Situation: A hotel in the Algarve during winter. The market price is low, and the hotel is losing money (\(P < ATC\)).

Two options:

. . .

Loss if operating at \(Q^*\) (where \(P = MC\)):

\[\text{Loss}_{\text{operate}} = TC - TR = (FC + VC) - TR\]

Loss if shut down (\(Q = 0\)):

\[\text{Loss}_{\text{shutdown}} = FC\]

Operate if the operating loss is smaller than the shutdown loss:

\[(FC + VC) - TR < FC\]

\[VC - TR < 0\]

\[TR > VC\]

Dividing both sides by \(Q\):

\[\boxed{P > AVC} \quad \Rightarrow \quad \text{Keep operating!}\]

💡 If revenue covers at least the variable costs, operating is less bad than shutting down. The revenue above VC contributes something toward fixed costs.

Recall the boat tour operator from last lecture’s exercise: FC = €200/day, P = €35/ticket.

Hypothetical illustrative example

👉 At Q* = 5: The firm loses €140/day. But if it shuts down, it loses €200/day (= FC).

Since \(P = €35 > AVC = €23\), operating saves €60 compared to shutting down!

That €60 = \(TR - VC = 175 - 115\) is the contribution toward fixed costs.

• At \(P > ATC_{\min}\): the firm earns positive profit 📈
• At \(P = ATC_{\min}\): zero economic profit — but the firm is still happy! It covers all costs including opportunity costs
• At \(P < ATC_{\min}\): the firm operates at a loss (but may still choose to operate — see shutdown rule)

. . .

💡 Remember: “zero economic profit” ≠ “zero accounting profit.” The firm’s owners earn a normal return — exactly what they could earn elsewhere. There’s no incentive to leave.

• At \(P > AVC_{\min}\): operate — revenue covers variable costs and contributes to FC
• At \(P = AVC_{\min}\): indifferent — loss equals FC whether you operate or not
• At \(P < AVC_{\min}\): shut down — every unit produced makes losses worse

. . .

The zone between shutdown and breakeven (\(AVC_{\min} < P < ATC_{\min}\)) is where the firm operates at a loss but is better off producing than closing. This is a very real situation in tourism!

This is the most common confusion students have. Let’s be very clear:

. . .

Why do Algarve hotels stay open in winter at very low occupancy?

. . .

⚠️ But if winter prices drop to €20/night (\(P < AVC = €25\)): now it’s cheaper to close temporarily.

We now have everything we need to derive the firm’s short-run supply curve:

Intuition: As the market price rises, the firm moves up along its MC curve, producing more. This is exactly what a supply curve shows — higher price → higher quantity supplied!

👉 The supply curve starts at the shutdown point (minimum AVC) and follows MC upward.

(a) \(P > ATC\): Produce, earn profit (green area). (b) \(AVC < P < ATC\): Produce at a loss (orange area), but operating is better than shutdown. (c) \(P < AVC\): Shut down, produce nothing.

💡 Steps 2 and 3 answer different questions: Step 2 = “should I produce?”, Step 3 = “am I profitable?”

The shutdown rule explains a major pattern in tourism businesses:

. . .

👉 This is why some Algarve restaurants close entirely from November to March (P < AVC), while hotels stay open at reduced capacity (AVC < P < ATC). Different cost structures, different shutdown prices!

Airlines face a similar decision for individual routes:

Should we keep flying the Lisbon–Faro route in January?

• 🔒 Fixed costs per flight: aircraft lease, crew salaries, airport fees → very high
• 🔄 Variable costs per passenger: meals, baggage, marginal fuel → quite low

Because AVC per passenger is very low, the shutdown price is low. Airlines will operate flights even at very low load factors because almost any ticket price > AVC.

. . .

This explains:

• 📉 Extremely cheap last-minute fares — as long as \(P > AVC\) (a few euros!), it’s worth filling the seat
• 🚫 Route cancellations only when demand is so low that even rock-bottom fares can’t cover variable costs
• 🔄 Seasonal route adjustments — winter routes to ski destinations replace summer beach routes

Today’s Key Takeaways:

1. Shutdown rule: In the short run, operate if \(P \geq AVC\); shut down if \(P < AVC\)
2. Breakeven price = \(ATC_{\min}\) — the price needed for zero economic profit
3. Shutdown price = \(AVC_{\min}\) — the price below which the firm should produce nothing
4. Between shutdown and breakeven (\(AVC_{\min} \leq P < ATC_{\min}\)): the firm operates at a loss, but this loss is smaller than the loss from shutting down (which = FC)
5. The firm’s supply curve = MC above AVC (the rising portion of MC, starting at the shutdown point)
6. For \(P < AVC_{\min}\): \(Q = 0\) (vertical segment along the y-axis)
7. Tourism application: explains seasonal openings/closings, low-season pricing, and last-minute deals

Connection: Today we derived the individual firm’s supply curve. Next lecture: the seller’s supply rule (\(P = MC\)) in more depth, and we start looking at market supply and producer surplus.

Next (Lecture 13, March 27): The Seller’s Supply Rule: P = MC. 📈

Question: A small pastelaria (pastry shop) near Belém Tower has fixed costs of €3,000/month and is currently losing €1,000/month. The owner considers closing for the winter. Should she?

A. Yes — she is making a loss, so she should close immediately

B. No — as long as her revenue exceeds her variable costs, she should stay open

C. Yes — she should close and reopen when she can make a profit

D. It depends on whether she likes making pastéis de nata

Question: A competitive firm has AVC min = €20 and ATC min = €35. If the market price is €25, the firm should:

A. Shut down because P < ATC

B. Produce where P = MC and earn positive profit

C. Produce where P = MC but operate at a loss

D. Produce where P = AVC

A kayak rental business on the Douro River in Porto has the following monthly cost structure:

Hypothetical illustrative example

a) Calculate AVC, ATC, and MC for each output level.

b) What is the shutdown price? What is the breakeven price?

c) If the market price is €22/kayak, should the firm operate? What is the profit-maximizing output? Calculate the profit (or loss).

d) If the market price drops to €14/kayak, should the firm operate? Explain and calculate the loss under each scenario (operate vs. shut down).

e) In the long run, if firms in this market are making losses, what would you expect to happen? How does this relate to the long-run breakeven condition?

MC calculation example: From Q = 100 to Q = 150: \(MC = \frac{3{,}900 - 3{,}300}{150 - 100} = \frac{600}{50} = €12\) per kayak.

Key observations: AVC is minimized at Q = 150–200 (AVC = €16). ATC is minimized at Q = 200 (ATC = €23.50). MC follows the U-shape: falls to €12, then rises.

b) Shutdown and breakeven prices:

• Shutdown price = \(AVC_{\min} = €16\) (at Q = 150–200)
• Breakeven price = \(ATC_{\min} = €23.50\) (at Q = 200)

c) At \(P = €22\):

Since \(P = €22 > AVC_{\min} = €16\): Yes, operate!

Find Q* where P = MC: MC = €16 at Q = 200, MC = €26 at Q = 250. Since P = €22 falls between, the firm produces between 200 and 250 kayaks. Since we only have discrete data, the firm produces Q* = 200 (the last quantity where MC ≤ P).

Profit at Q = 200: \(\pi = TR - TC = (22 \times 200) - 4{,}700 = 4{,}400 - 4{,}700 = -€300\)

The firm is operating at a loss of €300/month. But this is better than shutting down, which would cost −€1,500 (= FC).

d) At \(P = €14\):

Since \(P = €14 < AVC_{\min} = €16\): Shut down!

• If operating: Find Q where MC ≈ P = €14 (between Q = 100 and Q = 150). At Q = 150: \(TR = 14 \times 150 = €2{,}100\), \(TC = €3{,}900\), Loss = −€1,800.
• If shut down: Loss = FC = −€1,500.

Since \(|-€1{,}500| < |-€1{,}800|\), shutting down is better. ✅

👉 At P = €14, operating makes things worse by €300 compared to just paying FC.

e) In the long run, if firms are making losses:

Some firms will exit the market (they can now escape fixed costs too). As firms exit, market supply shifts left, which raises the equilibrium price. Firms keep exiting until \(P = ATC_{\min}\) for the remaining firms — the long-run breakeven condition. In the long run, perfectly competitive firms earn zero economic profit.