Two methods (same as we’ll use for supply):

Quick check — try these mentally before revealing the answers!

Q1: Algarve resort demand: \(P = 500 - 0.05Q\). At \(P = 100\), \(Q = 8{,}000\). Is demand elastic or inelastic?

Q2: If luxury cruise demand has \(|\varepsilon_d| = 2.5\) and operators raise prices by 8%, what happens to revenue?

. . .

👉 Now let’s apply the exact same logic to the supply side!

Key differences from demand elasticity:

👉 Same methods as demand elasticity — just applied to the supply curve!

Left: Supply through the origin → \(\varepsilon_s = 1\) at every point (P and Q always change proportionally).

Right: Supply with positive intercept (\(c > 0\)) → \(\varepsilon_s > 1\) near the intercept, falling as Q increases.

Why does supply through the origin always have \(\varepsilon_s = 1\)?

If \(P = dQ\): \(\quad \varepsilon_s = \frac{1}{d} \times \frac{P}{Q} = \frac{1}{d} \times \frac{dQ}{Q} = 1\)

The \(P/Q\) ratio always equals \(d\), which cancels perfectly with \(1/d\).

. . .

👉 Contrast with demand: demand elasticity varies from \(\infty\) to \(0\) along a linear curve. Supply elasticity is more “stable.”

The textbook identifies four key determinants (plus time):

The longer the time horizon, the more firms can adjust all inputs → supply becomes flatter (more elastic).

. . .

• 👉 Both elasticities together determine who bears the burden of taxes and price shocks! The side with less elastic response absorbs more of the burden.

• 👉 Both sides use the same formula and same classification. The determinants differ because they reflect different underlying decisions (buying vs producing).

Today’s Key Takeaways:

Demand elasticity recap:

1. \(\varepsilon_d = \frac{\%\Delta Q}{\%\Delta P}\) — negative, use \(|\varepsilon_d|\). Elastic > 1, inelastic < 1
2. Revenue test: elastic → P↑ means TR↓; inelastic → P↑ means TR↑
3. Determinants: substitutes, budget share, necessity/luxury, time, market definition

Supply elasticity (new):

4. \(\varepsilon_s = \frac{\%\Delta Q_s}{\%\Delta P}\) — always positive. Same formula, same classification
5. Linear supply through origin: \(\varepsilon_s = 1\) everywhere. Positive intercept: \(\varepsilon_s > 1\)
6. Determinants: flexibility, mobility, and replicability of inputs, time horizon
7. Time: very short run (inelastic) → short run → long run (elastic)
8. Both elasticities together determine price volatility and tax burden sharing

Next (Lecture 16, April 16): Short Run and Long Run Market Equilibrium ⚖️

Question: The supply of hotel rooms in Porto’s city center has \(\varepsilon_s = 0.3\). If room prices increase by 20%, what happens to the quantity of rooms supplied?

A. Quantity increases by 60%

B. Quantity increases by 6%

C. Quantity increases by 0.6%

D. Quantity increases by 20%

Question: Demand for TAP flights from Lisbon to London has \(|\varepsilon_d| = 1.8\). If TAP raises fares by 10%, what happens to total revenue from this route?

A. Revenue increases by 18%

B. Revenue increases because higher price means more money per ticket

C. Revenue falls because passenger numbers drop by more than 10%

D. Revenue stays the same

The market for tuk-tuk tours in Lisbon has the following estimated curves:

• Demand: \(P = 36 - 0.2Q\) (€ per tour)
• Supply: \(P = 6 + 0.1Q\) (€ per tour)

a) Find the equilibrium price and quantity.

b) Calculate the price elasticity of demand at the equilibrium point. Is demand elastic or inelastic?

c) Calculate the price elasticity of supply at the equilibrium point. Is supply elastic or inelastic?

d) At the equilibrium, if the city council imposes a small price increase (say €1), would you expect total revenue to rise or fall? Use the revenue test from part (b).

e) The supply has a positive intercept (\(c = 6\)). Using the shortcut formula \(\varepsilon_s = \frac{P}{P - c}\), verify your answer from part (c). At what price would supply elasticity equal exactly 2?

f) The city council considers a €3 per-tour tax on operators. This shifts supply to \(P = 9 + 0.1Q\). Find the new equilibrium. Who bears more of the tax burden — tourists or operators? Relate your answer to the elasticities you calculated.

a) Equilibrium: \(36 - 0.2Q = 6 + 0.1Q\) → \(30 = 0.3Q\) → \(Q^* = 100\), \(P^* = 36 - 0.2(100) = €16\)

b) Demand elasticity at \((Q^* = 100, P^* = 16)\):

Demand slope = \(-0.2\), so \(\frac{1}{\text{slope}} = \frac{1}{-0.2} = -5\)

\[\varepsilon_d = -5 \times \frac{16}{100} = -0.8\]

\(|\varepsilon_d| = 0.8 < 1\) → Demand is inelastic at the equilibrium.

c) Supply elasticity at \((Q^* = 100, P^* = 16)\):

Supply slope = \(0.1\), so \(\frac{1}{\text{slope}} = 10\)

\[\varepsilon_s = 10 \times \frac{16}{100} = 1.6\]

\(\varepsilon_s = 1.6 > 1\) → Supply is elastic at the equilibrium.

d) Since demand is inelastic (\(|\varepsilon_d| = 0.8 < 1\)), the revenue test says: a price increase → total revenue rises. Quantity falls, but by a smaller percentage than price rises. The €1 increase would increase TR.

e) Shortcut: \(\varepsilon_s = \frac{P}{P - c} = \frac{16}{16 - 6} = \frac{16}{10} = 1.6\) ✅ Matches part (c)!

For \(\varepsilon_s = 2\): \(\frac{P}{P - 6} = 2\) → \(P = 2P - 12\) → \(P = €12\)

At \(P = 12\): \(Q = \frac{12 - 6}{0.1} = 60\) tours. So supply is more elastic at lower prices (closer to the intercept).

f) New supply with €3 tax: \(P = 9 + 0.1Q\)

New equilibrium: \(36 - 0.2Q = 9 + 0.1Q\) → \(27 = 0.3Q\) → \(Q^* = 90\), \(P^* = 36 - 0.2(90) = €18\)

Of the €3 tax: tourists pay €2 more, operators receive €1 less.

👉 Tourists bear more (€2 out of €3) because demand is more inelastic (\(|\varepsilon_d| = 0.8\)) than supply is (\(\varepsilon_s = 1.6\)). The side with less elastic response absorbs more of the tax.

💡 This is a general rule: tax burden falls more heavily on the side of the market that is less responsive to price changes.