Why? The cost-benefit principle (from Lecture 3!) applied to each unit:

• The benefit of producing one more unit = the revenue it brings = \(P\)
• The cost of producing one more unit = \(MC\)

👉 Keep producing as long as \(P \geq MC\). Stop when the next unit would cost more than it earns.

This is just marginal analysis — the same logic we’ve used since the very beginning of the course!

The bottle factory (from the textbook): P = €0.35/bottle, FC = €40/day

Source: Course textbook (sebenta), Table 10

MC is U-shaped — it may intersect the price line twice. Which intersection is correct?

At Q₁ (falling MC): if you produce one more unit, MC is still falling — you can increase profit further! At Q* (rising MC): producing one more unit would cost more than the price. This is the true optimum.

This rule answers three questions at once:

The textbook shows what happens when the bottle price rises from €0.35 to €0.45:

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

• At P = €0.35: Q* = 400 (MC ≈ 0.30, next batch MC = 0.40 > P)
• At P = €0.45: Q* = 500 (MC ≈ 0.40, next batch MC = 0.50 > P)

👉 Higher price → produce more → earn more profit. The firm moves up along its MC/supply curve.

What if wages rise from €10/hour to €12/hour (keeping P = €0.35)?

Source: Course textbook (sebenta), Tables 10 & 12

• At w = €10/hr: Q* = 400, max profit = €30
• At w = €12/hr: Q* = 300, max profit = €17

👉 Higher wages → MC rises at every Q → firm produces less at the same price. The supply curve has shifted left!

The textbook also shows: when FC rises from €40 to €70 (price stays at €0.35):

• Q* stays at 400! The profit-maximizing quantity doesn’t change.
• Profit drops from €30 to €0, but the production decision is unchanged.

. . .

👉 Movement along the supply curve: caused by a change in the product’s own price

👉 Shift of the supply curve: caused by a change in input prices (wages, materials), technology, or number of firms

Left: When the product’s own price rises, the firm moves along its supply curve → \(Q\) increases.

Right: When input costs rise (wages, energy), the entire supply curve shifts left → less supplied at every price.

💡 Exactly the same logic as demand (Lecture 8): own-price = movement along; other factors = shift!

. . .

👉 Both examples change variable costs, which shifts MC and therefore the supply curve.

Why is the supply of tourism services different in summer vs winter?

The \(P = MC\) rule explains it:

. . .

💡 Combined with demand shifts: In summer, both supply and demand are higher. In winter, both shift left. The net effect on price depends on which shift is larger — this is market equilibrium (Lecture 17)!

Throughout the course, we’ve built mirror-image tools for consumers and producers:

Today’s Key Takeaways:

1. The seller’s supply rule: Produce where \(P = MC\) on the rising portion of MC, provided \(P \geq AVC\)
2. This follows directly from the cost-benefit principle — produce as long as \(P \geq MC\)
3. The rule answers three questions: how much, whether, and how profitable
4. Higher product price → movement along the supply curve (more produced)
5. Higher input costs (wages, energy) → MC shifts up → supply curve shifts left
6. Better technology → MC shifts down → supply curve shifts right
7. Fixed costs don’t shift supply in the short run (they don’t affect MC)
8. Supply and demand are mirror images — built from the same marginal analysis logic

Connection: We now have the individual firm’s supply curve. Next lecture: producer surplus and how to build the market supply from individual firms.

Next (Lecture 14, April 9): Producer Surplus, Market Supply, and Linear Supply 📈

Question: A sardine restaurant in Lisbon operates in a competitive market. Currently, \(P = €12\) per meal and \(MC = €10\) at the restaurant’s current output level. The restaurant should:

A. Keep output the same — it is already maximizing profit

B. Increase output — producing more will add to profit

C. Decrease output — the restaurant is overproducing

D. Shut down — it is not covering costs

Question: The Portuguese government introduces a new tourist tax of €2 per hotel night, paid by the hotel. Which of the following is correct?

A. The hotel’s supply curve shifts right by €2

B. The hotel’s supply curve shifts left (up by €2) — at each price, less is supplied

C. The hotel moves along its existing supply curve

D. The hotel’s demand curve shifts left

a) Apply \(P = MC\) on the rising portion:

Q* = 7 tours/day (last tour where \(P \geq MC\)).

Profit: \(\pi = TR - TC = (40 \times 7) - 433 = 280 - 433 = -€153\)

The firm makes a loss of €153/day. But should it still operate? AVC at Q = 7: \(\frac{133}{7} = €19\). Since \(P = €40 > AVC = €19\): yes, operate! Shutdown loss would be −€300 (= FC), which is worse.

b) New MC = old MC + €10:

New Q* = 6 tours/day (down from 7).

New VC at Q = 6: old VC + 6 × €10 = €96 + €60 = €156. New TC = 300 + 156 = €456.

New profit: \(\pi = (40 \times 6) - 456 = 240 - 456 = -€216\) (loss worsened from −€153 to −€216).

c) This is a shift of the supply curve, not a movement along it. The price didn’t change (still €40) — what changed was the input cost (fuel). Higher variable costs shift MC upward, which shifts the supply curve left. At the same price, the firm now supplies fewer tours (6 instead of 7).