Shutdown Rule vs Exit: When a Firm Should Shut Down

A fishing boat loses money every single week. Yet every morning, it still heads out to sea. Why would anyone keep working at a loss? And when should the boat stay tied up instead? This is Module 3.6, firms' entry and exit decisions.

Meet the boat. It's one of hundreds selling the same fish at the same dock, so it takes the dock price as given: it's a price taker. Some of its costs are fixed: the boat loan and the dock fee. It owes them every week, even if it never leaves the dock. Other costs are variable: fuel, ice and the crew's pay. They grow with every crate caught. That's the key: in the short run, shutting down wipes out variable cost, but never fixed cost.

On the boat's graph: marginal cost, MC, and two U-shaped averages, AVC and ATC. MC passes through the lowest point of each. AVC bottoms out at $30 a crate, at 40 crates a week.

Last season, fish sold high and the boat made a profit. Now the dock price falls to $41 a crate.

Quick refresher from Module 3.5: produce where marginal revenue equals marginal cost. For a price taker, marginal revenue is the price. MC reaches $41 at 50 crates, so 50 is the best the boat can do.

At 50 crates, ATC is $48 and AVC is $31.

Quick refresher from Module 3.4: economic profit is price minus ATC, times quantity. $41 minus $48 is negative $7 a crate, times 50 crates: negative $350 a week.

The other choice is to stay in port. Then the boat sells nothing, but it still owes its fixed cost.

Quick refresher from Module 3.2: total fixed cost is ATC minus AVC, times quantity. $48 minus $31 is $17 a crate, times 50: $850 a week.

So fishing loses $350 a week, and staying in port loses $850. That answers the opening question: fishing loses less. Here's why it works. Total revenue is price times quantity: $41 times 50 is $2,050. Total variable cost is AVC times quantity: $31 times 50, or $1,550. Revenue pays every fuel bill and every crew wage, with $500 left over toward the $850 of fixed cost.

So what just happened at $41? One: fishing lost $350. Two: staying in port would lose the whole $850 fixed cost. Three: revenue beat variable cost by $500, so the boat keeps fishing.

That's the short-run rule: compare price with average variable cost, or total revenue with total variable cost. If price covers AVC, produce. If price is below AVC, shut down and produce zero. Exam trap: the short-run test uses AVC, not ATC. Price below ATC means a loss, not a shutdown. At $41, price was $7 below ATC, and fishing was still the right call.

Now the price crashes to $25, below the lowest point of AVC, $30. If the boat fished anyway, its best output would be 30 crates, where MC equals the new $25 price. There, AVC is $31: each crate sells for $25 but costs $31 in fuel, ice and pay. That's $6 short on every crate, times 30 crates: $180 lost on top of the fixed cost. Fishing would lose $850 plus $180, or $1,030. Port loses $850. Tie up the boat.

So what just happened at $25? One: price fell below the lowest AVC. Two: each crate fell $6 short of its variable cost. Three: fishing would lose $1,030 and port only $850, so the boat shuts down.

Now slide the price line down the graph. Above the bottom of ATC: profit. At $41, between the two bottoms: a loss, but keep fishing. At $25, below the bottom of AVC: shut down. The price at the bottom of AVC, $30, is called the shut-down price. At any price at or above $30, the boat produces where MC equals price. So its short-run supply curve is its MC curve at and above minimum AVC. Below $30, it supplies zero.

So what just happened on the graph? One: above the bottom of ATC, profit. Two: between the bottoms, a loss, but keep producing. Three: $30, the lowest AVC, is the shut-down price; at or above it, supply follows MC, and below it, output is zero.

That's the short run. In the long run, the boat can be sold and the loan paid off, so no cost is fixed. With no barriers to entry or exit, firms leave a market when they expect economic losses, and enter one where they can earn economic profit. Say the dock price stays at $41, below the bottom of ATC. Every boat keeps losing money, so some owners sell up and exit.

Quick refresher from Unit 2: a change in the number of sellers shifts the whole market supply curve. A change in the good's own price only moves along it.

So on the market graph, fewer boats shift supply left, from S1 to S2. Read the new equilibrium where S2 crosses demand: a higher price, P2, and a smaller quantity, Q2. Exit stops when the price has risen enough that the boats still fishing earn zero economic profit, a normal profit. Module 3.7 shows that point.

Now flip it. If the dock price stays above the bottom of ATC, boats earn economic profit, and that attracts new boats. More sellers shift market supply right. The price falls, and entry stops when economic profit is back to zero.

So what just happened? It's the four-step chain the exam wants. One: the price sets profit or loss. Two: profit brings entry, and losses bring exit. Three: the number of firms shifts market supply. Four: supply moves the price.

Exam trap: in the long run, shift market supply, not demand. Exit doesn't make buyers want more fish. On a recent long question, shifting demand was the most common error. Exam trap: firms enter because of economic profit. Answers that said demand went up, or revenue went up, missed the point. And firms don't enter and then exit: entry just stops once the profit is gone.

Exam moment: two questions the way the AP exam asks them, then one free-response part.

Question 1. A perfectly competitive pallet maker's best output, if it operates, is 80 pallets a day, where price equals marginal cost. There, ATC is $33, AVC is $27, and the price is $24. If it shuts down instead, how much smaller is its daily loss? A) $2,160 B) $1,920 C) $720 D) $480 E) $240

The answer is E. Operating loses ($33 − $24) × 80, or $720. Shutting down loses only the fixed cost, ($33 − $27) × 80, or $480. The difference is $240. Option A: the variable cost it avoids, forgetting the revenue it gives up. B is that lost revenue. C is the operating loss, and D is the fixed cost: each stops one step early.

Question 2. Firms in the perfectly competitive firewood market are earning positive economic profit, and nothing blocks entry or exit. Which describes the move to long-run equilibrium? A) Firms exit, market supply decreases, price rises. B) Firms enter, market demand decreases, price falls. C) Firms enter, market supply increases, price falls. D) Firms enter, market supply decreases, price rises. E) Demand increases, firms enter, price rises.

The answer is C. Profit attracts new firms, more sellers shift market supply right, and the price falls until economic profit is gone. B shifts demand instead of supply, the trap from earlier. E gives demand as the reason, but firms enter because of profit. D shifts supply the wrong way, and in option A, firms flee a profit.

Free response. Brightwater Farm, a typical firm in a perfectly competitive egg market, is earning negative economic profit. As the market adjusts to long-run equilibrium, what will happen to the market price? Explain.

To earn the point: the price will increase. Because of the losses, some firms exit the market. Fewer firms means market supply decreases, shifting left, so the equilibrium price rises. The costly mistake: writing that firms exit and stopping there, or saying exit raises demand. On a recent AP exam, fewer than three students in ten earned this point. Name the decrease in supply every time.

So what just earned the point? One: say the price rises. Two: losses cause some firms to exit. Three: exit decreases market supply, so the equilibrium price rises.

Recap: in the short run, produce if price covers AVC, since fixed cost is owed either way. In the long run, losses bring exit, profit brings entry, and the supply shift moves the price. Next: Module 3.7, Perfect Competition.