The Sunk-Cost Mistake in Shutdown Decisions

Introduction

A firm can make an economic loss and still be better off producing than shutting down. The key is not whether revenue covers every cost recorded for the period. It is whether producing brings in more revenue than the costs the firm can avoid by not producing. In the short run, a cost that has already been committed and cannot be recovered does not change when the firm chooses between those options.

This distinction corrects a tempting but unreliable rule: “Shut down whenever price is below average total cost.” Average total cost includes fixed costs. If those fixed costs must be paid whether the firm operates or temporarily stops production, they do not determine which short-run choice is better. This tutorial focuses on that comparison, including cases where some costs called fixed are in fact avoidable at the shutdown decision.

Definition: A sunk cost is a cost already incurred, or otherwise committed, that cannot be recovered or avoided by changing the current decision. An avoidable cost is a cost the firm will not incur if it chooses the alternative under consideration. “Fixed” describes how a cost varies with output over a specified range; it does not, by itself, establish whether that cost is sunk or avoidable.

Compare the Two Short-Run Choices

Assume a competitive firm takes the market price $P$ as given and is deciding whether to produce during a particular short-run period or to shut down temporarily. For the basic shutdown comparison, suppose shutdown produces no revenue, avoids variable production costs, and does not cancel any fixed cost already committed. Let $F$ be that unavoidable fixed cost, $VC(q)$ the variable cost of producing $q$, and $q>0$ a proposed operating quantity.

Operating profit at that quantity is revenue less variable and fixed cost. Shutdown still leaves the firm responsible for the unavoidable fixed cost. The relevant comparison is therefore not operating profit against zero; it is operating profit against the payoff from shutdown.

\begin{aligned} \pi_{\mathrm{operate}}(q) &= Pq-VC(q)-F,\\ \pi_{\mathrm{shutdown}} &= -F,\\ \pi_{\mathrm{operate}}(q)-\pi_{\mathrm{shutdown}} &=Pq-VC(q). \end{aligned}

The common cost $F$ cancels. For a given positive output, producing is better if revenue exceeds variable cost; if revenue equals variable cost, the firm is indifferent between producing that quantity and shutting down; if revenue is less than variable cost, shutdown is better than producing that quantity. These comparisons say nothing by themselves about whether the firm earns a positive total profit.

Theorem: When the only costs avoided by temporary shutdown are variable production costs, compare the greatest operating contribution $Pq-VC(q)$ available at positive output with zero. Operate if that greatest contribution is positive. Shut down if it is negative. If it equals zero, operating at the maximizing output and shutting down give the same payoff.

For the usual competitive-firm model with positive output choices and an average variable cost curve that has a well-defined minimum, the familiar shutdown condition is stated using price and minimum average variable cost. Since $Pq-VC(q)=q(P-AVC(q))$, a positive-output choice contributes positively when $P>AVC(q)$. Under the usual cost-curve assumptions, the firm shuts down when price is below minimum average variable cost and is indifferent at the minimum. The fixed cost is not part of this short-run cutoff.

AVC(q)=\frac{VC(q)}{q}, \qquad ATC(q)=\frac{VC(q)+F}{q}

Average total cost remains useful for identifying whether the firm earns a profit or a loss at a particular output. If $P<ATC(q)$, operating profit is negative. But if the firm must pay $F$ under either choice, shutdown also produces a loss of $F$. Whether the operating loss is smaller or larger than the shutdown loss depends on the operating contribution $Pq-VC(q)$.

Why the Sunk Cost Drops Out

The result follows by comparing the actual payoffs rather than treating a sunk cost as though it were a fresh expense caused by operating. In both choices, the firm pays the same $F$. Subtracting the shutdown payoff from the operating payoff removes that shared payment, leaving only the revenue and costs that differ between the choices. This is an incremental comparison: a cost that is identical under both alternatives cannot decide between them.

Write each alternative’s payoff.
Include revenue and costs incurred under operation; include costs incurred under shutdown. Keep costs common to both alternatives visible at first.

Subtract shutdown from operation.
Common unavoidable costs cancel. The remaining expression measures how much better or worse operation is than shutdown.

Interpret the sign, including zero.
A positive difference favors operation, a negative difference favors shutdown, and a zero difference means indifference between the two choices.

The conclusion changes if shutting down avoids a cost beyond variable production cost. For example, a firm may be able to cancel an operating permit charge, while shutting down may itself trigger a one-time fee. Those costs belong in the comparison because they differ between the alternatives. The general form makes that explicit.

\begin{aligned} \pi_{\mathrm{operate}}(q)&=Pq-C_O(q)-K,\\ \pi_{\mathrm{shutdown}}&=-C_S-K,\\ \pi_{\mathrm{operate}}(q)-\pi_{\mathrm{shutdown}} &=Pq-C_O(q)+C_S. \end{aligned}

Here $K$ denotes costs that are unavoidable under either choice, $C_O(q)$ denotes costs incurred only if the firm operates, and $C_S$ denotes costs incurred only if it shuts down. The firm should compare the best available operating difference with zero. In the basic model, $C_O(q)=VC(q)$ and $C_S=0$. An avoidable operating charge increases $C_O(q)$; a shutdown fee increases $C_S$ and makes shutdown less attractive.

Worked Applications

Worked Example: Price Below Average Total Cost, but Operation Is Better

A competitive workshop can sell each unit for $18. Its variable cost of producing $q$ units is $VC(q)=q^2$. It has already committed to a nonrefundable short-run facility charge of $180, payable whether it operates or shuts down. Find its best operating quantity, compare the operating and shutdown payoffs, and assess the claim that it must shut down because price is below average total cost.

Method. First maximize operating contribution, which excludes the common $180 charge. Then compare the resulting operating payoff with the shutdown payoff. The facility charge is sunk for this decision because neither choice avoids it.

Operating contribution is $18q-q^2$. Completing the square shows its maximum directly:

18q-q^2=81-(q-9)^2\leq 81

The maximum occurs at $q=9$, giving revenue $18(9)=162$ dollars and variable cost $9^2=81$ dollars. The operating contribution is $162-81=81$ dollars.

At $q=9$, average total cost is $(81+180)/9=261/9=29$ dollars per unit. Thus price, $18, is below average total cost, $29, and operating profit is negative: $162-81-180=-99$ dollars. If the workshop shuts down, it still pays the $180 facility charge, so its payoff is $-180$ dollars. Operation is better by $(-99)-(-180)=81$ dollars.

Check. The payoff difference equals revenue less variable cost: $162-81=81$ dollars. The firm operates despite its loss and despite price being below average total cost. The mistake avoided is treating a loss, or $P<ATC$, as sufficient evidence for shutdown.

Worked Example: Revenue Exactly Equals Variable Cost

A seasonal packaging firm is considering a one-day production run of 8,000 cartons at a market price of $12 per carton. The variable cost of that run is $96,000. A fixed warehouse charge of $70,000 is already committed and cannot be recovered. Compare producing the run with shutting down for the day.

Method. Compare revenue with variable cost, then calculate both payoffs to verify the equality case. The warehouse charge is common to the two alternatives.

Revenue from the run is $8{,}000\times \$12=\$96{,}000$. Its operating contribution is $\$96{,}000-\$96{,}000=\$0$. Operating profit is therefore $\$0-\$70{,}000=-\$70{,}000$. Shutdown also leaves the firm with the warehouse charge, so its payoff is $-\$70{,}000$.

The payoffs are equal. The firm is indifferent between this production run and shutdown; operation does not improve its payoff, but it does not make it worse either. If average total cost at this quantity is calculated, it is $(\$96{,}000+\$70{,}000)/8{,}000=\$20.75$ per carton, above the $12 price. That fact identifies a loss but does not break the tie.

Check. The operating-minus-shutdown difference is $-\$70{,}000-(-\$70{,}000)=\$0$, equal to revenue minus variable cost. The mistake avoided is interpreting “revenue covers variable cost” as a strict improvement when the two are equal.

Worked Example: Include an Avoidable Operating Charge

A small processor can sell 80 batches at $15 per batch. Producing those batches costs $880 in variable inputs. A $250 maintenance contract charge applies only if the processor operates; it can cancel the contract without penalty if it shuts down. A separate $4,000 equipment lease payment is already committed under either choice. Should it operate?

Method. Compare revenue with all costs that operation incurs and shutdown avoids, not just variable cost. Treat the committed lease payment as common to both alternatives.

Revenue is $80\times \$15=\$1{,}200$. Operation incurs $880 of variable cost and the avoidable $250 maintenance charge, so its operating contribution relative to shutdown is $\$1{,}200-\$880-\$250=\$70$. Including the common lease payment, operating profit is $\$1{,}200-\$880-\$250-\$4{,}000=-\$3{,}930$.

If the processor shuts down, it avoids both the variable inputs and the maintenance charge but still pays the committed lease payment. Its payoff is $-\$4{,}000$. Operating is better by $-\$3{,}930-(-\$4{,}000)=\$70$, so it should operate even though its total profit is negative.

Check. The $70 payoff advantage matches the revenue left after both avoidable operating costs. The mistake avoided is applying the basic revenue-versus-variable-cost comparison without checking whether another operating cost can also be avoided by shutdown.

Worked Example: A Sunk Purchase Cost and a Resale Alternative

A firm bought a specialized press for $1,000 in an earlier period. That purchase cannot be refunded. For the current period, operating the press would generate $700 in sales revenue and require $500 in variable cost. If the firm shuts down now, it can sell the press immediately for $250. Ignore all other costs and any later value of the press. Which choice gives the higher current-period payoff?

Method. Exclude the unrecoverable past purchase from the comparison, but count the $250 resale value that shutdown makes available. That resale value is an opportunity cost of operating because the firm gives it up if it keeps using the press.

The current operating contribution before the past purchase is $\$700-\$500=\$200$. Shutdown gives the firm $250 from the sale. Comparing these alternatives, shutdown is better by $\$250-\$200=\$50$.

The same result appears if the past purchase is included in both payoffs. Operating gives $\$700-\$500-\$1{,}000=-\$800$. Shutdown gives $\$250-\$1{,}000=-\$750$. The difference is $-\$750-(-\$800)=\$50$ in favor of shutdown.

Check. The $1,000 purchase cost cancels because it cannot be changed now; the $250 resale proceeds do not cancel because only shutdown earns them. The mistake avoided is either counting the sunk purchase as a new operating cost or ignoring the value of an available alternative.

Common Exam Traps

A frequent wrong calculation is to write “price is below average total cost, so shut down,” without comparing the payoff under shutdown. In the first example, that rule would select shutdown because $\$18<\$29$. But the actual comparison is operating payoff $-\$99$ against shutdown payoff $-\$180$, so shutdown would make the firm worse off by $81. The corrected calculation subtracts only the costs that change between the alternatives.

Do not equate a loss with a reason to shut down. A firm can lose money under both choices and still prefer the smaller loss from operating.
Do not assume every fixed cost is sunk. A fixed charge that can be canceled by shutting down is avoidable and belongs in the comparison.
Do not treat “equal” as “greater.” If revenue equals all costs avoided by shutdown, the operating advantage is zero and the firm is indifferent.
Do not ignore a valuable alternative. Resale proceeds or another payoff available only under shutdown affect the comparison, even though a past purchase price does not.

Key takeaway: For the short-run shutdown decision, compare operation with shutdown—not operating profit with zero. Costs common to both choices cancel. In the basic model, operation improves the firm’s payoff when revenue exceeds variable cost, equality produces indifference, and revenue below variable cost favors shutdown. Include any additional cost or benefit that differs between the alternatives.

Check Your Understanding

For each problem, compare the relevant operating payoff with shutdown. Treat costs described as committed or unrecoverable as unavoidable unless the problem states otherwise.

A print shop can produce 30 batches at $24 per batch. Variable cost is $600, and a $900 short-run rent payment is unavoidable under either choice. Calculate both payoffs and decide whether it should produce. (Answer: Operate; operating payoff is $-\$780$, shutdown payoff is $-\$900$, so operation is better by $120.)
A kiln can produce 40 tiles for revenue of $400. Variable cost for the run is $400, and an unavoidable fixed charge is $250. What is the shutdown comparison? (Answer: Indifferent; operating and shutdown payoffs are both $-\$250$.)
A processor receives $2,100 in revenue from a proposed run, incurs $1,700 in variable cost, and must pay a $300 operating permit charge only if it runs. A $5,000 lease payment is unavoidable either way. Find the better choice and the payoff difference. (Answer: Operate; operating payoff is $-\$4,900$, shutdown payoff is $-\$5,000$, so operation is better by $100.)
A firm can operate an asset for revenue of $700 with variable cost of $500. The asset was purchased for $1,000 in the past and cannot be returned, but it can be sold for $250 if the firm shuts down. Compare the current choices. (Answer: Shut down; operating payoff including the sunk purchase is $-\$800$, while shutdown payoff is $-\$750$, so shutdown is better by $50.)
A competitive firm has variable cost $VC(q)=4q+q^2/10$, a market price of $14, and an unavoidable fixed cost of $800. Find the output that maximizes operating contribution, then compare the best operating payoff with shutdown. (Answer: $q=50$; maximum contribution is $14(50)-[4(50)+50^2/10]=700-450=\$250$, so operating payoff is $-\$550$ versus shutdown payoff $-\$800$; operate, by $250.)

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