Elasticity
Elasticity = % change in quantity ÷ % change in price. Steep curve = inelastic. Flat curve = elastic. And the punchline that carries into taxes: the inelastic side bears the tax.
Formula
Classify
| Value | Name | Curve | Example |
|---|---|---|---|
| |ε| > 1 | Elastic | Flat | Gasoline, long run |
| |ε| < 1 | Inelastic | Steep | Eggs, gasoline short run |
| ε = 0 | Perfectly inelastic | Vertical | Planted soybean crop |
| |ε| = ∞ | Perfectly elastic | Horizontal | Demand facing one small firm |
What makes demand elastic
- Substitutes
- More substitutes → more elastic. No 1:1 substitute (eggs) → inelastic.
- Time
- Longer horizon → more elastic. You can't change your commute this week; you can in two years.
- Necessity
- Things you can do without → elastic. Things you can't → inelastic.
- Supply side
- Hard resource constraint (short run) → inelastic. New capacity and technology (long run) → elastic.
Rules that earn points
- Elasticity is not slope. ε = (1/slope) × (P/Q). Since P/Q changes as you move, elasticity varies along a straight-line demand curve even though slope doesn't.
- Expenditure test. Supply contracts → inelastic demand means total spending rises; elastic demand means it falls.
- A given supply shift lands mostly in price against steep demand, mostly in quantity against flat demand.
- At high enough prices demand always becomes elastic — budgets are finite.
Expenditure, worked
| Case | Price +10% | Quantity | P × Q |
|---|---|---|---|
| ε = −0.75 inelastic | 100 → 110 | 200 → 185 (−7.5%) | 20,000 → 20,350 ▲ |
| ε = −1.50 elastic | 100 → 110 | 200 → 170 (−15%) | 20,000 → 18,700 ▼ |
- Saying elasticity equals slope, or that a linear demand curve has constant elasticity.
- Dividing the wrong way. Quantity change goes on top.
- Justifying elasticity with "people need it" instead of substitutes and time horizon.
The price of lunches around Berkeley rises from $10 to $11 and quantity demanded falls from 50,000 to 47,500. The price elasticity of demand is:
- A−2.0, elastic
- B−0.5, inelastic
- C−5.0, elastic
- D−0.05, inelastic
Answer
B — −0.5, relatively inelastic.
Price rose 10%. Quantity fell 2,500 on a base of 50,000, which is 5%. So ε = −5%/10% = −0.5. Magnitude below 1 means inelastic.
C is the trap: it divides the wrong way (10 ÷ 5 rather than 5 ÷ 10).
Which demand is most likely to be elastic?
- AEggs, over the next month
- BGasoline, over the next week
- CGasoline, over the next five years
- DInsulin, for a diabetic patient
Answer
C — gasoline over five years.
Time opens up substitution margins: buy an electric or efficient car, move closer to work, switch to transit. A and B are short-run with poor substitutes; D has essentially no substitute at any horizon.
Supply contracts in a market where demand is inelastic. Total expenditure on the good:
- ARises
- BFalls
- CIs unchanged
- DCannot be determined
Answer
A — rises.
Expenditure is P × Q. With inelastic demand the percentage fall in quantity is smaller than the percentage rise in price, so the price effect dominates.
This is the textbook drug-crackdown result: raising the price of an inelastically demanded good increases total spending on it.
Which statement about a straight-line demand curve is correct?
- ABoth slope and elasticity are constant along it
- BSlope is constant; elasticity varies along it
- CElasticity is constant; slope varies along it
- DElasticity equals the slope at every point
Answer
B — slope constant, elasticity varies.
ε = (1/slope) × (P/Q). The slope term is fixed on a straight line, but P/Q falls as you move down and to the right, so elasticity falls with it. Elasticity is constant only when demand is a straight line in logs.
There is no single substitute for eggs — you can bake an eggless cake and scramble tofu, but the substitute depends on the dish. (a) What does this imply about the shape of the market demand curve for eggs? (b) Avian flu kills a large share of laying hens. Draw the market and describe what happens to price and quantity.
Model answer
(a) With no obvious 1:1 substitute, demand for eggs is inelastic — steep, close to vertical, at least in the short run. Cooks and bakers need eggs across many dishes, so willingness to pay stays high as the price climbs.
(b) Avian flu is a supply shock: supply shifts inward. Because demand is steep, the new equilibrium shows a large rise in price and only a small fall in quantity.
- Naming the curve inelastic and steep — say both.
- Justifying it by absence of substitutes, not by "people need eggs."
- Shifting supply, not demand. Flu kills hens; it does not change willingness to pay.
- Stating the asymmetry explicitly: big ΔP, small ΔQ. That is the whole point of the question.
- Both equilibria labelled on the diagram.
European countries tax gasoline far more heavily than the United States, and European pump prices are correspondingly higher. What does this tell you about the relative elasticities of gasoline supply and demand, and who bears the tax?
Model answer
Prices rising roughly with the tax means consumers bear most of it. That happens when demand is much less elastic than supply.
This fits the economics: supply is the world oil price plus the cost of running a station, which is very elastic, while short-run demand is a commute with no good substitute.
- The general rule stated once: the inelastic side bears the tax.
- Identifying demand as the inelastic side from the price evidence, not by assertion.
- One concrete reason each side has the elasticity it does.