Why Price Versus Cost Determines the Result
A competitive firm takes the market price as given. Once its output is chosen, the firm can determine whether that output earns positive economic profit, produces an economic loss, or breaks even. The key comparison is between the market price per unit and the firm’s average total cost at that output.
This comparison is useful because it turns a total-dollar question into a per-unit test. If each unit sells for more than the cost of producing it on average, total revenue exceeds total cost. If the price is lower, total cost exceeds revenue. If price and average total cost are equal, revenue exactly covers total cost.
The word economic matters. Economic cost includes the value of the best alternative use of a firm’s resources, not just expenses paid in cash. Therefore, zero economic profit means that revenue covers all economic costs, including opportunity costs. It does not mean that the owner received no compensation for resources committed to the business.
The classification assumes the firm produces a positive quantity and compares price with average total cost at that quantity. The output must be the firm’s chosen output for the price and cost conditions in the problem. A price–cost comparison at an arbitrary quantity classifies the result at that quantity; it does not establish that the firm would choose to produce it.
The Sign Test
In perfect competition, the firm is a price taker: it sells each unit at the market price. For a given positive output, average total cost is the total economic cost per unit. Comparing these two per-unit amounts identifies the sign of the firm’s total economic profit.
| Comparison at chosen output | Per-unit difference | Economic result |
|---|---|---|
| \(P>ATC\) | \(P-ATC>0\) | Positive economic profit |
| \(P=ATC\) | \(P-ATC=0\) | Break-even: zero economic profit |
| \(P<ATC\) | \(P-ATC<0\) | Economic loss: negative economic profit |
The per-unit difference is not itself total profit. It must be multiplied by the number of units produced. For example, if the firm earns $3 more than average total cost per unit and produces 100 units, its economic profit is $300. A small per-unit difference can add up to a substantial total result when output is large.
Why the Comparison Works
The result follows directly from the definitions of revenue and average total cost. For a competitive firm, selling \(q\) units at price \(P\) produces revenue \(Pq\). Since average total cost is total cost divided by output, total cost can be written as output multiplied by average total cost. Subtracting total cost from revenue gives the profit formula.
Because the firm is producing a positive quantity, \(q>0\). Multiplication by a positive number does not change the sign of a value. Therefore, the sign of \(\pi\) is the sign of \(P-ATC\). This establishes the three-way classification without requiring total revenue and total cost to be calculated separately, although those totals are a useful check.
Worked Applications
Worked Example: Positive Economic Profit From Cost Data
A price-taking greenhouse has already selected its output of 120 trays of seedlings. The market price is $48 per tray. At this output, its fixed economic cost is $1,800 and its variable economic cost is $3,120. Classify the result and calculate the firm’s economic profit.
Method. First add fixed and variable costs to obtain total economic cost. Then divide by output to find average total cost, compare it with price, and calculate total profit.
Step 1: Total economic cost. The two stated costs are $1,800 and $3,120, so \(TC=\$1{,}800+\$3{,}120=\$4{,}920\).
Step 2: Average total cost. Divide total cost by the 120 trays: \(ATC=\$4{,}920/120=\$41\) per tray.
Step 3: Classify. The price is $48 per tray and average total cost is $41 per tray. Since \(\$48>\$41\), the firm earns positive economic profit. The difference is \(\$48-\$41=\$7\) per tray.
Step 4: Calculate and check total profit. Multiply the per-tray difference by output: \(\pi=120\times\$7=\$840\). As a check, total revenue is \(120\times\$48=\$5{,}760\), and revenue minus cost is \(\$5{,}760-\$4{,}920=\$840\). The two methods agree.
The common mistake is to report $7 as the firm’s total profit. It is the profit per tray relative to average total cost; multiplying by 120 gives the total economic profit of $840.
Worked Example: An Economic Loss at the Chosen Output
A small producer of reusable crates has chosen to produce 80 crates. The market price is $30 per crate. Its fixed economic cost at this output is $960, and its variable economic cost is $1,920. Find its average total cost and classify its economic result.
Method. Sum the cost components before dividing by output. Compare the resulting average total cost with the market price, then calculate the total-dollar result.
Step 1: Total economic cost. \(TC=\$960+\$1{,}920=\$2{,}880\).
Step 2: Average total cost. \(ATC=\$2{,}880/80=\$36\) per crate.
Step 3: Compare price and cost. The market price is $30, below the $36 average total cost. The difference is \(P-ATC=\$30-\$36=-\$6\) per crate. Because this difference is negative, the firm has an economic loss at the chosen output.
Step 4: Calculate and check the loss. \(\pi=80\times(-\$6)=-\$480\). Total revenue is \(80\times\$30=\$2{,}400\), and subtracting total cost gives \(\$2{,}400-\$2{,}880=-\$480\). The loss is $480.
A common error is to treat the $1,920 variable cost as total cost and conclude that revenue exceeds cost by $480. That calculation omits the $960 fixed cost. The classification uses average total cost, which includes fixed as well as variable cost.
Worked Example: Break-Even at a Specified Output
A workshop has chosen to produce 75 repair kits. Its fixed economic cost is $900, and its variable economic cost at this output is $3,000. The market price is $52 per kit. Determine whether the workshop earns positive economic profit, makes a loss, or breaks even.
Method. Find total cost and average total cost, then compare the price with average total cost. Confirm the classification by checking total revenue against total cost.
Step 1: Total economic cost. \(TC=\$900+\$3{,}000=\$3{,}900\).
Step 2: Average total cost. \(ATC=\$3{,}900/75=\$52\) per kit.
Step 3: Compare. The market price and average total cost are both $52 per kit. Therefore \(P-ATC=\$0\), and \(\pi=75\times\$0=\$0\). The workshop breaks even in the economic sense.
Step 4: Check using totals. Total revenue is \(75\times\$52=\$3{,}900\). Since total revenue equals total economic cost of $3,900, economic profit is zero.
Break-even does not mean that the workshop produced nothing or had no expenses. It produced 75 kits and received revenue equal to its full economic cost. The common mistake is to interpret zero economic profit as zero revenue; here revenue is $3,900.
Interpretation and Common Traps
The result describes the firm’s economic outcome at its chosen output and the stated market price. A positive result means revenue exceeds total economic cost. A negative result means revenue falls short of total economic cost. Break-even means the two totals are equal. These terms concern economic profit, so opportunity costs are included in the cost comparison.
Use the following sequence to avoid mixing up a per-unit comparison and a total-dollar result:
Use the positive quantity the firm has selected and the market price per unit.
If total economic cost is given, divide it by output. If cost components are given, add them first.
Price above average total cost means positive economic profit; equality means break-even; price below average total cost means an economic loss.
Multiply \(P-ATC\) by output, or subtract total cost from total revenue. Both calculations must give the same result.
Several errors recur in problems of this kind. First, do not compare price with total cost: price is measured in dollars per unit, whereas total cost is measured in dollars. Compare price with average total cost, or compare total revenue with total cost. Second, do not forget to multiply a per-unit difference by output when the question asks for total economic profit. Third, do not omit fixed cost when calculating total cost or average total cost. Finally, do not treat zero economic profit as proof that explicit and opportunity costs are absent; it means revenue covers them.
The classification itself does not determine whether the firm should change its output or stop producing. Those are separate decisions. Here the task is to assess the economic result at the stated chosen output, not to infer an unasked decision from the sign of profit.
Check Your Understanding
For each problem, calculate or compare the relevant costs at the stated positive chosen output, then classify the result. Answers include the essential calculation for checking.
- A maker of ceramic tiles produces 60 tiles at its chosen output. The market price is $27 per tile, and total economic cost is $1,500. Find average total cost and economic profit. (Answer: \(ATC=\$1{,}500/60=\$25\); profit \(=60(\$27-\$25)=\$120\).)
- A firm produces 50 insulated containers. Its fixed economic cost is $400, variable economic cost is $650, and market price is $19 per container. Classify its result and find the total amount. (Answer: \(TC=\$1{,}050\), \(ATC=\$21\); economic loss \(=50(\$19-\$21)=-\$100\).)
- A producer has chosen an output of 90 units and has total economic cost of $3,780 at that output. What price gives break-even, and what is the result if the market price is $42 per unit? (Answer: Break-even price is \(ATC=\$3{,}780/90=\$42\); at $42, economic profit is $0.)
- A firm produces 40 units at a market price of $75 per unit. Its fixed economic cost is $800 and its variable economic cost is $2,400. Calculate average total cost and the total economic result. (Answer: \(TC=\$3{,}200\), \(ATC=\$80\); loss \(=40(\$75-\$80)=-\$200\).)
- A workshop produces 125 units at its chosen output. Fixed economic cost is $1,500, variable economic cost is $3,500, and the market price is $44 per unit. Calculate average total cost, total revenue, and economic profit, and classify the result. (Answer: \(TC=\$5{,}000\), \(ATC=\$40\), revenue \(=125\times\$44=\$5{,}500\), profit \(=\$5{,}500-\$5{,}000=\$500\); positive economic profit.)