Managerial Economics A monopolistic firm faces the following demand curve. Q = 7

Question

Managerial Economics

A monopolistic firm faces the following demand curve.
Q = 7800 -12 P  
This monopoly's cost function has been estimated as follows:

TC = 460,000 + 50 Q

a. What price should this monopoly charge to maximize its profit?
b. What would be its equilibrium profit?
c. What price should it charge if it were to maximize its revenue?
d. What would be its profit if it maximized its revenue?
e. If this monopoly were to behave like a competitive firm, what price should it charge and what quantity should it produce?
f. Would this monopolist still make an economic profit if it were to behave like a competitive firm?

g. What is the break-even quantity of this monopoly?

Explanation / Answer

Q = 7800 -12P

12P = 7800-Q

P = 650 – Q/12

TR = P*Q = 650Q – Q2/12

TC = 460,000 + 50Q     

Profits= TR-TC = 650Q – Q2/12 - 460,000 - 50Q

Max profits take first derivative

= 650- Q/6-50

600 - Q/6 = 0

Q/6 = 600

Q = 3600

For Q = 3600, the price will be Q = 7800 -12P

3600 = 7800 -12P

12P = 7800-3600

12P = 4200

P= 350

Profits= 650*3600-36002/12-460000-50*3600

=620000

For revenue maximization

TR = P*Q = 650Q – Q2/12

d(TR)/dQ = 650 –Q/6

650 = Q/6

Q = 3900

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