Muddy Manufacturing finds it convenient to discharge some of its waste into near
ID: 1189746 • Letter: M
Question
Muddy Manufacturing finds it convenient to discharge some of its waste into nearby Crystal River, upstream from the town of Midville. Authorities in Midville estimate that each pound of waste costs the town $5.50 in terms of purification at the water plant, damage to fisheries, pollution of beaches, etc. They have asked Muddy to reduce emissions, but so far Muddy has not complied. Engineers at Muddy estimate that the company’s profits are increased as more waste is dumped into the river, as follows:
Pounds of Waste Emitted per Minute
Total Cost Savings per Minute
1
$10
2
19
3
27
4
34
5
40
6
45
7
49
8
52
9
54
10
55
11
55
How much waste does Muddy dump into Crystal River each minute?
From a social point of view, what is the optimal amount of waste emission?
What tax on Muddy’s emissions would lead it to produce the optimal emissions?
If the government found a subsidy more politically palatable, how much would it have to pay Muddy to convince the firm agree to discharge at the socially optimal level?
Pounds of Waste Emitted per Minute
Total Cost Savings per Minute
1
$10
2
19
3
27
4
34
5
40
6
45
7
49
8
52
9
54
10
55
11
55
Explanation / Answer
Muddy will dump 10 pounds of waste because after 10 pounds muddy is not getting any benefit. Socially optimal amount will be where maginal cost is equal to marginal emission. here marginal cost > marginal saving at 6 pounds. So socially optimal amount will be 5 pounds.
A tax of $5 per pound of emission will make muddy produce optimal emissions because after producing 5th unit of waste the marginal benefit is zero.
A subsidy of ($55-$40)/(10-5) = $3 will agree Muddy to discharge waste at socially optimal level
Pounds of emission Total Saving(TS) Tax Total tax TS-Tax Marginal saving after Tax Marginal Saving Marginal cost of pollution Total cost of pollution TS-TC 1 10 5 5 5 5.5 5.5 4.5 2 19 5 10 9 4 9 5.5 11 8 3 27 5 15 12 3 8 5.5 16.5 10.5 4 34 5 20 14 2 7 5.5 22 12 5 40 5 25 15 1 6 5.5 27.5 12.5 6 45 5 30 15 0 5 5.5 33 12 7 49 5 35 14 -1 4 5.5 38.5 10.5 8 52 5 40 12 -2 3 5.5 44 8 9 54 5 45 9 -3 2 5.5 49.5 4.5 10 55 5 50 5 -4 1 5.5 55 0 11 55 5 55 0 -5 0 5.5 60.5 -5.5Related Questions
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