Answer to Question #251054 in Microeconomics for Lisa

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?

Answer 1

Solution:

a.). To maximize profits, et MR = MC

First, derive TR:

TR = P $\times$ Q

Find the inverse demand function of the demand function:

Q = 50 – P

P = 50 – Q

TR = (50 – Q)$\times$Q = 50Q – Q²

MR = $\frac{\partial TR} {\partial Q}$ = 50 – 2Q

MR = 50 – 2Q

MR = MC

MC = 6

50 – 2Q = 6

50 – 6 = 2Q

44 = 2Q

Q = 22 units

 

As a profit maximizer, Sluggo should produce 22 units to maximize profits.