Elasticity
Price elasticity of demand and supply, cross-price elasticity, income elasticity, and total revenue
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Elasticity
Elasticity measures how responsive one variable is to a change in another. The most important is the price elasticity of demand (PED), which captures how sensitive quantity demanded is to a change in price.
Price Elasticity of Demand
By convention we take the absolute value. Demand is:
- Elastic if — quantity reacts more than price (luxuries, goods with many substitutes, narrowly defined goods, long time horizons).
- Inelastic if — quantity reacts less than price (necessities, goods with few substitutes, addictive goods, short horizons).
- Unit-elastic if .
Total Revenue and the Total-Revenue Test
Total revenue is . The relationship between and price changes depends entirely on elasticity:
| Demand is… | If P rises… | If P falls… |
|---|---|---|
| Elastic | TR ↓ | TR ↑ |
| Inelastic | TR ↑ | TR ↓ |
| Unit | TR unchanged | TR unchanged |
This is the total-revenue test: change the price slightly and see what happens to revenue — that tells you the elasticity in that price range.
Determinants of Price Elasticity
Demand is more elastic when (1) close substitutes are available, (2) the good takes a large share of the consumer's budget, (3) the good is a luxury, (4) the time horizon is longer (consumers and producers can adjust), and (5) the good is narrowly defined (e.g., "Honda Civic" is more elastic than "cars in general").
Other Elasticities
- Cross-price elasticity: . Positive ⇒ substitutes. Negative ⇒ complements. Near zero ⇒ unrelated.
- Income elasticity: . Positive ⇒ normal good (>1 = luxury). Negative ⇒ inferior good.
- Price elasticity of supply: mirrors PED but applies to producers; depends mainly on time and excess capacity.
Why Elasticity Matters for Policy
Tax incidence, the deadweight loss from price controls, and the revenue impact of business pricing all hinge on elasticity. The side of the market that is more INELASTIC (less responsive) bears the larger share of any tax burden, because that side has fewer ways to escape the tax.
📚 Practice Problems
1Problem 1easy
❓ Question:
When the price of breakfast cereal rises from $4.00 to $4.40 per box (a 10% increase), the quantity demanded falls from 1,000 to 850 boxes. (a) Compute the price elasticity of demand using the simple % method. (b) Is demand elastic, inelastic, or unit-elastic?
💡 Show Solution
(a) . .
(b) ⇒ demand is elastic in this range.
2Problem 2easy
❓ Question:
A bakery raises its bread price by 5% and observes total revenue from bread INCREASE. Without doing any further calculation, is demand for the bakery's bread elastic, inelastic, or unit-elastic? Justify with the total-revenue test.
💡 Show Solution
Total revenue and price moved in the SAME direction (both up). By the total-revenue test, that means demand is inelastic (): the percentage drop in quantity is smaller than the percentage rise in price, so rose.
3Problem 3medium
❓ Question:
When the price of margarine rises by 8%, the quantity of butter demanded rises by 12%. (a) Compute the cross-price elasticity. (b) State the relationship between the two goods.
💡 Show Solution
(a)
(b) ⇒ butter and margarine are substitutes (and rather close ones, since the magnitude is large).
4Problem 4medium
❓ Question:
When household income rises by 10%, demand for restaurant meals rises by 18%, and demand for instant ramen falls by 4%. Compute the income elasticity for each and classify each good (normal/inferior, and if normal, luxury or necessity).
💡 Show Solution
Restaurant meals: . Positive ⇒ normal. Greater than 1 ⇒ normal luxury good.
Instant ramen: . Negative ⇒ inferior good (consumers buy less of it as income rises).
5Problem 5hard
❓ Question:
The government imposes a per-unit excise tax on cigarettes. Using elasticity, explain (a) who bears more of the tax burden — buyers or sellers — given that the demand for cigarettes is highly inelastic, and (b) why this tax raises substantial revenue but creates relatively little deadweight loss.
💡 Show Solution
(a) The side of the market that is less elastic (more inelastic) bears more of the tax burden, because it has fewer ways to escape it. Cigarette demand is highly inelastic ⇒ buyers absorb most of the tax through a higher consumer price; sellers' net price falls only slightly.
(b) Revenue: Because consumers reduce smoking only modestly, stays high and the per-unit tax × quantity yields large revenue.
Deadweight loss (DWL): DWL is proportional to the reduction in quantity caused by the tax. With inelastic demand, that reduction is small, so DWL is small. This is the classic "Ramsey rule" intuition: governments minimize efficiency losses by taxing inelastic goods — at the cost of placing more burden on the buyers of those goods.
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