Question

The municipality of a small University town has decided that air pollution in the town and surrounding area should be reduced and is trying to determine the optimal level of reduction. There are benefits from reducing air pollution (better health, and less health care spending etc.), but there are also costs. The municipality estimates that the marginal benefit of each unit of reduction is $1,400 - 5R, where R is units of reduction, and the marginal cost is 2R.                                (3 pts)

a. If the town wants to maximize the net benefit from reducing acid rain, what is the optimal level of pollution reduction?

b. What is marginal cost at the optimal level of reduction?

c. What is the maximum level of net benefits at optimal level of pollution reduction?

Answer 1

a)

Net benefit is maximized when Marginal Benefit is equal to Marginal Cost. So,

Put Marginal Benefit=Marginal Cost

1400-5R=2R

7R=1400

R=200

Optimal level of pollution reduction=200 units

b)

Marginal Cost at optimal level of pollution reduction is given by

Marginal Cost=2R=2*200=$400

c)

Marginal Benefit=MB-MC=1400-5R-2R=1400-7R

Maximum level of net benefit (ONB) is given by

200 ONB=/ (1400 – 7R) * dR

ONB= 1400R - (7/2) R 1200

ONB=[1400*200-(7/2)*200²]-[1400*0-(7/2)0²]=280000-140000=$140000