A monopolist is seeking to price discriminate by segregating the market. The dem
ID: 1120646 • Letter: A
Question
A monopolist is seeking to price discriminate by segregating the market. The demand in each market is given as follows:
Market A: P = 120 - 1Q
Market B: P = 115 - 3Q
The monopolist faces a marginal cost of $21 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 positivenumber.
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
Profit is maximized when MR = MC in each market.
In market A,
Total revenue (TR) = P x Q = 120Q - Q2
Marginal revenue (MR) = dTR / dQ = 120 - 2Q
Equating with MC,
120 - 2Q = 21
2Q = 99
Q = 49.5
In market 2,
Total revenue (TR) = P x Q = 115Q - 3Q2
Marginal revenue (MR) = dTR / dQ = 115 - 6Q
Equating with MC,
115 - 6Q = 21
6Q = 94
Q = 15.67
Total quantity with price discrimination = 49.5 + 15.67 = 65.17
With perfect competition, we first compute market quantity.
In market A: PA = 120 - QA
QA = 120 - PA
In market B: PB = 115 - 3QB
3QB = 115 - PB
QB = (115 - PB) / 3
Market quantity (QM) = QA + QB = 120 - P + (115 - P) / 3 [Since PA = PB = P]
QM = (360 - 3P + 115 - P) / 2
QM = (475 - 4P) / 2
2QM = 475 - 4P
4P = 475 - 2QM
P = 118.75 - 0.5QM
A perfect competitor maximizes profit by equating P and MC.
118.75 - 0.5QM = 21
0.5QM = 97.75
QM = 195.5
Difference in quantity = 195.5 - 65.17 = 130.33