uestion 4 Explain how a profit-maximising monopolist would decide what amount of
ID: 1151713 • Letter: U
Question
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)?Explanation / Answer
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.
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