. . .

💡 Key parallel: Just as consumers face trade-offs with limited income, producers face trade-offs with limited resources and technology.

Before we can find the profit-maximizing quantity (next lecture), we need to master costs.

Today we answer:

• 1️⃣ What types of costs does a firm face?
• 2️⃣ How do costs change as output increases?
• 3️⃣ What is the difference between short run and long run?

. . .

All short-run costs derive from three building blocks:

. . .

⚠️ Important: FC is a sunk cost in the short run — it cannot be recovered. Remember Lecture 3!

Imagine a small beach bar in Albufeira. The owner pays €500/month in rent (fixed), and hires staff and buys supplies (variable).

Output = drinks served per month (hypothetical illustrative example)

👉 Notice: FC stays at €500 always. VC increases — and it increases faster and faster (diminishing returns to the staff in the small bar!).

👉 TC and VC have the same shape — TC is just VC shifted up by FC. The vertical gap between TC and VC is always exactly €500 (the fixed cost).

Total costs tell us the whole bill, but firms need to know the cost per unit to set prices and make decisions.

Intuition: If producing 100 drinks costs €850 total and producing 101 drinks costs €856, then \(MC = €6\).

Why is MC so important?

• It tells the firm whether producing one more unit adds to or subtracts from profit
• Rule of thumb: produce more if the price you receive > MC
• MC is the foundation of the supply curve (Lectures 12–14)

Hypothetical illustrative example

👉 Key observations:

• AFC always falls (spreading the fixed cost)
• AVC falls then rises (U-shaped) — minimum at Q = 100 (AVC = €3.50)
• ATC falls then rises (U-shaped) — minimum at Q = 200 (ATC = €6.50)
• MC falls then rises — and crosses AVC and ATC at their minimums!

Think of it like your grade point average 🎓

. . .

⚠️ Don’t confuse: MC can be below ATC while ATC is still falling. ATC rises only after MC crosses above it.

. . .

💡 The difference between FC and VC explains why low-season pricing exists: covering variable costs and some fixed costs is better than covering none.

In the long run, the firm can adjust all inputs — including building size, number of machines, and technology.

Think of it this way:

• Short run: “Given our current hotel (100 rooms), what’s our cost?”
• Long run: “What size of hotel minimizes our cost per guest?”

The LRAC curve is formed by choosing the best short-run plant size for each output level.

👉 The LRAC is the “envelope” of all possible short-run ATC curves.

Each dashed curve = one plant size (short run). The bold red LRAC = lowest cost achievable at each Q.

👉 In the long run, the firm chooses the plant size that minimizes cost for its desired output.

The shape of the LRAC curve reveals three zones:

. . .

💡 Minimum Efficient Scale (MES): the smallest output where LRAC reaches its minimum. Firms should aim to operate at or beyond this point.

Why do big hotel chains (Marriott, Accor, Hilton) have cost advantages?

Today’s Key Takeaways:

1. Short run: at least one input is fixed; Long run: all inputs are variable
2. Total costs: \(TC = FC + VC\) — fixed costs don’t depend on output
3. Average costs: ATC = AFC + AVC — both per-unit measures
4. Marginal cost: the extra cost of one more unit — the most important curve
5. MC crosses AVC and ATC at their minimums (the “exam grade” rule)
6. LRAC: the envelope of short-run ATC curves — shows optimal plant size
7. Economies of scale explain why large hotel chains exist; diseconomies explain why they don’t grow forever

Connection: Costs are the foundation of supply. Next lecture we use MC to find the profit-maximizing output.

Next (Lecture 11, March 20): Companies — Profit Maximization 💰

Question: A tour operator in Lisbon has monthly fixed costs of €10,000 (office lease, software) and variable costs that depend on the number of tours sold. Currently, they sell 200 tours per month with an ATC of €80 per tour. If they increase to 250 tours and ATC falls to €72 per tour, what can we conclude?

A. Marginal cost of the additional tours is below €72

B. Marginal cost of the additional tours is above €80

C. The firm is experiencing diseconomies of scale

D. Fixed costs have increased

Question: In the short run, a small hotel in Sintra has fixed costs of €6,000/month. When occupancy rises from 80 to 90 guests/month, total costs rise from €14,000 to €15,500. What is the marginal cost per additional guest?

A. €150

B. €155

C. €172

D. €175

A small surf school in Ericeira has monthly fixed costs of €2,000 (equipment rental, insurance) and the following cost structure:

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

b) At what output level is AVC minimized? At what output is ATC minimized?

c) Verify that MC = AVC at the minimum of AVC, and MC = ATC at the minimum of ATC.

d) The school charges €90 per student. At what output level would you expect MC to equal this price? What does this tell us about the profit-maximizing output? (We’ll formalize this in the next lecture!)

e) In the long run, the school considers expanding to a second location. Explain, using the concept of economies of scale, under what conditions this expansion would lower the cost per student.

MC calculation example: From Q = 20 to Q = 30: \(MC = \frac{3{,}900 - 3{,}400}{30 - 20} = \frac{500}{10} = €50\) per student.

b) AVC is minimized at Q = 30 (AVC = €63.33). ATC is minimized at Q = 50 (ATC = €110.00).

👉 AVC minimum comes before ATC minimum — this is always the case because AFC is still pulling ATC down even after AVC starts rising.

c) At Q = 30 (AVC minimum): MC just shifted from €60 (at Q=20) to €50 (at Q=30), and then rises to €70 (at Q=40). MC passes through the AVC minimum range, consistent with theory. At Q = 50 (ATC minimum): MC = €90, while ATC = €110. Between Q=40 and Q=50, MC (€90) is still below ATC (€110), pulling it down. At Q=60, MC = €130 > ATC = €113.33, so ATC starts rising. The crossing happens between Q=50 and Q=60. ✅

d) Price = €90. MC = €90 at Q = 50. This suggests the profit-maximizing output is around 50 students. At this level, each additional student brings in exactly as much revenue (€90) as they cost to add. Producing more (Q=60) would mean MC = €130 > €90 = price → losing money on each extra student.

e) Expanding to a second location would lower the cost per student if the school can achieve economies of scale:

• 🤝 Shared equipment purchases: buying boards and wetsuits in bulk at a discount
• 💻 Single booking/marketing system serving both locations
• 🎓 Instructor training: standardized program developed once, used at both sites
• 📈 Brand recognition: marketing costs spread over more students

However, expansion could also create diseconomies if:

• Coordination between locations is difficult (travel time, communication)
• Quality control drops when the owner can’t supervise both sites
• Each beach has unique conditions requiring different approaches

👉 Expansion makes sense if the LRAC falls at the combined output — that is, if the firm is still in the economies of scale region.