Answer to Question #253242 in Microeconomics for Mim

Question

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.

 

(a)  As a profit maximizer how much would Sluggo like to produce?

(b) Is the amount you find in (a) 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)

At maximum profit:

Marginal cost is found by differentiating total cost function w.r.t Q.

$MC=\frac{d(8+4Q)}{d(Q)}$

$MC=4$

The market price $P=MC$

$\implies P=4$

$Q=50-P$

$Q=50-4$

$Q=46$

(b)

The amount found in (a) is not a socially desirable level of output. This is because it does not consider the marginal external cost of $6 that is given.

(c)

At socially desirable level of output:

P= marginal cost+ marginal external cost.

$P=4+6=10$

$\therefore Q= 50-P=50-10=40$

(d)

Tax will be:

$10-4=6$

=$6.

(e)

Subsidy:

$10+4=14$

=$14.