Fassbender Widgets, Inc. has opened a new widget factory next to Lake Dunn. In the production of widgets, WWI dumps 5 thousand gallons of a pollutant, red dye #308, into the lake. The pollutant reduces the fish population and results in a loss to those who wish to fish there. The table below shows the total cost of reducing the volume of discharge and the total loss to those who fish at each level of reduction. Assume that it is only possible to reduce the volume of red dye #308 by these fixed amounts.
Reductions in Annual Cost to WWI Annual Loss to
Red Dye #308 of Reducing Discharge Those Who Fish
(1000 gallons) (millions of $) (millions of $)
0 0 20
1 1 16
2 4 12
3 9 8
4 16 4
5 25 0
(a) What is the efficient reduction in the discharge of red dye #308?
(b) As a specialist with the EPA, you must choose between imposing a tax on the discharge and doing nothing. Under what conditions, if any, is each of the proposals appropriate?
(c) Suppose you determine the tax is appropriate. What size tax per 1000 gallons of discharge would you choose?
(d) Suppose you determine that it is better to do nothing. Will the amount of pollution depend on whether WWI has the legal right to dump red dye #308 into the lake or those who fish there have the right to fish in unpolluted water?