A straight demand line has changing elasticity
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| unitary elasticity/ˈjuːnɪtəri ɪlæˈstɪsɪti/ | 单位弹性 | dān wèi tán xìng |
| price elasticity of demand/praɪs ɪlæˈstɪsɪti ɒv dɪˈmænd/ | 需求价格弹性 | xū qiú jià gé tán xìng |
A decision you can investigate
- A seller sees a straight demand line and assumes responsiveness must be constant.
- The same change in units is a different percentage of a large or small starting quantity.
Build the explanation
- PED is percentage quantity-demanded change divided by percentage own-price change. Interpret absolute magnitude: 0 perfectly inelastic, below 1 inelastic, 1 unitary, above 1 elastic; perfectly elastic demand is the horizontal limiting case. For a linear demand curve, a constant units-per-price slope does not imply constant PED.
- With Q = 100−2P, local PED = −2 × P/Q. The ratio changes along the line. Substitutes, branding, expenditure share, addiction and durability affect responsiveness; durable goods can allow postponement, while strong attachment can limit switching.
Work through the evidence
- At P=10, Q=80: local PED=−2 × 10/80=−0.25; TR=P × Q=800. At P=25, Q=50: local PED=−1 and TR=1250. At P=40, Q=20: local PED=−4 and TR=800.
- Below the midpoint, a small price rise increases revenue; above it, a small price cut increases revenue. The midpoint is the maximum of TR in this particular linear model. A point elasticity is local: it is not a claim that a large finite change has exactly the same percentage ratio.
What is local PED at P=40 and Q=20?
The local expression is −2 × 40/20 = −4.
Which point has the greatest revenue among those supplied?
1250 exceeds the two revenues of 800.
A local elasticity rounded to 1 guarantees unchanged revenue for any large price change.
A point estimate is local; check the actual price and quantity values over a finite change.
Test the limits
- Unitary elasticity 单位弹性 implies no first-order revenue effect locally; revenue over a finite interval must be checked as P × Q, rather than assuming unchanged revenue from a rounded estimate. Profit also depends on costs.
- A slope comparison needs the same axis scales, and even then the price/quantity point matters. Taxes on addictive products may reduce quantity little over a short period while raising spending; the policy aim and distribution still matter.
Why does constant slope not establish constant PED?
The bases vary along the line.
Apply and explain your answer
- Why is demand more elastic at price 40 than at price 10 in this same model?
- The constant slope is multiplied by a larger price-to-quantity ratio: 40/20 versus 10/80.
Match the terms to their meanings.
Use each term for its stated economic relationship.
Use the terms precisely
- price elasticity of demand 需求价格弹性: Percentage quantity-demanded response relative to percentage own-price change.
- unitary elasticity: The magnitude of percentage quantity response equals the percentage stimulus.
At P=10, Q=80: local PED=−2 × 10/80=−0.25; TR=P × Q=800. At P=25, Q=50: local PED=−1 and TR=1250. At P=40, Q=20: local PED=−4 and TR=800. Below the midpoint, a small price rise increases revenue; above it, a small price cut increases revenue. The midpoint is the maximum of TR in this particular linear model. A point elasticity is local: it is not a claim that a large finite change has exactly the same percentage ratio.
Unitary elasticity implies no first-order revenue effect locally; revenue over a finite interval must be checked as P × Q, rather than assuming unchanged revenue from a rounded estimate. Profit also depends on costs. A slope comparison needs the same axis scales, and even then the price/quantity point matters. Taxes on addictive products may reduce quantity little over a short period while raising spending; the policy aim and distribution still matter.
PED is percentage quantity-demanded change divided by percentage own-price change. Interpret absolute magnitude: 0 perfectly inelastic, below 1 inelastic, 1 unitary, above 1 elastic; perfectly elastic demand is the horizontal limiting case. For a linear demand curve, a constant units-per-price slope does not imply constant PED.