CFA Level IEconomicsMedium
A monopolist faces the demand curve P = 100 - 2Q and has constant marginal cost of $20. What price and quantity maximize the monopolist's profit?
- AP = $60, Q = 20
- BP = $50, Q = 25
- CP = $70, Q = 15
- DP = $40, Q = 30
Show answer & explanationAnswer & explanation
Correct answer: A. P = $60, Q = 20
Total revenue = PQ = 100Q - 2Q², so MR = 100 - 4Q. Setting MR = MC: 100 - 4Q = 20, so Q = 20. Substituting into demand: P = 100 - 2(20) = $60.
Why the other options are wrong
- B. Does not satisfy MR = MC condition.
- C. Understates quantity; price too high relative to MR=MC solution.
- D. Overstates quantity beyond profit-maximizing level.
Monopoly Profit Maximization
A monopolist maximizes profit where marginal revenue equals marginal cost (MR=MC), then sets price from the demand curve at that quantity.
- MR curve has twice the slope of a linear demand curve
- Monopolist prices above marginal cost (P>MC)
- Output is lower than the competitive equilibrium
Memory trick: Double the slope, halve the output — MR falls twice as fast as demand.