Two local firms, A and B, are responsible for all of the pollution in Dirty Lake

Question

Two local firms, A and B, are responsible for all of the pollution in Dirty Lake. Currently, firm

A emits 8 tons of noxious pollutants into the lake each year and firm B emits 6 tons for a total of

14 tons of pollutants. The EPA's SuperFund has targeted DirtyLake for clean up. Specifically,

the EPA wants to reduce the total amount of pollutants in Dirty lake by 10 tons per year, i.e.,

reduce the amount of pollutants from the current 14 tons down to only 4 tons. The marginal costs

of clean up for the two polluters are given respectively by:

MCa = 75 + 20Xa and MCb = 125 + 30Xb

where the MCs are the marginal costs of abatement (not emitting) and the Xs are the number of

tons of pollutants eliminated per year. Use this information to answer the following questions:

a. If the EPA simply orders each polluter to eliminate 5 tons of pollutants per year, what

will be the cost -- for each polluter and in total -- of cleaning up DirtyLake?

b. Suppose the EPA were to use an effluents tax approach (a tax on pollution) to clean up

the lake.

i. At what dollar amount per ton of pollutants should the tax be set?

ii. How many tons of pollutants would be eliminated by each polluter and at what

cleanup cost? What would the total cost of the clean up be (don’t include the taxes

since they are a transfer within society)?

iii. How much tax revenue would the EPA collect?

c. Suppose that the EPA decides to auction pollution permits, each allowing the holder to

emit one ton of pollutants into DirtyLake each year. Because it wants to limit the amount

of pollutants to 4 tons, it limits the number of permits to 4. Assume (1) that the auction is

blind; that is, each firm bids once and does not know what the other firm bids and (2) no

firm emits without a permit.

i. What is the most that firms A and B, respectively, would offer for the first

permit auctioned off? Who would buy it?

ii. Do the above analysis for the second, third and fourth permits. How many does

each polluter buy? How much pollution does each eliminate?

iii. What is the cost of the pollution clean up using the permit approach? Exclude

the cost of the permits themselves, since these are just transfers within society.

How does this compare to the total cost of the emissions tax approach?

d. Suppose that, before the permit auction takes place, firm A and firm B convince the

EPA that the most equitable way to allocate the permits is to give each of them 2. If the

two polluters can bargain costlessly, will this equal allocation be stable, or will it be

modified? Explain.

Explanation / Answer

an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent. That is, the consumer has no preference for one combination or bundle of goods over a different combination on the same curve. One can also refer to each point on the indifference curve as rendering the same level of utility (satisfaction) for the consumer. In other words, an indifference curve is the locus of various points showing different combinations of two goods providing equal utility to the consumer. Utility is then a device to represent preferences rather than something from which preferences come.[1] The main use of indifference curves is in the representation of potentially observable demand patterns for individual consumers over commodity bundles.[2]

There are infinitely many indifference curves: one passes through each combination. A collection of (selected) indifference curves, illustrated graphically, is referred to as an indifference map.

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