Result: No single firm can influence the market price. Each firm is a price taker.

Think of it this way:

• A wheat farmer can’t charge €5/kg when the market price is €3/kg — nobody would buy
• There’s no reason to charge €2/kg either — they can sell all they want at €3/kg
• So the only decision is: how many kilograms to produce?

. . .

Tourism analogy: Imagine dozens of identical beach umbrella rental stands on a long Algarve beach. If one charges €12/day when all others charge €10/day, tourists just walk to the next stand. The market price is €10 — take it or leave it.

Left: Market supply and demand determine the equilibrium price \(P^*\).

Right: Each individual firm faces a perfectly horizontal demand curve at \(P^*\). It can sell as much as it wants at this price — but nothing above it.

👉 For a price taker: Price = Marginal Revenue. Every extra unit sold brings in exactly \(P^*\).

The firm’s question: At what quantity \(Q\) is \(\pi = TR - TC\) as large as possible?

Two equivalent approaches to find the answer:

Both give the same answer! Approach 2️⃣ is more practical and leads us to the supply curve.

👉 Profit = vertical gap between TR and TC. Maximum profit is where this gap is widest — at around Q* ≈ 52 students.

This uses the surf school data from last lecture’s exercise, with P = €120/student.

Why does this work? Think about it one unit at a time:

• If \(P > MC\) for the next unit → producing it adds to profit → produce more! ➡️
• If \(P < MC\) for the next unit → producing it reduces profit → produce less! ⬅️
• If \(P = MC\) → you’re at the sweet spot — no way to increase profit further 🎯

💡 This is just marginal analysis from Lecture 3 applied to the firm!

. . .

👉 Next lecture we’ll explore the loss case in detail: when should a firm shut down vs. keep operating at a loss?

In all three cases, the firm produces where P = MC. What changes is the relationship between P and ATC at that quantity.

The sebenta’s glass bottle factory has FC = €40/day and the following cost structure:

Source: Course textbook (sebenta), Table 10

👉 Maximum profit (€30/day) at Q = 400 bottles/day. This is where MC is closest to the price (€0.35/bottle) on the rising portion of MC!

The textbook shows what happens when the bottle price rises to €0.45/bottle:

Source: Course textbook (sebenta), Tables 10 & 11

💡 Key insight: When price rises from €0.35 to €0.45, the firm produces more (400 → 500 bottles) and earns more profit (€30 → €75). The new optimum is where MC ≈ €0.40, closer to the new higher price.

The textbook shows an important result: when fixed costs rise (from €40 to €70/day), the profit-maximizing quantity stays the same (Q = 400).

Why? Because \(P = MC\) doesn’t involve FC at all! MC only reflects changes in variable costs.

. . .

⚠️ FC does matter for the stay or exit decision — which we cover next lecture!

Marginal Revenue is the extra revenue from selling one more unit:

\[MR = \frac{\Delta TR}{\Delta Q}\]

In perfect competition, the firm sells every unit at the same market price \(P\):

\[TR = P \times Q \quad \Rightarrow \quad \text{If Q goes up by 1:} \quad \Delta TR = P\]

So \(MR = P\) for every unit. That’s why the firm’s demand curve (\(d_i\)) is also its MR curve — a horizontal line at \(P\).

. . .

⚠️ This is specific to perfect competition! A monopolist (single seller) must lower the price to sell more, so \(MR < P\). We’ll see this in later courses.

For now: Price taker → \(P = MR\) → profit-maximizing rule is simply \(P = MC\).

Applying the P = MC rule to the bottle factory (P = €0.35/bottle):

💡 This step-by-step reasoning confirms the table’s answer: Q* = 400 bottles/day.

Why do hotels charge different prices at different times?

The \(P = MC\) rule explains dynamic pricing:

. . .

👉 The \(P = MC\) rule doesn’t just say “how much to produce” — it explains the seasonal rhythm of tourism businesses!

Today’s Key Takeaways:

1. Perfect competition: many firms, identical product, price taker
2. Price taker: the firm faces a horizontal demand curve at the market price → \(P = MR\)
3. Profit = \(TR - TC = (P - ATC) \times Q\)
4. Two approaches: maximize the gap between TR and TC (total curves), or set \(MR = MC\) (per-unit curves)
5. The golden rule: in perfect competition, produce where \(P = MC\) (on the rising portion of MC)
6. If \(P > ATC\) → positive profit; \(P = ATC\) → zero economic profit; \(P < ATC\) → loss
7. Fixed costs don’t affect the optimal Q — only variable costs (through MC) matter for the production decision
8. Higher price → higher quantity → higher profit — this is the seed of the supply curve

Connection: Lecture 10 gave us the cost curves. Today we used them to find \(Q^*\). Next lecture: what if the firm is making a loss? When should it shut down vs. continue?

Next (Lecture 12, March 26): Profits, Shutdown and Breakeven Price Levels. Supply.

Question: A small souvenir shop in Sintra operates in a competitive market. The market price for a standard Sintra tile replica is €8. The shop’s marginal cost of producing the 50th tile per day is €6, and the marginal cost of the 51st tile is €8.50. How many tiles should the shop produce?

A. 49 tiles

B. 50 tiles

C. 51 tiles

D. Cannot be determined without knowing fixed costs

Question: A perfectly competitive firm is producing at Q* where P = MC = €25. At this quantity, ATC = €20. What can we say about this firm?

A. The firm is making a loss and should shut down

B. The firm is earning zero economic profit

C. The firm is earning a positive economic profit of €5 per unit

D. The firm should increase output to reduce ATC further

b) Using the \(P = MC\) rule:

• At Q = 4: MC = €25 < P = €35 → produce the 4th tour ✅
• At Q = 5: MC = €35 = P = €35 → produce the 5th tour ✅ (MR = MC exactly)
• At Q = 6: MC = €50 > P = €35 → don’t produce the 6th tour ❌

So the rule gives Q* = 5, consistent with the table! ✅

c) At Q* = 5:

\[ATC = \frac{TC}{Q} = \frac{€315}{5} = €63 \text{ per tour}\]

Since \(P = €35 < ATC = €63\), the firm is earning negative economic profit (a loss):

\[\pi = (P - ATC) \times Q = (35 - 63) \times 5 = -€28 \times 5 = -€140\]

The firm is losing €140/day. 📉

d) At P = €20:

• Q = 1: MC = €20 = P → this is where P = MC on the rising portion
• Q = 2: MC = €15 < P → but this is the falling portion of MC (careful!)
• Q = 3: MC = €20 = P → this is on the rising portion ✅

The profit-maximizing quantity is Q* = 3 (where P = MC on the rising portion of MC).

Profit at Q = 3: \(TR = 20 \times 3 = €60\), \(TC = €255\), \(\pi = 60 - 255 = -€195\).

The loss worsened from −€140 to −€195. The lower price hurts!

e) If FC rises from €200 to €300:

No, the profit-maximizing quantity does not change! FC does not appear in the MC calculation. MC stays the same at every quantity, so \(P = MC\) still gives Q* = 5 at P = €35.

However, profit falls by exactly €100 (the FC increase): \(\pi = -€140 - €100 = -€240\).

👉 Fixed costs affect how much profit you earn, but not how many units to produce.