uestion 4 Explain how a profitmaximising monopolist would de

uestion 4 Explain how a profit-maximising monopolist would decide what amount of product to sell. If a monopolist is pricing to maximise profit and has a price-cost margin of 45 percent, what is the elasticity of demand at that price? A monopolist has the total cost function C- 40 and marginal cost is MC-sQ. It faces the demand curve P 1,400-Q i. What is the profit-maximizing price and output? ii. What is the total profit? iiWhat price ceiling would maximise total surplus (consumer surplus plus producer ?? surplus)?

Solution

4.

A.

A monopolist identifies an output level at that, marginal cost equals marginal revenue. At his level of output, profit is maximized.

So, for a monopolist,

MR = MC to maximize the profit and at this point, the output is produced to sell by the monopolist.

B.

(P-MC)/P = 1/-E

Here, P = MC*1.45

Then,

(1.45MC – MC)/1.45MC = 1/-E

E = -(1.45/.45)

E = -3.22

C.

1.

P = 1400-Q

Multiply by Q to the both sides of above equation and differentiation w.r.t. Q, will give MR.

MR = d(P*Q)/dQ = 1400-2Q

For profit maximizing output,

MR = MC

1400-2Q = 8Q

Q = 1400/10

Q = 140 unit

Price = 1400-140

Price = $1260

2.

Total profit = revenue – cost = P*Q – 4Q^2

Total profit = 1260*140 – 4*140^2

Total profit = 98000

3.

For maximum social welfare,

MC = Price

8Q = 1400-Q

Q = 1400/9

Q = 155.56

Price = 1400 – 155.56 = $1244.44 or $1244

At this price, level, social welfare will be maximized.