Question

Question : A monopoly market structure firm is facing the following demand curve Q = 1800 - 25P. Its short-run total cost is given by :100+7Q+0.025Q2. Find the following for this firm:

a. His profit maximizing quantity, price and TR?

b. If this firm want to incur an average selling cost of Rs 33 per unit will the firm face below, above or just normal profits?

Answer 1

a)

Q = 1800 - 25P

25P = 1800 - Q  

P = 72 - 0.04Q

MR = 72 - 0.08Q

TC = 100 + 7Q + 0.025Q²

MC = 7 + 0.05Q

MR = MC

72 - 0.08Q = 7 + 0.05Q  

72 -7 = 0.05Q + 0.08Q

65 = 0.13Q

Q = 65/0.13

Q = 500

P = 72 - 0.04Q

P = 72 - 0.04(500)

P = 72 - 20  

P = 52

So profit maximising quantity is Q = 500 and price is P = 52

TR = PQ = 52500 = 26,000

b)

Profit = TR - TC  

= PQ - ATCQ  

= (P - ATC)Q

Since Q > 0 so the expression (P - ATC) determines whether firm makes normal profits, above normal profits and below normal profits.

If P > ATC , firm makes profits above normal profits

If P = ATC , firm makes just normal profits

P < ATC , firms makes profits below normal profits

Now firm wants to incur ATC is 33 and profit maximising price is 52

Clearly P > ATC therefore firm will be making or earning profits above normal profits