3-7. A monopolist is seeking to price discriminate by segregating the market. Th
ID: 1119460 • Letter: 3
Question
3-7.
A monopolist is seeking to price discriminate by segregating the market. The demand in each market is given as follows:
Market A: P = 148 - 2Q
Market B: P = 176 - 4Q
The monopolist faces a marginal cost of $28 and has no fixed costs. Given this information, what is the difference between the total quantity the price-discriminating monopolist will supply across both markets and the total quantity that would be supplied in a perfectly competitive market with the same marginal costs for firms at equilibrium?
Round your answer to two decimal places. Do not include a $ sign. Your answer should be a positive number.
Note: The demand equations presented above show P equal to a function of Q, rather than the usual other way around. This is so you can use the same trick used in Unit 11 to find the marginal revenue curve.
Explanation / Answer
Under price discriminating monompoly
at equlibrium MR1 = MR2 = MC
Market A
P = 148 - 2Q
MR = 148 - 4Q
MR = MC
148 - 4Q = 28
148 - 28 = 4Q
120 = 4Q
Q = 30
P = 148 - 2Q
= 148 - 2(30)
= 148 - 60
= 88
Market B
P = 176 - 4Q
MR = 176 - 8Q
MR = MC
176 - 8Q = 28
176 - 28 = 8Q
148 = 8Q
Q = 18.5
P = 176 - 4(18.5)
= 176 - 74
= 102
Total quantiy thant monopoly will supply across the market = QA + QB
= 30 + 18.5
= 48.5
Perfect competition
market A
P = MC
P = 148 - 2Q
148 - 2Q = 28
148 - 28 = 2Q
120 = 2Q
Q = 60
Market B
P = MC
176 - 4Q = 28
176 - 28 = 4Q
148 = 4Q
Q = 37
So total quantity under perfect competition = 60 + 37
= 97
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