A price taker (Perfect Competition and Price Takers) can't choose its price, only its quantity. The marginal rule from Marginal Benefit, Marginal Cost and Sunk Costs, with the cost curves from How Marginal and Average Costs Relate, tells it how much to make.
Key idea
To maximize profit, produce every unit whose marginal revenue is at least its marginal cost, and stop where $MR = MC$ (on the rising part of MC). For a price taker $MR = P$, so the rule is $P = MC$.
Why it works
Each unit changes profit by $MR - MC$. If a unit brings in more than it costs, making it adds to profit; if it costs more than it brings in, it subtracts. So profit grows until the last unit where $MR \ge MC$ and shrinks after. That point is not where revenue is largest (revenue keeps rising as long as you sell more) and not where profit per unit is largest (that's at the bottom of ATC).
| q | TC | MC | TR at \$28 | Profit |
|---|---|---|---|---|
| 0 | \$30 | \$0 | −\$30 | |
| 1 | \$50 | \$20 | \$28 | −\$22 |
| 2 | \$62 | \$12 | \$56 | −\$6 |
| 3 | \$72 | \$10 | \$84 | \$12 |
| 4 | \$84 | \$12 | \$112 | \$28 |
| 5 | \$110 | \$26 | \$140 | \$30 |
| 6 | \$144 | \$34 | \$168 | \$24 |
Worked example: Using MR = MC
Using the table, how many units should the firm produce at a price of \$28?
- Compare MR = \$28 with each unit's MC: units 1 to 5 cost \$20, \$12, \$10, \$12 and \$26, all below \$28.
- Unit 6 costs \$34, more than the \$28 it brings in.
- Produce 5 units. Profit: $\$140 - \$110 = \$30$, the largest in the table.
Answer: 5 units, for a profit of \$30.
Worked example: Not the most revenue, not the most per unit
At 6 units revenue is highest (\$168). At 4 units, profit per unit ($P - ATC = \$28 - \$21$) is highest. Why choose 5?
- At 6 units, revenue rises \$28 but cost rises \$34: profit falls by \$6.
- At 4 units, the 5th unit would add \$28 of revenue for \$26 of cost: \$2 of profit left on the table.
Answer: Total profit, not revenue or profit per unit, is the goal; MR = MC finds it.
Common mistake
Picking the output with the highest total revenue or the highest profit per unit instead of the one where $MR = MC$. Check: for the quantity you picked, the next unit's MC should be above the price, and the last unit's MC at or below it.