Problem Set 4 Answer Key

1.  The class in which students earn their own grades will have the higher class average. The class in which students earn the class average as their grade will attract a lot of free riders. The free riders are likely to be (how should I say) academically-challenged, thereby ensuring an overall lower class average.

2.  This is in your notes and the text book.

3.  Parsons Guards I
a)    Guards provide a general sense of security for all residents that exhibits non-rivalry and non-exclusivity.
b)    The marginal cost of hiring a guard is greater than the marginal benefit to any single individual.
c)    See below.

Number of Guards Total Cost
of Guards
Marginal Cost
of a Guard
Marginal Benefit
per Resident
Marginal Benefit
to all Residents
Total Benefit Net Benefit
1 $300 $300 $10 $1000  $1000 $700
2 $600 $300 $4 $ 400 $1400 $800
3 $900 $300 $2  $ 200 $1600 $700
4 $1200 $300 $1  $ 100 $1700 $500

4.  Parsons Guards II
a)    2 guards with a net benefit of $800.
b)    See table above. 
c)    Perhaps the Apartment Council could levy an annual security fee of $6 per resident to fund the 2 guards.

5.    This is for you to ponder.

6.    Mosquito abatement program.
a) Under majority rule, only Charlie would vote in favor of the abatement program (since he values the program at $100, which is more than the cost to each owner of $35). Thus, the abatement program would not be approved. From society's point-of-view this would be inefficient since the total value of the program to the three guys ($120) is greater than the total cost ($105).
b) Unanimity could be reached by having Charlie subsidize Art and Bob's "tax bill." Assuming Art and Bob are willing to pay their values, Charlie could pay $34 on behalf of Art and $16 on behalf of Bob in order to pay for the abatement program. All parties would thus benefit.

7.  How would you argue?

8.  Think about the in-class exercise on pollution abatement.

9.  Private costs = $10,000;  External costs = $5000 + 4000 + 1000 = $10,000; Social costs = private + external = $20,000

10.  Perhaps property values are lower around airports, thus housing is relatively cheaper.

11.  Fishermen and sludge.
a) The fishermen will buy the nets at a cost of $3250.
b) The factory will buy the nets for the fishermen at a cost of $3250.
c) The tax is likely to be set equal to the damage done by the sludge to the fishermen, namely, $5000. Given this potential tax liability, the factory will try to minimize its costs by avoiding the tax. Since the factory is precluded from bargaining with the fishermen as in part (b), they will be unable to buy the net system. The next best option is to install the water filter system at a cost of $4100 (which is better than paying $5000 in taxes).
d) As Coase would argue, the outcomes in parts (a) and (b) are identical: as long as property rights are well-defined and transaction costs are low, private bargaining will result in the most efficient outcome. In this case, efficiency requires that the nets be used. However, in part (c), transactions costs were high enough to prevent bargaining so that only a "second best" outcome prevailed.

12.  We did one very similar to this one in class.

13.    Kramer is the median voter.  Politicians will tend to propose a tax rate of 30%. If Elaine changes her mind, then a tax rate of 40% will now be proposed. If Elaine changes her mind again, then a tax rate of 30% will be proposed.

14.    Think about rent-seeking behavior on the part of special interest groups and politicians.

15.    Pollution
a)    Cost to Factory A = (10)($60) = $600;  Cost to Factory B = (10)($100) = $1000.  Thus the total cost to the town of cutting 20 units of pollution is $1600.
b)    If each firm is given only 10 permits, they must each reduce their total pollution from 20 to 10 just as described in part (a) above.  However, since Factory A can eliminate their pollution cheaper than Factory B can, Factory A is likely to sell their permits to Factory B at some price between $60 and $100 per permit.  For example, a price of $80 would make both Factories better off.
c)    Suppose that the price of a permit is $80.  Then, Factory A can cut its emissions by another 10 units (at a cost of an additional $600) and sell the permits to Factory B for $800.  The net cost to Factory A is = 600 + 600 - 800 = $400.  Factory B, therefore, is able to continue producing 20 units of pollution because they've now bought 10 additional permits at a cost of $800.  The total cost to the town is $1200.  Note that this is cheaper than the solution proposed in part (a) above!

16.    This is for you to ponder.