Suppose a perfectly discriminating monopolist faces market demand: P = 100 – 10Q and marginal cost:...
Suppose a perfectly discriminating monopolist faces market demand: P = 100 – 10Q and marginal cost: MC = 20.
1. How much output does the perfectly discriminating monopolist produce? a. Q = 20 b. Q = 4 c. Q = 8 d. Q = 10 e. Q = 12
2. How much profit does the perfectly discriminating monopolist earn (assume that fixed cost = 0)? a. Profit = $0 b. Profit = $160 c. Profit = $20 d. Profit = $640 e. Profit = $320
Homework Answers
1. c. Q = 8
Under perfect discrimination, price is maximized at the point
where P = MC.
So, 100 - 10Q = 20
So, 10Q = 100 - 20 = 80
So, Q = 80/10 = 8
Thus, Q = 8
(P = 100 - 10Q = 100 - 10(8) = 100 - 80 = 20)
2. e. Profit = $320
Under perfect price discrimination, producer surplus =
profits.
Maximum possible price (When Q = 0) is P = 100
So, Profit = Producer surplus = (1/2)*(maximum P - MC)*(Q) =
(1/2)*(100-20)*(8) = (1/2)*80*8 = $320
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