Suppose a monopolist practices price discrimination in selling his product, char
ID: 1147622 • Letter: S
Question
Suppose a monopolist practices price discrimination in selling his product, charging different prices in two separate markets. In the market A the demand function is PA = 100-qA and in B it is PB = 84-qB, where qA and qB are the quantities sold per week of A and B, PA and PB are the respective prices per unit . If the cost function of the monopolist is c = 600 + 4 (qA + qB)
A.How much should be sold in each market to maximize the benefit?
B. What selling prices give the maximum benefit? Find the maximum benefit.
Explanation / Answer
A)
PA = 100 -Q
TR = 100Q - Q ^2
On differentiating TR
MR = 100 - 2Q
TC = 600 +4(QA+QB)
On differentiating TC
MC = 4
Equilibrium MR=MC
100 -2Q =4
96 = 2Q
Q = 96/2
= 48
Profit maximizing Q for market A = 48
Market B:
PB = 84-Q
TR = 84Q - Q^2
MR = 84 - 2Q
MR = MC
84 - 2Q = 4
Q = 40
Profit maximizing Q of B = 40
B)
Selling Price of Market A = 84 - 48
=$52
Selling Price of Market B = 84 - 40
= $ 44
Profit = TR - TC ( TC = 600 +4(QA+QB)
=48*52 +44*40 - 600 - 4*88
=2496+1766 - 600 -352
=$3310
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