Tietenberg Tom, Lewis Lynne. Environmental & Natural Resource Economics

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Therefore, the area of the rectangle is 6,400/9. The area of the right

triangle is

3. The policy would not be consistent with efficiency. As the firm considers mea-

sures to reduce the magnitude of any spill, it would compare the marginal costs of

those measures with the expected marginal reduction in its liability from reduc-

ing the magnitude of the spill. Yet the expected marginal reduction in liability

from a smaller spill would be zero. Firms would pay $X regardless of the size of

the spill. Since the amount paid cannot be reduced by controlling the size of the

spill, the incentive to take precautions that reduce the size of the spill will be

inefficiently low.

4. If “better” means efficient, this common belief is not necessarily true. Damage

awards are efficient when they equal the damage caused. Ensuring that the

award reflects the actual damage will appropriately internalize the external cost.

Larger damage awards are more efficient only to the extent they more closely

approximate the actual damage. Whenever they promote an excessive level of

precaution that cannot be justified by the damages, awards that exceed actual

cost are inefficient. Bigger is not always better.

5. a. Descriptive. It is possible to estimate this linkage empirically.

b. Normative. A descriptive analysis could estimate the impacts of expenditures

on endangered species, but moving from that analysis to a conclusion that

expenditures would be wasted requires injecting values into the analysis.

c. Normative. A descriptive analysis could compare the effects of privatized and

nonprivatized fisheries, but moving from these results to a conclusion that

$12,800

6 $1,600

$3,200

6 $800

$9,600

7 $800

$3,200

Consumer surplus =

$9,600

Producer surplus =

3,200

6,400

3,200

601Answers to Self-Test Exercises

the fisheries must be privatized to survive normally requires an injection of

values. If the data revealed that all privatized fisheries survived and none of

the others did, the move to “must” would have a very strong descriptive

underpinning.

d. Descriptive. This linkage could be estimated empirically directly from the data.

e. Normative. This statement could be descriptive if it was stated as “birth control

programs actually contribute to a rise in population” since this is an empirical

relationship that could be investigated.

However, as stated it allows a much wider scope of aspects to enter the debate and

weighing the importance of those aspects will normally require value judgments.

6. a. A pod of whales is a common-pool resource to whale hunters. It is characterized

by nonexclusivity and divisibility.

b. A pod of whales is a public good to whale watchers since it is characterized by

both nondivisibility and nonexclusivity.

c. The benefits from reductions of greenhouse gas emissions are public goods

because they are both nondivisible and are nonexclusive.

d. For residents a town water supply is a common-pool resource because it is both

divisible and nonexclusive to town residents. It is not a common-pool resource

for nonresidents since they can be excluded.

e. Bottled water is neither; it is both divisible and exclusive. In fact it is private

good.

Chapter 3

1. With risk neutrality, the policy should be pursued because the expected net

benefits (0.85 × $4,000,000 + 0.10 × $1,000,000 + 0.05 ×−$10,000,000 =

$3,000,000) are positive. Related Discussion Question: Looking at these

numbers do you think risk neutrality is how you would actually think about

this situation? Or would you be more risk averse and weigh the third out-

come more heavily than its expected likelihood?

2. a. Cost-effectiveness in this case (according to the second equimarginal principle)

requires that that target be met (10 fish removed) and the marginal costs of each

method be equal. We know that q

+ q

= 10 and that MC

= MC

The key is to reduce this to one equation with one unknown. Since MC

= MC

we know that $10q

will equal $5q

, or q

= .5q

. Similarly MC

= MC

, so $5q

= $2.5q

or q

= 2q

. Substituting these values into the first equation yields .5q

+ 2q

= 10. So q

= 10/3.5 = 2.86 (to two decimal places.) That means q

1.43 and q

= 5.72. (The fact that this adds to 10.01 rather than 10.00 is due to

rounding.)

b. All three of these methods have a marginal cost that increases with the amount

removed. Thus the cost of removing the first fish for each is cheaper than

removing the second fish with that method, etc. Consider the marginal cost of

602 Answers to Self-Test Exercises

removing the last fish if all fish are removed by method three. In that case the

marginal cost would be $2.5 × 10 or $25. Notice that the cost-effective alloca-

tion, the cost of removing the last fish when the marginal costs are equal

(using q

for the calculation) is $10 × $1.43 = $14.30. In the case of increasing

marginal costs using a combination is much cheaper.

c. In this case you would only use method three because the marginal cost of

removing each fish would be $2.5. This is lower than the MC for method 1

($10) and lower than the MC for method 2 ($5). Note that the marginal

costs only have to be equal for the methods that are actually used. The mar-

ginal costs for unused methods will be higher.

3. Since the benefit cost test requires that the present value of benefits be greater

than the present value of the costs, we can find the maximum allowable current

cost by calculating the present value of the benefits. This can be calculated as:

$500,000,000,000/(1+r)

where r is either 0.10 or 0.02. Whereas with a 10 per-

cent discount rate the present value is approximately $4.3 billion, with a 2 percent

discount rate it is approximately $185.8 billion. Clearly the size of the discount

rate matters a lot in determining efficient current expenditures to resolve a long-

range problem.

Chapter 4

1. In order to maximize net benefits, Coast Guard oil-spill prevention enforce-

ment activity should be increased until the marginal benefit of the last unit

equals the marginal cost of providing that unit. Efficiency requires that the

level of the activity be chosen so as to equate marginal benefit with marginal

cost. When marginal benefits exceed marginal cost (as in this example), the

activity should be expanded.

2. a. According to the figures given, the per-life cost of the standard for unvented

space heaters lies well under the implied value of life estimates given in the

chapter, while per-life cost implied by the proposed standard for formalde-

hyde lies well over those estimates. In benefit–cost terms the allocation of

resources to fixing unvented space heaters should be increased, while the

formaldehyde standard should be relaxed somewhat to bring the costs back

into line with the benefits.

b. Efficiency requires that the marginal benefit of a life saved in government

programs (as determined by the implied value of a human life in that context)

should be equal to the marginal cost of saving that life. Marginal costs should

be equal only if the marginal benefits are equal and, as we saw in the chapter,

risk valuations (and hence the implied value of human life) depend on the risk

context, so it is unlikely they are equal across all government programs.

3. a. The total willingness to pay for this risk reduction is $200 million ($50 per

person × 4 million exposed people.) The expected number of lives saved would

be 40 (1/100,000 risk of premature death × 4,000,000 exposed population).

603Answers to Self-Test Exercises

604 Answers to Self-Test Exercises

The implied value of a statistical life would be $5,000,000 ($200,000,000 total

willingness to pay/40 lives saved).

b. The program is expected to save 160 lives ((6/100,000 − 2/100,000) × 4,000,000).

According to the value of a statistical life in (a) the program will have more

benefits than costs as long as it costs no more than $800,000,000 ($5,000,000

value per life × 160 lives saved).

Chapter 5

1. a. Ten units would be allocated to each period.

b. P = $8 − 0.4q = $8 − $4 = $4

c. User cost = P − MC = $4 − $2 = $2

2. Because in this example the static allocations to the two periods (those that ignore

the effects on the other period) are feasible within the 20 units available, the

marginal user cost would be zero. With a marginal cost of $4.00, the net benefits

in each period would independently be maximized by allocating 10 units to each

period. In this example no intertemporal scarcity is present, so price would equal

$4.00 marginal cost.

3. Refer to Figure 5.2. In the second version of the model, the lower marginal

extraction cost in the second period would raise the marginal net benefit curve in

that period (since marginal net benefit is the difference between the unchanged

demand curve and the lower MC curve). This would be reflected in Figure 5.2 as

a parallel leftward shift out of the curve labeled “Present Value of Marginal Net

Benefits in Period 2.” This shift would immediately have two consequences: it

would move the intersection to the left (implying relatively more would be

extracted in the second period), and the intersection would take place at a higher

vertical distance from the horizontal axis (implying that the marginal user cost

would have risen).

4. a. The higher discount rate would lower the present value of the net benefit

function in the second period. This would be reflected as a rotation of that

function downward to the right. The new function would necessarily cross

the PVMNB1 function at a point further to the right and lower than before

the discount rate change. The fact that the intersection is further to the right

implies that more is being allocated to period 1 and less to period 2. The fact

that the intersection is lower implies that the present value of the marginal

user cost has declined.

b. Since a higher discount rate lowers the present value of allocations made to

the second period, allocating relatively more of the resources to the first pe-

riod will increase the present value derived from them. The present value of

the marginal user cost is lower since the marginal opportunity cost of using

the resources earlier has gone down.

5. a. Increasing the second period demand is reflected in the two-period model by

a shift (not a rotation) in the PVMNB2 curve upward and to the left. After

the shift, this new function will necessarily intersect the PVMNB1 curve

closer to the left-hand axis and higher up on the Y-axis. This implies an

increase in the relative amount allocated to the second period (thereby reduc-

ing the amount allocated to the first period) and a higher present value of the

marginal user cost.

b. When demand is increasing in the future (hence making the marginal re-

sources relatively more valuable then), it makes sense to save more for the

future. This is accomplished by a rise in the marginal user cost, which

results in higher prices. The higher prices provide the incentive to save

more for the future. More is consumed in the second period despite the

higher prices because the demand curve has shifted out.

Chapter 6

1. From the hint, MNB

/MNB

= (1 + k)/(1 + r). Notice that when k = 0, this

reduces to MNB

= MNB

(1 + r), the case we have already considered. When

k = r, then MNB

= MNB

; the effect of stock growth exactly offsets the

effect of discounting, and both periods extract the same amount. If r > k,

then MNB

> MNB

. If r < k, then MNB

< MNB

2. a. With a demand curve shifting out over time, the marginal net benefits from a

given future allocation increase over time. This raises the marginal user cost

(since it is the opportunity cost of using the resource now) and, hence, the

total marginal cost. Thus, the initial user cost would be higher.

b. Less of the resource would be consumed in the present; more would be saved

for the future.

3. a. This turns out to have the same effect as the environmental cost pictured in

Figures 6.6a and 6.6b. The tax serves to raise the total marginal cost and, hence,

the price. This tends to lower the amount consumed in all periods compared to

a competitive allocation.

b. The tax also serves to reduce the cumulative amount extracted because it

raises the marginal cost of each unit extracted. Some resources that would

have been extracted without the tax would not be extracted with the tax; their

after-tax cost to the producer exceeds the cost of the substitute. The price

would be higher with the tax in all periods prior to the without-tax switch

point. After that time the price would be equal to the price of the substitute

with or without the tax.

4. The cumulative amount ultimately taken out of the ground is determined by the

point at which the marginal extraction cost equals the maximum price con-

sumers will pay for the depletable resource. In this model the maximum price is

the price of the substitute. Neither the monopoly nor the discount rate affects

either the marginal extraction cost or the price of the substitute, so they will

have no effect on the cumulative amount ultimately extracted. The subsidy,

however, has the effect of lowering the net price (price minus subsidy) of the

substitute. The intersection of marginal extraction cost and the net price will,

605Answers to Self-Test Exercises

therefore, occur when a smaller cumulative amount has been extracted than

would be the case in the absence of the subsidy.

5. They would not produce the same switch point. The switch would be faster

under the subsidy. While they would result in the same cumulative amount

of the depletable resource being extracted, the speed with which it would be

extracted would be faster with the subsidy. By raising the after-tax price the

tax would reduce demand (and hence the speed with which the depletable

resource would be used up), while the subsidy would, by lowering the mar-

ginal user cost, increase demand (and hence increase the rate at which the

depletable resource was extracted).

Chapter 7

1. During a recession, the demand curve shifts inward, causing downward pressure

on prices. If price is supported, then the quantity supplied must be reduced.

Since the burden of holding the price up falls on the cartel, while the competi-

tive fringe can keep on producing, the demand reduction causes production to

fall most heavily in OPEC nations. This causes the cartel market share to fall. To

protect their individual market shares, members start cutting prices. In growing

markets, cartel market shares can be protected without cutting prices.

2. a.

b. This is the mirror image of the monopoly allocation. The net benefits are

identical in the two allocations, but they are distributed among producers

and consumers rather differently. With this form of price control, the

consumer surplus is larger and the producer surplus is smaller than the

corresponding concepts when the allocation is governed by a monopoly.

Essentially, the rectangle discussed in the answer to part (b) of the second

problem in Chapter 2 goes to consumers with price ceilings and to pro-

ducers in a monopoly.

3. The paper company. The high-cost energy is appropriately assigned to the five

paper machines because that is the energy cost that would be eliminated if the

machines were shut down. The company would not shut down all energy sources

in proportion; it would shut down the most expensive sources. In making a shut-

down decision, therefore, it is essential that the machines in question cover the

cost of the energy that would be saved if the machines were shut down; otherwise

the company is losing money.

4. Peaking plants run only a small percentage of the time, so the capital expendi-

tures remain unused most of the time. Operating costs are incurred only when

they are needed. It makes sense, therefore, for utilities to design peaking plants

Consumer surplus =

$9,600

q =

$80

Producer surplus =

$3,200

P = MC

$80

606 Answers to Self-Test Exercises

so as to keep capital costs as low as possible, even if it means incurring higher

operating cost. Base-load plants, on the other hand, run almost continuously, so

the capital costs are prorated over a very large number of kilowatt-hours and

therefore are less of a burden.

5. No. This could internalize some of the externalities associated with oil, but it

would not internalize the climate change externalities of other fuels such as coal

and indeed might exacerbate them as consumers switched from oil to coal.

6. a. False. While cartel members with small stocks of the depletable resource

would be generally supportive, cartel member holding large reserves would

be afraid that the high early price increases would force an earlier switch to

renewables, leaving them with unsold stocks.

b. False. By holding prices lower than they would otherwise be, placing a price

control on a depletable resource would increase the speed with which the

resource is extracted over time but it would lower the cumulative amount

ultimately extracted.

c. False. By lowering the marginal user costs a price control influences the

extraction path of a depletable resource well before the time that the market

price actually reaches the level of the price control.

d. Uncertain. While internalizing the externality, as proposed here, is generally a

move toward efficiency, the details do matter. For example, the level of com-

pensation could be too high or too low. Remember that for efficiency the pay-

ments should exactly equal the damages caused. Excessive compensation can

be inefficient because, by raising the expected cost of future operations above

the efficient levels, it could preclude some efficient oil drilling. On the other

hand, inadequate compensation, by ultimately understating the future

expected cost, could promote excessive oil drilling.

7. The existence of a renewable energy credit market would lower the compliance

costs associated with meeting a renewable portfolio standard by providing more

flexibility to compliance units. For example, without such a market utilities

would have to assure that they supplied the requisite amount of renewable

power within their market area regardless of whether that market area was suit-

able for that renewable power or not. With a renewable energy credit market,

producers can create the renewable power in those areas that are most suitable

(e.g., have the requisite wind flow, water flow, or solar flux) and sell any excess to

jurisdictions that could only generate their own renewable power only at a much

higher cost. Substituting this more efficiently produced (and hence lower-cost)

power for the more inefficiently produced (and hence higher-cost) power, allows

the standard to be met at a lower cost.

8. Incorporating national security concerns, but ignoring climate change impact

means that domestic production is determined by the intersection of S

with P

and total consumption is determined by the intersection of P

with domestic de-

mand. Note that this results in a lower price level (P

rather than P

), more

domestic production (since domestic producers are ignoring the climate-change

impact), and more domestic consumption (due to the lower price).

607Answers to Self-Test Exercises

Chapter 8

1. a. Assume that only virgin ores are used. In this case P = MC

, so 10 − 0.5q

0.5q

or q

= 10. This implies MC

= 5. The marginal cost of producing any

units using recycled products is clearly higher than 5, so none will be used.

Therefore, 10 units would be produced, and all of them would be produced

using virgin ores.

b. With the higher demand curve the price will be high enough to stimulate the

producer to make some of the product with recycled materials. The key to

solving this problem is recognizing that the producer will equate the mar-

ginal costs of products made with recycled materials and those made with vir-

gin ores. Using this fact, we can set 0.5q

= 5 + 0.1q

or q

= 10 + 0.2q

Substituting this into the demand function yields

Solving for P = MC yields

and

The solution can be verified by showing

2. a. They will not have the same effect. Because the royalty is a per-ton fee, it

raises the marginal cost of extraction to the firm, but the bonus bid, which

does not affect the marginal cost of extraction, does not. If the mineral has an

increasing marginal cost of extraction, less will be extracted with a royalty

system than with a bonus bid system because the marginal cost of extraction

(including the royalty payment) will hit the backstop price at a smaller cumu-

lative amount extracted.

b. The bonus bid is consistent with efficiency because it does not distort the

allocation over time. The allocation that maximized firm profits before the

bonus bid will still maximize it after the bonus bid. While the government

shares the profits, it does so without distorting incentives. By raising the mar-

ginal cost of extraction, royalty schemes distort incentives.

c. With a bonus bid scheme, the firm bears the risk. The government gets a

fixed payment. The firm can either win big or lose big, depending on how

valuable the deposit turns out to be. With the royalty scheme, the risk is

shared. If the mine turns out to be very valuable, profits and government

P = MC

= MC

= 10 + 0.2a

100

b =

15 - 0.6q

= 5 + 0.1q

or q

100

P = 15 - 0.6q

P = 20 - 0.5(10 + 0.2q

+ q

) or

608 Answers to Self-Test Exercises

fees both go up. If the deposit turns out not to be very valuable, the firm

gains little but so does the government.

3. Rising societal disposal cost is certainly one of the factors that should stimulate

higher recycling rates, but it is by no means the only one. And as long as it is not

the only factor, recycling rates will not automatically increase in response. First,

this higher social cost must be reflected in increasing marginal disposal costs fac-

ing individuals in order to provide the incentive to recycle; rising social costs do

not automatically result in rising individual marginal costs. Second, markets must

exist for the recycled materials. Collecting them does no good if they can’t be put

to good use.

4. a. The sticker system would tend to be more efficient. Because the property tax

approach to financing is not related to the amount of trash disposed of, the

marginal cost of disposing of an additional bag under this system is zero. This

is considerably lower than the cost to the town of disposing of the waste. The

marginal cost to the consumer does not reflect the marginal cost to the town.

In contrast, the sticker system imposes a marginal cost per bag that could, if

the sticker price were calculated correctly, exactly equal the marginal cost to

the town.

b. Since the cost of the sticker does not have to be paid for illegally disposed

trash, requiring stickers could promote illegal dumping. (They do, of course,

have to pay any imposed fines if they get caught.) If illegal disposers tend not

to get caught so illegal disposal is rampant, it could raise the costs to the town

above $30.00 to recover and process the dispersed trash and would under-

mine the efficiency of the sticker system. A property tax financing system

provides no incentives for illegal disposal since the cost is paid however a

household chooses to manage its trash.

Imposing a deposit-refund on some large components of the trash would help to

reduce illegal disposal because illegal disposal would now cost something—the

consumer loses the deposit. However, a deposit refund system would raise no rev-

enue for the town to cover its disposal costs since the deposit is returned to the

consumer once the object is transported to the collection site.

Chapter 9

1. Since the amount of capacity needed would depend on the maximum flow dur-

ing the year, the extra cost of expanding capacity during this high-flow period

should be reflected in higher prices charged to users during these periods.

2. Assuming the rate was correct, the flat rate would be more efficient because it

would confront the user with a positive marginal cost of further consumption.

The marginal cost of further consumption with a flat fee is zero.

3. a. For the case where the ground water comes from a private well that taps a

private aquifer, with perfect information the owner would have an incentive

to extract the water at an efficient rate. The private owner would face all

609Answers to Self-Test Exercises

costs, both present and future, and be able to balance them accordingly. The

social present value of marginal net benefit curves for both periods would be

identical to the private present value of marginal net benefit curves for both

periods. Note, however, the very important “full information” caveat. If the

owner doesn’t know what is there, he/she can’t very well allocate it efficiently

regardless of how good the incentives are.

b. For the case where the ground water is obtained from your private well that is

drilled into an aquifer that is shared with many other users who have also drilled

private wells, an efficient allocation would not be expected. Perverse incentives

would arise both within any particular time period and over time. Because this is

a divisible resource, within a time period each user would know that any unit not

extracted by his/her could well be extracted by a neighbor. The incentive is to

take more than the efficient amount to avoid losing it. Over time, the users would

act as if the marginal user cost is zero since the trade-off between the present and

the future that characterizes the situation in part (a) is lost. Whereas in a private

well whatever I don’t use now I can simply use later, that is not true in a shared

aquifer. Water not used by me now may well be used by someone else and be

gone forever. This particular institutional arrangement encourages the overuse of

water and thereby serves to intensify any problems of scarcity.

4. The key to using the tiered system for this purpose is to distinguish water needs

by monthly volume. Specifically, the first block could contain a basic amount of

water that fulfills essential purposes, while the second block contains all other

water above that amount. The first block would be priced at a low level, while

the second block price would reflect all of the scarcity rent generated by the

marginal user cost as well as the marginal cost of extraction and distribution.

Since the positive marginal user cost means that the marginal revenue for that

block would be above the marginal extraction plus distribution cost, the utility

could still cover its expenses despite the low cost of the first units. Meanwhile,

because most households would consume at least some more water than allowed

in the first block, the price they would face for the additional water would be the

efficient (marginal cost) price in the second block. The fact that the price for the

additional water would be the efficient price would preserve incentives to con-

serve an efficient amount.

Chapter 10

1. The congestion charge would raise the cost of transportation for commuters,

while the increased number of lanes would reduce it (considering travel time).

According to the bid rent function analysis, the congestion charge would make

the residential bid rent function steeper and encourage more density in the urban

area and less expansion into the suburban areas served by those expressways.

Conversely the new lanes would make the bid rent function less steep and en-

courage more people to move into the suburbs.

2. Land confers a bundle of entitlements to the owner. Conservation easements

allow the transfer of only the specific entitlements of interest (typically the

610 Answers to Self-Test Exercises

Tietenberg Tom, Lewis Lynne. Environmental &amp; Natural Resource Economics

Подождите немного. Документ загружается.

Tietenberg Tom, Lewis Lynne. Environmental & Natural Resource Economics