How to Find the Profit-Maximizing Quantity
The profit-maximizing quantity is where marginal revenue equals marginal cost, with marginal cost rising through that point.
The Profit Max Quantity formula
Calculator
Enter the price, the marginal cost of each unit and ATC to get the MR = MC output and the profit there.
A price taker sells every unit at the market price, so marginal revenue equals price.
Marginal cost rises as output grows, which is why the crossing is a profit maximum.
Average total cost at the quantity where MR = MC. It decides profit, not the quantity.
Marginal cost stays at or below the $12 price through unit 5, and the next unit would cost more than it earns.
- Profit at that quantity
- $15
- Profit or loss
- Profit
- Total revenue
- $60
- Total cost
- $45
- Profit per unit (P − ATC)
- $3
Price sits $3 above average total cost on each of 5 units.
Compare price with ATC. The MR = MC rule picks the quantity; ATC decides whether that quantity earns or loses.
Price multiplied by the quantity the MR = MC rule selected.
Average total cost multiplied by that same quantity.
The vertical gap between price and ATC at the chosen output.
How to calculate Profit Max Quantity, step by step
- 1Build the MR column. Find marginal revenue at each output; for a price taker MR equals the market price at every quantity.
- 2Build the MC column. Find the marginal cost of each additional unit from the cost table or the MC curve.
- 3Find where MR meets MC. Produce the largest quantity at which MR is still at least MC, and stop before the first unit whose MC exceeds MR.
- 4Check that MC is rising. The correct output is where MC cuts MR from below; a crossing on a falling MC curve is a profit minimum, not a maximum.
- 5Calculate the profit. Profit = (P − ATC) × Q at that quantity, which is negative if price sits below average total cost.
Worked example: Profit Max Quantity
A perfectly competitive firm faces P = $12, so MR = $12 at every unit. Marginal cost for the first six units is $4, $6, $8, $10, $12, and $15, so MR = MC at the 5th unit and the firm produces 5 units. With ATC of $9 at that output, profit = (12 − 9) × 5 = $15.
Profit Max Quantity questions
What if MR and MC never meet exactly?
Produce the largest quantity where MR is still greater than or equal to MC, since every unit that adds more revenue than cost adds to profit.
Why must marginal cost be rising at the profit-maximizing quantity?
A crossing where MC is still falling marks a profit minimum; only where MC rises through MR does the next unit start costing more than it earns.
Does a monopoly use the same rule?
Yes, every firm produces where MR = MC, but a monopoly then charges the price read off the demand curve above that quantity, which is higher than MR.
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