Answer to Question #251958 in Microeconomics for Lisa

Question

1.    The oil is produced by a single refinery (a monopolist) which is owned by an entrepreneur called Sluggo. The demand for oil which is produced in Sluggo's refinery is Q= 50-P. The cost function of the refinery is given as: C(Q)=8+4Q.

It is also known that there is a (constant) marginal external cost of 6$ per unit of oil production resulting from environmental damage associated with production.

(b)  Is the amount you 22 units to maximize profits socially desirable level of output? Why or why not?

(c)  If your answer to (b) is no, what is the socially desirable level of output?

(d)  If the government decides to use corrective tax to force Sluggo to produce the socially desirable level of output, how much will Sluggo's tax bill be?

(e)If the government chooses to subsidize Sluggo for each unit that he does not produce, how much subsidy should be given to Sluggo?

Answer 1

a)

Profit maximization

Marginal benefit=marginal cost

$P=MC\\Q=50-P\\P=50-Q\\MC=\frac{dC(Q)}{dQ}\\\frac{d}{d(Q)}(8+4Q)\\MC=4\\50-Q=4\\Q=46$

b.

The output is not socially desirable.This is because it does not take into account marginal external cost. Of $ 6.

c.

$P=MSC$

MSc=social marginal cost =marginal cost +marginal external cost

$=4+6=10$

$p=MSC\\50-Q=10\\Q=40$

d.

Tax=10-4=$6

e.

$Tax=10+4=\$14$