Who sells permits and how many do they sell who buys

Question

Assignment

1. There are three industrial firms in Happy Valley.

Firm	Initial Pollution Level	Cost of Reducing Pollution by 1 Unit
A	20 units	$10
B	40	$20
C	60	$30

The Government wants to reduce pollution to 90 units, so it gives each firm 30 tradable pollution permits.

a. Who sells permits and how many do they sell? Who buys permits and how many do they buy? What is the total cost of pollution reduction in this situation?

b. How much higher would the costs of pollution reduction be if the permits could not be traded?

2. Suppose that market demand for leather products is P = 50 - ½ Q and market supply is determined by P = ½ Q. Unfortunately, production of leather causes chemical residue to leak into ground water supplies. The external marginal damage caused by the residues grows with the amount of output and is measured as EMD = Q.

a) How many units of this product will the free market produce? What is the socially optimal level of output?
b) Graphically illustrate your answer in (a) and shade the deadweight loss associated with ignoring externality.

3. Carrboro has three groups of people: (1) Type A people consistently prefer more police protection to less (H>M>L); (2) Type B people prefer either high levels or low levels of police protection to less (H>L>M); (3) Type C people prefer medium levels to either high or low levels (M>H>L).

a) Is this social preference profile single-peaked?
b) Will majority voting generate consistent outcomes in this case? Why or why not?

4. Abe, Betty and Charlie are the only three students in my graduate Public Finance class and I am trying to determine how many office hours to hold per week for this class. Since my office and blackboard are reasonably large, all three can attend the hours I provide and simultaneously consume all the "wisdom" I offer during those hours. That is, there is no rivalry in the consumption of my attention and time during office hours. However, not every student values these hours the same. Suppose, in fact, that the marginal benefit each student receives is as follows:

MB^Abe = 10 - (1/3)H; MB^Betty = 12 - (1/3)H; MB^Charlie = 14 - (1/3)H.

ASSUME that the marginal cost of my time per hour is constant and equal to $24 per hour.

a) How many office hours should I hold per week if, like any good Public Finance professor, I want to offer the Pareto efficient number of office hours?

b) Suppose office hours don't come with tuition so I charge Abe, Betty and Charlie according to what they would pay in a Lindahl equilibrium, that is, according to the benefit principle of taxation. What would I charge each student per hour for the total number of office hours I provide? Would the cost of my time per hour be covered? How much money in total would the students pay? (Assume each student must pay for ALL the hours I provide whether they attend or not.)

5. Abe, Betty, and Charlie have adjoining houses near a swamp, and they would like to reduce the number of mosquitoes which bite them during their barbecues. Their "demand" or marginal-willingness-to-pay functions for mosquito repellant canisters are given below. The supply curve for mosquito repellant canisters is completely elastic at a price of $9.00 per canister.

$mwtp	Abe	Betty	Charlie
$1.00	6 canisters	6 canisters	9 canisters
$2.00	5	5	8
$3.00	4	4	7
$4.00	3	3	6
$5.00	2	2	5
$6.00	1	1	4
$7.00	0	0	3
$8.00	0	0	2
$9.00	0	0	1

a) Assuming they treat repellant as a purely private good, how many units will each individual purchase?

b) Suppose Abe is a hot shot economics major, and realizes that mosquito repellant is actually a pure public good. Intuitively he thinks that the three would be better off if they collectively purchased the repellant rather than individually buying repellant. Assuming that Abe is correct and repellant is a pure public good, what is the socially optimal number of repellant canisters for this three person collectivity? In the aggregate, is more or less repellant purchased after collective provision? How should the collective level of production be financed, assuming the group does not want to run a deficit.

c) Suppose the three decide to split the cost of each canister purchased evenly and that they will determine the number of canisters to buy via the method of majority voting. What is the outcome? How does it compare to the efficient outcome?

6. The town of Greenville has three families, each with one child, and each of which earns $20,000 per year (pre-tax). Each family is taxed $4,000 per year to finance the public school system in the town, which any family can then freely attend. Education spending is $6,000 per student in the public schools. The three families differ in their preferences for education. Though families A and B both send their children to public school, family B places a greater value on education than family A. Family C places the greatest relative value on education and sends its child to private school.

a. Graph the budget constraints facing each of the three families and draw a possible indifference curve that could correspond to the choice each family makes.

The town is considering replacing its current system with a voucher system. Under the new system, each family would receive a $6,000 voucher for education, and families would be still be able to send their children to the same public school. Since this would be more costly than the current system, they would also raise taxes to $6,000 per household to pay for it.

b. Draw the budget constraint the families would face under this system.

Suppose that, when the new system is introduced, family A continues to send their child to public school, but family B now send their child to private school (along with family C's child).

c. Explain how you know that family C is made better off and family A is made worse off by the voucher policy.

d. Show, using diagrams, that family B could be made better or worse off by the voucher policy.