Finding the profit-maximizing quantity is the central problem in the theory of the firm, and the rule for it — produce where marginal revenue equals marginal cost — sounds simple until you're staring at a cost table. This walkthrough takes you through the MR = MC method step by step, with a worked table and a graph reading, so you can locate the profit-maximizing quantity reliably and explain why it works.
Why MR = MC, Not "Lowest Cost" or "Highest Revenue"
A common first instinct is to produce where average cost is lowest, or where total revenue is highest. Both are wrong, and seeing why makes the real rule stick.
A firm's goal is to maximize profit, which is total revenue minus total cost. Think at the margin — one unit at a time. Producing one more unit adds marginal revenue to revenue and marginal cost to cost.
- If MR > MC, the next unit adds more to revenue than to cost — it raises profit, so make it.
- If MR < MC, the next unit adds more to cost than to revenue — it lowers profit, so don't.
- Profit stops rising and starts falling exactly where MR = MC.
That's the logic: keep producing as long as each extra unit pays for itself, and stop the moment it doesn't. The profit-maximizing quantity is the last unit for which MR is still at least MC.
The Walkthrough: A Worked Table
Take a firm in a competitive market that can sell each unit for a fixed price of $9 — so its marginal revenue is $9 on every unit. Here is its cost schedule:
| Quantity | Total revenue | Total cost | Marginal revenue | Marginal cost | Profit |
|---|---|---|---|---|---|
| 1 | $9 | $10 | $9 | $4 | −$1 |
| 2 | $18 | $15 | $9 | $5 | $3 |
| 3 | $27 | $22 | $9 | $7 | $5 |
| 4 | $36 | $31 | $9 | $9 | $5 |
| 5 | $45 | $43 | $9 | $12 | $2 |
Step 1 — find marginal revenue. In a competitive market MR equals the price, so MR is $9 at every quantity.
Step 2 — find marginal cost. MC is the change in total cost. From unit 2 to 3, total cost rises $22 − $15 = $7, so MC of the third unit is $7.
Step 3 — compare MR and MC unit by unit. Units 1, 2, and 3 all have MR ($9) above MC, so each adds to profit. Unit 4 has MR exactly equal to MC ($9 = $9). Unit 5 has MC ($12) above MR ($9), so it would reduce profit.
Step 4 — pick the quantity. Produce every unit where MR ≥ MC and stop. That's 4 units. Confirm it in the profit column: profit climbs to $5 at quantity 4 and falls to $2 at quantity 5. The MR = MC rule landed on the maximum directly.
Note that the fourth unit added exactly $0 to profit ($9 in, $9 out). That's expected — the MR = MC unit is the break-even unit at the margin. Including it or not doesn't change profit, so by convention you produce it.
Reading It Off a Graph
The same answer appears on the standard cost-curve diagram. Plot the marginal cost curve (rising) and the marginal revenue curve. For a competitive firm, the MR curve is a horizontal line at the price, $9. They intersect at one quantity — drop a vertical line from that intersection to the horizontal axis, and that's the profit-maximizing quantity.
For a monopoly the graph reads slightly differently: marginal revenue slopes downward and sits below the demand curve, so MR = MC still finds the quantity — but you then go up to the demand curve to read the price. The quantity rule is identical; only the price step changes. The full contrast is in the comparison of perfect competition vs. monopoly.
The Check That Tells You Whether to Produce at All
MR = MC finds the best quantity, but it doesn't tell you whether the best quantity earns a profit — it could still be the least-bad loss. Two checks finish the job:
- Profitable? Compare price to average total cost at the chosen quantity. If price > ATC, the firm earns a profit; if price < ATC, it's making a loss even at its best output.
- Shut down? If the firm is losing money, compare price to average variable cost. If price covers AVC, keep producing in the short run — operating at least helps pay fixed costs. If price can't even cover AVC, shut down: producing would lose more than the fixed costs the firm owes anyway.
So the full procedure is two stages: use MR = MC to find the quantity, then use the ATC and AVC comparisons to decide whether to produce that quantity, accept a smaller loss, or shut down.
Conclusion
Finding the profit-maximizing quantity comes down to one rule applied carefully: produce every unit where marginal revenue is at least marginal cost, and stop at the last such unit. In a table, compute MR and MC column by column and find where they cross; on a graph, find where the MR and MC curves intersect. Then check price against average total cost and average variable cost to know whether that quantity actually earns a profit or merely limits a loss.
