Why a Firm Might Shut Down Temporarily
A firm can face a short-run choice between continuing production and suspending it. Suspending production does not necessarily end the business or cancel every bill. In the short run, some costs remain payable even when output is zero. The relevant question is therefore not simply whether the firm is making a profit: it is whether producing generates enough revenue to cover the costs that would be avoided by shutting down.
This distinction matters whenever an operating plan earns less than its full accounting cost. A firm may still prefer to operate if its revenue covers the costs that production adds, even though it cannot cover all of its fixed commitments. Conversely, if operating revenue does not cover the avoidable costs of production, continuing to produce makes the short-run outcome worse than suspending output.
The Shutdown Rule
Let \(Q>0\) be a proposed output level, \(TR(Q)\) the total revenue earned at that output, and \(AVC_T(Q)\) the total variable cost that the firm can avoid by shutting down instead of producing \(Q\). The subscript \(T\) emphasizes that this is a total dollar amount, not a per-unit average. The firm should operate at that plan rather than shut down when the revenue it earns covers the avoidable variable cost.
The same test can be expressed per unit. Define average revenue as \(AR(Q)=TR(Q)/Q\), and define average variable cost as \(AVC(Q)=AVC_T(Q)/Q\). Since \(Q>0\), dividing both sides of the total-revenue comparison by \(Q\) preserves the inequality.
Thus, average variable cost is the per-unit threshold for the proposed output: compare the revenue earned per unit with the avoidable variable cost per unit. If the firm receives a common price \(P\) for each unit sold, then \(TR(Q)=PQ\), so \(AR(Q)=P\). In that case, the comparison is \(P\) versus \(AVC(Q)\). This price form assumes the firm sells its output at that common price; the total-revenue form applies more generally.
Why Fixed Costs Do Not Set the Shutdown Threshold
The rule follows from comparing the two choices for the same short-run period. If the firm shuts down, it earns no production revenue and avoids the variable costs that production would have required. If it operates, it earns revenue and incurs those avoidable variable costs. Any cost that is payable under either choice does not change the difference between the choices.
Compare producing the proposed \(Q\) units with producing zero units during the same period.
Operating brings in \(TR(Q)\) and requires the variable costs avoidable by shutting down. Costs payable either way are unchanged.
Operating is preferable on this shutdown test when \(TR(Q)-AVC_T(Q)\) is nonnegative. If it is negative, shutdown avoids more variable cost than the revenue the firm would earn.
This is a short-run test, not a claim that the firm is profitable overall. It assumes the firm can suspend output for the period, that the identified variable costs really are avoidable by doing so, and that the revenue and cost figures refer to the same period and output plan. If a supposedly variable payment must still be made during shutdown, it is not avoidable for this decision. Likewise, if shutting down triggers an additional cost, that cost must be included in the comparison when it is relevant.
Worked Example: Revenue Covers Avoidable Variable Cost
A hypothetical parts producer is considering making 500 units this month. Each unit will sell for $24. The variable costs per unit are $7 for materials, $5 for production labor, and $2 for energy. A $6,200 facility lease is payable this month whether the firm operates or temporarily shuts down. Should it produce under the shutdown rule?
Method. Compute total revenue and the variable costs avoided if production stops. Do not include the lease in the avoidable-cost total because the firm owes it under either choice.
Step 1: Total revenue. The firm sells 500 units at $24 each: \(TR=500\times \$24=\$12{,}000\).
Step 2: Variable cost per unit. Add the three variable-cost components: \(\$7+\$5+\$2=\$14\) per unit.
Step 3: Total avoidable variable cost. \(AVC_T=500\times \$14=\$7{,}000\). The per-unit average variable cost is \(AVC=\$7{,}000/500=\$14\), while average revenue is \(AR=\$12{,}000/500=\$24\).
Step 4: Apply the test. Since \(\$12{,}000>\$7{,}000\), revenue covers avoidable variable cost. Equivalently, \(\$24>\$14\) per unit. The firm should produce under this rule. The $6,200 lease does not reverse the shutdown comparison because it remains payable if the firm stops producing.
Check and common mistake avoided. The total-revenue and per-unit comparisons agree: \(12{,}000-7{,}000=\$5{,}000\), and \(24-14=\$10\) per unit over 500 units. Comparing revenue with the lease plus variable costs would incorrectly treat an unavoidable commitment as a cost saved by shutdown.
Read Cost Data Carefully
Cost information may be presented as a per-unit amount, a total for the chosen output, or a list of cost items. Keep the units straight before applying the rule. Total revenue must be compared with total avoidable variable cost; average revenue must be compared with average variable cost. Comparing a total with a per-unit amount has no economic meaning.
| Comparison | Correct shutdown test | Common incorrect comparison |
|---|---|---|
| Total amounts | Total revenue versus total avoidable variable cost | Total revenue versus average variable cost |
| Per-unit amounts | Average revenue versus average variable cost | Average revenue versus total variable cost |
| Fixed commitments | Include only if shutdown actually avoids them | Automatically add every fixed cost to the shutdown threshold |
Worked Example: Average Variable Cost Is the Relevant Threshold
A hypothetical ice producer plans to sell 240 cases during a short operating period. Expected revenue is $4,080. Variable costs are $5.50 per case for packaging, $4.00 for inputs, and $3.00 for hourly production labor. A $5,400 facility charge is unavoidable during the period. Should the producer operate?
Method. First convert the variable-cost components into a per-case amount, then calculate total variable cost. Compare like units, and use the facility charge only if it would be avoided by shutdown.
Step 1: Variable cost per case. \(\$5.50+\$4.00+\$3.00=\$12.50\).
Step 2: Total avoidable variable cost. \(AVC_T=240\times \$12.50=\$3{,}000\).
Step 3: Calculate average revenue. \(AR=\$4{,}080/240=\$17.00\) per case.
Step 4: Compare. Average revenue of $17.00 exceeds average variable cost of $12.50. The totals confirm the same result: \(\$4{,}080>\$3{,}000\), a difference of $1,080. The producer should operate under the shutdown rule.
Check and common mistake avoided. If one incorrectly compares revenue with variable cost plus the unavoidable facility charge, the calculation is \(\$4{,}080-(\$3{,}000+\$5{,}400)=-\$4{,}320\), which does not answer the shutdown question. The $5,400 charge does not disappear when production stops, so it is not part of the avoidable variable cost threshold.
Worked Example: Total Revenue Below Avoidable Variable Cost
A hypothetical seasonal workshop has a proposed order of 150 units. The order will generate $2,850 in total revenue. If the workshop produces it, it must pay $950 for materials, $1,100 for hourly labor, and $500 for energy. All three amounts are avoided if production is suspended. A separate insurance payment is due either way. Should the workshop fill the order under the short-run shutdown rule?
Method. Add only the costs that the workshop can avoid by not producing, and compare their total with the order’s revenue.
Step 1: Total avoidable variable cost. \(\$950+\$1{,}100+\$500=\$2{,}550\).
Step 2: Revenue comparison. The order generates $2,850, so \(\$2{,}850-\$2{,}550=\$300\). Revenue exceeds avoidable variable cost by $300.
Step 3: Per-unit check. Average revenue is \(\$2{,}850/150=\$19.00\) per unit. Average variable cost is \(\$2{,}550/150=\$17.00\) per unit. The per-unit comparison also supports operating.
Decision and check. The workshop should fill the order under this test because it brings in $300 more than the costs avoided by shutdown. The insurance payment is excluded because it remains due either way. A common error is to see that the order does not cover every bill and conclude that shutdown is automatically better; the shutdown rule asks whether it covers the avoidable production cost, not every cost of the business.
Common Exam Traps
- Using total cost instead of avoidable variable cost. The shutdown test is not a comparison of revenue with every cost the firm records. Identify what changes if output becomes zero.
- Mixing totals and averages. Compare total revenue with total avoidable variable cost, or average revenue with average variable cost. Do not compare values with different units.
- Assuming every cost called “fixed” or “variable” is automatically treated one way. The decisive issue is whether the payment is avoided by shutting down for the period. Apply the facts of the scenario.
- Confusing shutdown with long-run exit. The rule concerns a temporary short-run suspension when some obligations may remain. It does not decide whether the firm should leave the market permanently.
- Testing an arbitrary output without checking the plan. The comparison applies to a proposed operating output. If several operating plans are available, compare the revenue and avoidable variable costs for each relevant plan before making the decision.
The shutdown rule is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus. Its practical value is the discipline of separating costs that change with the operating decision from costs that do not. That distinction prevents a firm from shutting down solely because it cannot cover all its fixed commitments, or from continuing production when revenue fails to cover the costs the firm could avoid.
Check Your Understanding
For each problem, use the stated short-run facts and compare like units.
- A hypothetical printer considers producing 100 posters at $15 each. Avoidable variable cost is $12 per poster. Find total revenue and total avoidable variable cost, then state whether it should operate. (Answer: Revenue is $1,500 and avoidable variable cost is $1,200; operate.)
- A hypothetical greenhouse has a proposed output of 80 trays and total revenue of $1,760. Its avoidable variable cost is $23 per tray. A lease payment remains due under shutdown. Should it operate? (Answer: Avoidable variable cost is \(80\times \$23=\$1,840\), greater than revenue; shut down.)
- A hypothetical food processor expects $5,250 revenue from 300 units. Total avoidable variable cost is $4,800. Calculate average revenue and average variable cost, then apply the rule. (Answer: Average revenue is $17.50 and average variable cost is $16.00; operate.)
- A hypothetical repair shop earns $2,000 from a short-run service plan. It can avoid $1,800 in labor and materials by suspending the plan, but must still pay $900 in rent. Should it operate under the shutdown rule, and why? (Answer: Operate; revenue exceeds avoidable variable cost by $200, and the rent remains payable either way.)
- A hypothetical producer can choose among three operating plans: at 50 units, revenue is $1,450 and avoidable variable cost is $1,300; at 100 units, revenue is $2,700 and avoidable variable cost is $2,500; at 150 units, revenue is $3,900 and avoidable variable cost is $4,200. If these are the only operating plans, which plan gives the largest revenue in excess of avoidable variable cost, and should the producer shut down instead? (Answer: The 50-unit plan gives $150 in excess, the 100-unit plan gives $200, and the 150-unit plan is $300 below cost. Choose 100 units; it gives the largest positive excess, so shutdown is not preferred.)