Econ 350
Answers to Problem Set 4

1. Under MC pricing, you would set P = MC and solve for Q and P:
        Q = 24.04
        P = 24.04

        CS = (0.96)(24.04)(0.5) = 11.54
        PS = (24.04)(24.04)(0.5) = 288.96
        Social Welfare = CS + PS = 300.50

    Under AC pricing, you would set P = AC and solve for Q and P:
        Q = 46.30
        P = 23.15

        CS = (1.85)(46.3)(0.5) = 42.83
        PS = 0  (since P = AC, the water supplier will make zero profits)
        Social Welfare = CS + PS = 42.83

    Thus, AC pricing will reduce social welfare by 257.67. 

2. This one is for you to ponder.

3. This one is for you to ponder.

4. This one is for you to ponder.

5. SO2 emissions at three electric power plants.  NOTE: THE CURRENT EMISSIONS FOR FIRM 2 SHOULD BE 200 AND FIRM 3'S CURRENT EMISSIONS SHOULD BE 50.

a) Efficient abatement is solved by setting each firm's MAC curve equal to the MD (= $50,000).

Plant 1: E1 = 50 (with TAC = $1,250,000)
Plant 2: E2 = 166.7 (with TAC = $832,500)
Plant 3: E3 = 43.75 (with TAC = $156,250)
Thus, the total cost of abatement under this scenario is $2,238,750.  Under this proposal total emissions are reduced by 89.55 units.

b) The total cost of each plant cutting emissions by 20% is:
Plant 1: reduces emissions by 20 units at a cost of $500,000
Plant 2: reduces emissions by 40 units at a cost of $1,000,000
Plant 3: reduces emissions by 10 units at a cost of $250,000
Thus the total abatement cost would be $1,750,000. Under this proposal total emissions are reduced by 70 units

c) [I screwed this question up: it was supposed to work out that the total emissions were reduced by the same amount in both part (a) and (b) above.  One would then see that the 20% emission reduction in part (b) would cost more than the outcome in part (a).  The discussion that follows, though, still holds for the case above.] 

The emissions tax necessary to achieve the result from part (a) would be t = $50,000 per ton of SO2. Clearly each firm would prefer the standards since they would avoid the high tax bill. Even though Plants 2 and 3 would end up paying more in abatement costs under the standards compared to the abatement costs under the efficient tax, their total tax payments would simply be too much to pay. From the economist’s point of view, the tax leads to the socially efficient outcome. Under the standards approach, the plants will still generate pollution that imposes uncompensated damages on the greater society. The tax, though quite costly from the plants’ point of view, generates tax revenue that could, in principle, be used to compensate the victims of pollution. A tradable discharge permit system might provide more flexibility for the firms. Or, the tax could be modified to exempt a specified amount of emissions before the tax would kick in.

6. Cleaner autos and gas taxes.
a) The clean auto mandate imposes the burden of cleaning the air on the automobile manufacturers. The gasoline taxes imposes the burden on consumers. Air pollution from autos can be described by the following equation:

Total Emissions = Number of vehicles x Average miles driven x Emissions per mile.

Federal regulations have concentrated on the last factor, while essentially ignoring th e first two. A gas tax would be expected to reduce the average miles driven. However, the relatively minor size of the gas tax (at least compared to most European nations) might suggest that federal regulators are not all that serious about controlling total emissions. This implicit signal may lead auto manufacturers to be less dedicated to the task of developing a "cleaner" car.

b) There are likely to be a variety of policies. Here are some samples from your answers:

7. I'll leave this one for you to ponder.

8. Surface ozone controls.
a) Sure. This is what this course was all about. A "scientific" study might involve a cost-benefit approach utilizing a variety of techniques as discussed in class.
b) I suspect that simply exercising less on those days in which the ozone level exceeded the standard would be more efficient. Several California television stations, for example, post smog alerts on a daily basis. This information could be used by people in order to decide when and where to exercise. A ban on excessive driving would seems to entail too much costs.
c) I suspect that the use of industrial solvents is more likely to be restricted since firms probably use large quantities that can be more easily monitored. A restriction on industrial use would not necessarily show that people are more important than profits. Rather, it simply reflects that a few hundred industrial users are easier to monitor than millions of individual households.

9.  I’ll leave this one for you to ponder.

10.  Consider taxes, deposit-refunds, and tradable permits. Opponents may argue that the marginal damages are so severe from even small amounts of PCBs that a ban is the socially optimal policy.

11.  Consider the "with/without" principle as part of your answer.

12. Mandatory beverage container laws.
a) It is difficult to say whether the mandatory-deposit law is "cost effective" without knowing more about other compliance costs and overall benefits. Would Michiganders be willing to pay $300 million per year to achieve this much litter reduction? It could be that an 82% decrease in beverage-container litter is too much or too little.
b) Even if Michigan residents valued the litter reduction at more than $300 million per year it is still not clear that the law is cost effective. We still do not have information on other compliance aspects. Is there a less-costly way to achieve the same result?
c) 30,000 full time workers. Your guess is as good as mine as to whether this "army" can do a better job at cleaning up bottles compared to the mandatory-deposit law. Even if they could do a "better" job, that doesn’t necessarily settle the issue. Some might prefer the mandatory-deposit law because it places the cost on the "guilty" parties.

13.   This is for you to ponder.

14. Billboards provide provide a social benefit in the sense that they provide consumers information about products and services.  Such information could, for example, reduce the costs consumers face when searching for products--consider the value to a family on a road trip trying to locate a place to eat or sleep.  On the other hand, billboards may be viewed as a blight on the rural landscape (a negative externality).

15. This is in the text.

16. The first part is in your text.  The second part was discussed in class.

17. The economic forces leading to extinction include (i) over-harvesting due to common resources problems, and (ii) habitat destruction due to the spread of development such as logging, farming, or urban sprawl. One might also argue that the introduction of non-native species could "crowd-out" native species.  The benefits of preserving biodiversity include the exploitation of genetic materials for medical research and farming, and the maintenance of species and ecosystems for ecological balance and adaptability purposes.   What sort of costs do you think are involved in preserving biodiversity?

18.  This is a question concerning the optimal harvesting rate for yew trees.  Harvest too fast (to save current cancer patients) and you'll not have enough trees to save future cancer patients.  What sort of factors would go into your calculation? 

19.  This is a question I usually work out in class, but did not get around to doing this semester.  The efficient number of species to preserve is found by setting the marginal benefit equal to the marginal cost of species. The marginal benefit is derived from the total benefit equation by taking the first derivative with respect to Q: thus, MB = 100 - 4Q.   The marginal cost is given as MC = 4(Q-15) = 4Q - 60.  Setting MB = MC we get:

100 - 4Q = 4Q - 60
160 = 8Q
Q = 20

The graph below illustrates the same analysis.

For part (b), to preserve all 30 species the MC would be $60 per species.  Thus, the external benefit would have to match this cost in order to justify saving all 30 species.

20.  More for you to ponder.