Econ 211 > Problem Set 4

1.  Suppose there are two classes made up of very similar students and students can choose which class they sign up for. In one class, each student receives the grade made on each test. In the other class, each student receives the class average as his or her grade. These policies are known by all. In what class would you expect the higher average grade? Explain.

2. Explain the nonrivalry and nonexcludability features of a pure public good. Why are both necessary for the good to be a pure public good?

3. Timblin Apartments has 100 resident who are all concerned about security. The table below gives the total cost per day of hiring a 24-hour security guard service and the marginal benefit per day to each of the residents.

Number of Guards Total Cost
of Guards
Marginal Benefit
per Resident
Marginal Benefit
to all Residents
1 $300 $10  
2 $600 $4  
3 $900 $2  
4 $1200 $1  

a) Why is a security guard a public good for the residents of Timblin Apartments?
b) Why will no guards be hired if each of the residents must act individually?
c) Complete the last column of the table by computing the marginal benefit of security guards to all the residents combined.

4. Now suppose that the residents of Timblin form an Apartment Council that acts as a governing body to address security issues.
a) What is the efficient number of guards? What is the net benefit of this amount?
b) Show that the net benefit is less for either one less guard or for one more guard than the net benefit for the efficient number of guards.
c) How might the Apartment Council pay for the guards it will hire?

5. If people are rational, how can public choice result in government actions with benefits that are less than the costs?

6. Art, Bob, and Charlie own a lake in Michigan that they use for recreational purposes. A mosquito abatement program will benefit all. Art place a value of $1, Bob places a value of $19, and Charlie places a value of $100 on a mosquito-free environment. A firm will spray the lake and charge each owner $35.
a) What decision would be reached under majority rule? Would the result be efficient?
b) What decision would be reached if Art, Bob, and Charlie could engage in costless negotiations? Could unanimity be achieved?

7. An environmentalist argues that all pollution must be eliminated. How would you try to convince her that her position is both unreasonable and impractical?

8.  What are the advantages of marketable permits compared to regulation of pollution where all firms are required to reduce pollution by a certain percent?

9. Factory A produces 1000 tons of sulfuric acid at a cost of $10,000. For the people in the community, the production of 1000 tons of sulfuric acid causes an increase of $5000 in medical payments, a loss of $4000 in wages by being sick, and an increase of $1000 in dry-cleaning bills. What are the private and social costs of the 1000 tons of sulfuric acid? Show your work.

10. Airport noise is certainly a negative externality. Why would people choose to live near airports?

11. A factory's production process creates sludge that pours into a river. This sludge makes it difficult to fish in the river, increasing the costs of the local fishermen by $5000. The factory can install a water filter system for $4100, and the fishermen can utilize a weighted fishing net system (to get under the sludge) for $3250. Both systems would remedy the sludge damage to the fishermen.
a) Suppose transactions costs are zero. If the factory is not liable and can continue to produce sludge, what outcome do you predict and why?
b) Suppose transactions costs are zero. If the factory is assigned liability for sludge damage, what outcome do you predict and why?
c) Now suppose transactions costs preclude the possibility of private bargaining between the factory and fishermen. If a pollution tax is levied on the factory with the proceeds given to the fishermen, then what outcome do you predict and why?
d) Discuss the results of parts (a), (b), and (c) in terms of the Coase Theorem.

12. Fishermen who use nets to catch tuna also sometimes net dolphins, which, because they are mammals, drown before they can be released. Currently, the price and quantity of tuna determined by the market does not take into account the cost to society of killing the dolphins (marginal external cost). Listed below are market demand and supply schedules for tuna as well as the marginal external social costs associated with dolphins killed in the process of catching tuna. All costs and values are listed in terms of dollars per pound of tuna.

Quantity of tuna
(1000s)
Consumer's valuation
of tuna
Marginal private cost
of tuna
Marginal external cost
of dolphins
1000 $5.50 $1.75 $2.05
2000 5.00 2.00 2.15
3000 4.50 2.25 2.25
4000 4.00 2.50 2.35
5000 3.50 2.75 2.45
6000 3.00 3.00 2.55
7000 2.50 4.50 2.65
8000 2.00 4.70 2.75

a) What output and price would the free market generate? Why?
b) What is the socially optimal output and price? Why?
c) In order to obtain the socially optimal equilibrium, what would the appropriate per-pound tax on suppliers need to be? Of this tax, how much would consumers end up paying?

13. The table below shows the citizens in a small democratic nation and their desired income tax rates. The political parties are trying to decide what income tax rate to propose.

Person Desired Income Tax Rate
George 80%
Jerry 40%
Elaine 25%
Kramer 30%
Newman 10%

a) Who is the median voter? What income tax rate will be proposed by the parties? Why?
b) Before the next election, Elaine changes her mind and decides that she wants an income tax rate of 50%. What income tax rate will now be proposed? How does this tax rate compare with that in part (a)? If it is different, why is it different; if it is the same, why is it the same?
c) Elaine continues to change her mind and before the third election she decides that she wants an income tax rate of 20%. Now what income tax rate will now be proposed? How does this tax rate compare with those in parts (a) and (b)? If it is different, why is it different; if it is the same, why is it the same?

14. "I don't see why the government would ever do anything that causes inefficiency. Inefficiency hurts the economy and I thought that the government would try to help us." Comment on this student's views and give an example of how the government might take actions that create inefficiency.

15.    In a small town, two factories--factory A and factory B--each produce 20 units of pollution so that the total pollution is 40 units.  Factory A can decrease its pollution at a constant marginal cost of $60 per unit; factory B can reduce its pollution at a constant marginal cost of $100.
a)  Suppose that the Environmental Protection Agency (EPA) determines that the efficient level of pollution in the town is 20 units.  If the EPA requires each factory to decrease its pollution by 10 units, what is the total cost of reaching a total of 20 units of pollution?  Show work.
b)  Suppose that the EPA introduces marketable pollution permits and allows each firm to produce 10 units of pollution.  What is likely to occur?  In particular, will factory A or B want to sell its permits to the other factory and is the other factory willing to buy them?  If there is a potential buyer and seller of the permits, what is the price range in which the permits will trade?
c)  From a social standpoint, which is the more desirable policy: when the EPA requires equal reductions in pollution, or when it introduces marketable permits?  Why is the one policy better than the other?  Show any relevant calculations.

16.    Consider two coastal communities.  In the first community, there are a lot of independent fishing boats that are fishing the coastline.  In the second community, there is one large fishing company that owns all of the boats that fish the coastline.  Considering the idea of common property rights, in which community would you expect more fish to be caught?  Explain why.