Once the firm has its quantity from $P = MC$ (Profit-Maximizing Output: MR = MC), the cost curves show its profit as an area. Remember that these are economic profits (Accounting and Economic Profit).
Key idea
$$\text{Profit} = TR - TC = (P - ATC) \times q.$$ On the graph, profit is a rectangle: height $P - ATC$ at the chosen quantity, width $q$. If $P > ATC$ the firm earns a profit; if $P < ATC$, a loss; if $P = ATC$, zero economic profit (it breaks even). The break-even price is the minimum of ATC.
Why it works
Total revenue is $P \times q$ and total cost is $ATC \times q$, because ATC is cost per unit. Subtract, and $q$ factors out: profit per unit times the number of units. The height uses ATC, not MC, because profit counts the cost of every unit, while MC is the cost of only the last one.
Worked example: A profit
A firm sells 8 units at \$30 each. At 8 units its ATC is \$24. Find its profit.
- Profit per unit: $\$30 - \$24 = \$6$.
- Profit: $\$6 \times 8 = \$48$. Check: $TR = \$240$, $TC = \$24 \times 8 = \$192$, difference \$48.
Answer: \$48.
Worked example: A loss
The price falls to \$20. The firm now makes 6 units, where ATC is \$23. Find its profit.
- $P - ATC = \$20 - \$23 = -\$3$ per unit.
- Profit: $-\$3 \times 6 = -\$18$, a loss of \$18.
Answer: A loss of \$18.
A loss doesn't automatically mean the firm should close. Whether it keeps producing in the short run depends on which costs it would still have to pay if it shut down, which is the subject of The Shutdown Rule.
Common mistake
Measuring profit per unit as price minus marginal cost. At the chosen quantity $P = MC$, so that would always give zero. Profit per unit is $P - ATC$. Check: profit must equal $TR - TC$; compute both to confirm.