is situation specific. Those living on
water and those who first used water sources may or may not value it more than the
competing interests at any given time.
6. a) One way to incorporate a positive marginal extraction cost into this analysis is to
replace the marginal value curves with net marginal value curves, meaning that the
marginal cost of extraction is subtracted from the marginal value. The will shift each
curve down by the amount of the marginal extraction cost. If that cost is constant, the
curves simply shift down by that constant amount, and intersection of the curves that
determines the efficient division of water will occur at the same allocation as without
the extraction cost. The optimal price determined by the height of the intersection of
the two net marginal value curves indicates the optimal price in addition to the
payment of the extraction cost.
b) If the demand for computer chips increases, the price of computer chips and the
marginal value of water with which to produce computer chips will increase. This is
because the computer industry demand for water is derived from the market demand
for chips. As the marginal value of water in industry increases, the intersection of the
two marginal value curves will move to the left. The efficient division will entail
more water for industry and less for agriculture, and the optimal price will rise. These
changes are illustrated in the following graph:
Dollars
per Unit
Marginal Value
in Agriculture
Optimal
Price
Marginal Value
in Industry
Old intersection
Efficient Division
Water for Agriculture
Water for Industry
Fixed Quantity of Water
c) The width of the above graph represents the total available quantity of water.
When the supply of water increases, the width of the graph increases, leading to a
lower optimal price and larger allocations of water to both interests.
7. In the context of water purchases, flat fee is a fixed amount paid per period regardless
of the quantity of water used, and a flat rate is a fixed amount paid per unit of water
used. As illustrated in the following graph, with a flat rate plan the price per unit is
constant. Under a flat fee plan, the price per unit falls steadily and eventually
approaches the horizontal axis asymptotically as the quantity gets very large.
Price
per unit
Flat Fee
Flat Rate
Quantity
8. [There is a typo in part (a) of this question: Under a decreasing block plan the price
would decrease after each 10-unit increase in usage.]
Price
per unit
Increasing Block
Decreasing Block
0
10
20
30
40
Quantity
9. Out of these options, the increasing block plan is the best for promoting efficient water
use because the price function rises like the social marginal cost function for water.
The flat rate plan is better than the other remaining alternatives because the price does
not fall as more water is used. The decreasing block plan does not encourage efficient
water use because as social marginal costs increase, the price of water decreases. And
the flat fee plan is the worst because the marginal cost of water to consumers is zero
and there is no incentive whatsoever to conserve water resources. Answers will vary
in terms of the actual price plan in place for water. Consumers face a fixed rate plan
for oil. The common fixed rate plans are simple to understand and administer. Flat
fees can sometimes be explained by the expense of installing monitoring equipment
such as water meters.
10. False. Waterways and aquifers are threatened by point and nonpoint sources of
pollution worldwide, and pollution constrains the usability of water supplies no matter
how abundant they may be.