1. Consider a pollution problem involving a paper mill located on a river and a
ID: 2506837 • Letter: 1
Question
1. Consider a pollution problem involving a paper mill located on a river and a commercial
salmon ?shery operating on the same river. The ?shery can operate at one of two
locations: upstream (above the mill) or downstream (in the polluted part of the river).
Pollution lowers pro?ts for the ?shery: without pollution, pro?ts are $300 upstream
and $500 downstream; with pollution, pro?ts are $200 upstream and $100 downstream.
The mill earns $500 in pro?t, and the technology exists for it to build a treatment plant
at the site that completely eliminates the pollution, but at a cost of $200. There are
two possible assignments of property rights: (i) the ?shery has the right to a clean
river and (ii) the mill has the right to pollute the river.
(a) What is the e?cient outcome (the maximum of total joint pro?t)? Speci?cally,
where does the ?shery locate and does the mill build a treatment plant or not?
(b) What are the outcomes under the two di?erent property rights regimes when there
is no possibility of bargaining? What are the pro?ts of the ?shery and mill in
each case?
(c) How does your answer to (b) change when the two ?rms can bargain costlessly?
Explanation / Answer
a. What is the efficient outcome (the maximum of total joint profit)?
There are two operating modes for each of two parties. Consider a matrix with the
individual and aggregate payoffs.
Mill
Pollute Abate
Fishery Upstream Fishery: 200
Mill: 500
Total: 700
Fishery: 300
Mill: 300
Total: 600
Downstream Fishery: 100
Mill: 500
Total: 600
Fishery: 500
Mill: 300
Total: 800
The aggregate profit maximizing outcome is for the mill to abate pollution and the
fishery to operate downstream.
b. What are the outcomes under the two different property rights regimes, when there is
no possibility of bargaining?
Without bargaining:
If right goes to mill: mill pollutes and fishery will operate upstream. Total profit is only
$700.
If right goes to fishery: mill does not pollute. Total profit: $800, allocative efficiency is
attained.
c. How does your answer to (b) change when the two firms can bargain costlessly?
Costless bargaining:
Nothing changes if the right goes to the fishery
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