Practice
Profit maximization in perfect competition
Where a price-taking firm sets marginal revenue equal to marginal cost, its profit or loss, and when it shuts down.
The skill
A perfectly competitive firm is a price taker, so its marginal revenue is the market price. Work out marginal cost for each unit from the total cost table, and produce up to the last unit where the price is at least marginal cost. Then check whether to operate at all: in the short run the firm shuts down if the price is below average variable cost, and its loss is then just its fixed cost. Profit is total revenue minus total cost. A common slip is subtracting only variable cost.
A worked example
A firm in a perfectly competitive market can sell as many units as it wants at the market price of $24. Its short-run total cost is shown.
| Output (units) | Total cost ($) |
|---|---|
| 0 | 20 |
| 1 | 31 |
| 2 | 39 |
| 3 | 45 |
| 4 | 58 |
| 5 | 78 |
| 6 | 103 |
| 7 | 133 |
| 8 | 170 |
What is the firm’s economic profit at its best choice in the short run, in dollars? Give a negative number for a loss.
Solution
- Marginal revenue is the price, $24. Marginal cost of each unit: 1st unit: 11, 2nd unit: 8, 3rd unit: 6, 4th unit: 13, 5th unit: 20, 6th unit: 25, 7th unit: 30, 8th unit: 37.
- Marginal cost rises through $24 between unit 5 (MC $20) and unit 6 (MC $25), so MR = MC there: produce 5 if the firm operates.
- At 5 units, total revenue is 24 × 5 = $120, total variable cost is $58, and average variable cost is $11.6.
- The price covers average variable cost, so the firm operates. Profit = 120 − 78 = $42.
Answer: 42