IAI Actuarial Core Principles · Business Economics · Profit maximisation under imperfect competition
A monopolistically competitive firm in the short run faces the demand curve P = 100 - 2Q and has a constant marginal cost of Rs 20 per unit. What are its profit-maximising output and price?
The firm produces 20 units at a price of Rs 60. Marginal revenue is 100 - 4Q, and equating it to the marginal cost of Rs 20 gives Q = 20. Substituting into the demand curve gives P = 100 - 2(20) = 60.
- AQ = 20, P = 60Correct
- BQ = 30, P = 40
- CQ = 40, P = 20
- DQ = 20, P = 20
- Q = 25, P = 50
Explanation
Total revenue = 100Q - 2Q^2, so MR = 100 - 4Q. Setting MR = MC gives 100 - 4Q = 20, so Q = 20. Price from demand is 100 - 40 = 60. Q = 40 and P = 20 is the perfectly competitive outcome (P = MC), which is wrong because MR lies below price. Q = 30, P = 40 results from using MR = 100 - 2Q.
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