Three factories are each emitting eight tons of waste into a lake. The state’s p
ID: 1212158 • Letter: T
Question
Three factories are each emitting eight tons of waste into a lake. The state’s pollution authority would like to cut the total emissions by twelve tons. The factories have the following marginal cost of abatement schedules:
Tons Abated
MCA
MCB
MCC
1
$1
$2
$ 8
2
$4
$3
$11
3
$7
$4
$14
4
$10
$5
$17
5
$13
$6
$20
6
$16
$7
$23
7
$19
$8
$26
8
$22
$9
$29
A. One way to reduce emissions by twelve tons would be to have each factory reduce emissions by four tons. What would be the total cost of this? B. What is the lowest cost way of reducing emissions by twelve tons? How much abatement does each factory do and how much does this save over the answer from part A? C. What per ton emission fee would lead to a twelve ton reduction in emissions? D. If twelve tons of emissions permits were sold at auction, how many would each of the three emitters purchase?
C. Unintended consequences are the bane of a policymaker’s existence. Consider the example of early attempts to reduce emissions of sulfur dioxide from coal burning power plants. Because retrofitting older plants with pollution control equipment would have been very expensive, the decision was to apply clean air standards only to new plants (so-called New Source Performance Standards). What was the response of utilities to these regulations?
D. Imagine a production possibilities frontier with stuff (donuts, cigarettes, gasoline, electricity, etc.) on one axis and environment (clean air, clean water, etc.) on the other axis. How will the choice that a society makes about which point on the frontier it chooses today affect the position of the frontier next year?
E. Draw the following externality diagrams.
A. A negative externality resulting from production
B. A positive externality resulting from production
C. A negative externality resulting from consumption
D. A positive externality resulting from consumption
F. Imagine that a company has two plants that make donuts. The marginal cost, per hundred dozen donuts, of each plant is given in the following table:
Quantity
MCA
MCB
1
$ 35
$ 5
2
$ 40
$15
3
$ 50
$25
4
$ 60
$35
5
$ 70
$45
6
$ 80
$55
7
$ 90
$65
8
$100
$75
A. What is the total cost of producing eight hundred dozen donuts by producing four hundred dozen at each plant?
B. What is the lowest cost way to produce eight hundred dozen donuts and how much is saved over your answer from part A?
C. What price per hundred dozen donuts will result in the production of eight hundred dozen donuts by a profit maximizing producer?
D. Holding the marginal cost of making donuts constant, how will the quantity of donuts produced change if the price increases?
E. Holding the price of donuts constant, how will the quantity of donuts produced change if the marginal cost of making donuts falls?
G. Three factories are each emitting eight tons of waste into a lake. The state’s pollution control authority would like to cut the total emissions by nine tons. The factories have the following marginal cost of abatement schedules:
Tons Abated
MCA
MCB
MCC
1
$1
$2
$ 8
2
$4
$3
$11
3
$7
$4
$14
4
$10
$5
$17
5
$13
$6
$20
6
$16
$7
$23
7
$19
$8
$26
8
$22
$9
$29
Explanation / Answer
First question: Involving three factories.
A. Total pollution need to be reduced by 12 tons: 4 tons by each factory. Then the cost of reducing 4 tons pollution by factory A would be (1+4+7+10)=$22
The cost of reducing 4 tons of pollution by factory B would be (2+3+4+5)= $14
Similary for facory C total cost would be (8+11+14+17)= $50
Therefore total cost =( 22+14+50)= $86.
B. It is seen that for factory B pollution abatement cost is lowest, after that for facory A abatement cost is lower. Thus the lowest cost would be if facory B abates maximum pollution that 8 tons and facory A reduces 4 tons of pollution. In that case the cost would be lowest and the lowest cost would be
(2+3+4+5+6+7+8+9+22)= $66
C. To achieve lowest cost facory B reduces 8 tons and factory A reduces 4 tons of pollution but nothing by factory C.
Toatl save would be (86-66)=$20
D. The purchase of pollution permits depend on the price. If the priceis >marginal cost then factory would not buy any pollution permits. Therefore the amount of pollution permit can not be determined without the information about price.