IAI Actuarial Core Principles · Business Economics · Profit maximisation under imperfect competition
A firm faces the linear demand curve P = 120 - 2Q. At which output is total revenue maximised?
Total revenue is maximised at Q equal to 30. Marginal revenue is 120 minus 4Q, which is zero at 30 units. Beyond that point extra sales reduce total revenue because the price fall outweighs the added volume.
- AQ = 60
- BQ = 15
- CQ = 20
- DQ = 40
- Q = 30Correct
Explanation
TR = 120Q - 2Q^2, so MR = 120 - 4Q. Total revenue is maximised where MR = 0, giving Q = 30. Q = 60 is where price falls to zero, a common error from setting P = 0, and Q = 15 comes from halving wrongly.
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