Slipshod Plastics Corp. produces both plastic materials and water pollution. Sup

Question

Slipshod Plastics Corp. produces both plastic materials and water pollution. Suppose that Slipshod currently produces 40 gallons per minute of polluted water. Company officials estimate that the cost of reducing pollution is C(Q)-20Q, + ½ , where Q, is measured in gallons of polluted water abated per minute. Health officials estimate that the benefits of reducing emissions from Slipshod are: B(Q,) = 800,- a. Find the optimal level of abatement, and the level of remaining pollution. b. What level of tax per unit on pollution yields an efficient outcome? c. Imagine now that Slipshod Plastics can eliminate its pollution entirely by installing a filter. This 10. filter costs $800. Is it efficient to install the filter?

Explanation / Answer

a)

C = 20Q + (1/2)Q^2

On differentiating

MCa = 20 + 2Q

B=80Q-Q^2

MB = 80 -2Q

Equilbrium

MB=MC

80-2Q =20+Q

3Q = 60

Q = 60/3

=20

b)

Cost of abatement = 20(20) +(1/2) (20)^2

                              =400 +200

                              =600

Cost of abtement when output level is 40 Gallons:

=20(40) + (1/2)*(40)^2

=800 +800

=1600

Pollution reduction cost when 40, is 1600 while efficient level cost is 600,

thus, tax should be 1,000

c)

Cost of installing filter is less than cost of externalities, thus it would be efficient to install filter.

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