Calculating profit
Key Idea
- Profit or loss = TR − TC, the surplus of total revenue over total cost.
- Equivalently, profit or loss = (AR − AC) × Q, the per-unit gap multiplied by output.
- AR > AC gives supernormal profit, while AR < AC gives subnormal profit, a loss.
Two calculation routes
- Per unit: take AR − AC to find profit per unit, then multiply by output Q.
- Totals: take TR − TC directly, using TR = P × Q and TC = AC × Q.
- Both routes give the same profit or loss figure, so either can check the other.
Worked example
Example
- A firm sells 100 units at a price of £10 while average cost is £7, so cost is 70% of the price.
- Total revenue is £10 × 100 = £1,000, spread over 100 units.
- So average revenue is £10, matching the price.
- Per unit: AR − AC = £10 − £7 = £3, so supernormal profit = £3 × 100 = £300.
- By totals: TC = £7 × 100 = £700, so profit = £1,000 − £700 = £300, matching the per-unit route.
- If AC instead rises to £12, AR − AC = £10 − £12 = −£2 per unit.
- Subnormal profit (a loss) = −£2 × 100 = −£200, confirmed by TR £1,000 − TC £1,200.
Profit area on a diagram
- Mark the profit-maximising output where MC = MR.
- Draw the rectangle between average revenue and average cost at that output.
- Its area is the supernormal profit if AR > AC, or the loss if AR < AC.
Exam technique
- Use (AR − AC) × Q, and shade the matching rectangle on the diagram.
- Label whether the area is supernormal profit or a loss.
Common Mistake
- Do not stop at the per-unit gap without multiplying by output.
- Total profit is the (AR − AC) gap multiplied by the quantity produced.
Self review
- How is supernormal profit calculated per unit?
- How is it calculated from totals?
- Work out profit when AR is £10, AC is £7 and output is 100.
- Where is the profit or loss area on the diagram?
