Price elasticity of demand
- Price elasticity (midpoint)
- E = (ΔQ/Q̄)/(ΔP/P̄)
- Elastic / inelastic
- |E| > 1 elastic, |E| < 1 inelastic
- Revenue
- TR = P·Q
Microeconomics: cram pack
Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Price elasticity of demandMedium
When the price of a ticket changes from €2.00 to €4.50, weekly sales change from 500 to 250. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €2.00P2 = €4.50Q1 = 500Q2 = 250
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1250 − 25P, with P in euros. At which price P is the price elasticity of demand equal to −0.25?
Q = 1250 − 25PE = −0.25
P = €
3.Economics conceptsMedium
A Gini coefficient of 0 indicates:
- AZero unemployment
- BZero economic growth
- CPerfect equality of income
- DPerfect inequality of income
4.Economics conceptsHard
The Phillips curve originally suggested:
- AA trade-off between inflation and unemployment in the short run
- BThat inflation and unemployment always rise and fall together in the short run
- CThat unemployment has no link to inflation
- DThat higher taxes always reduce inflation
3Solutions
1.Price elasticity of demand
Answer: E = −0.8667
Price elasticity of demand measures how strongly the quantity demanded reacts to price: E = (% change in quantity)/(% change in price). It is negative for normal goods. |E| > 1 is elastic (revenue falls when price rises), |E| < 1 is inelastic.
Relative change in quantity
(250 − 500)/((500 + 250)/2) = −250/375 = −0.6667
Relative change in price
(4.5 − 2)/((2 + 4.5)/2) = 2.5/3.25 = 0.7692
Elasticity
E = −0.6667/0.7692 = −0.8667
Answer
E = −0.8667
2.Price elasticity of demand
Answer: P = 10 €
Price elasticity of demand measures how strongly the quantity demanded reacts to price: E = (% change in quantity)/(% change in price). It is negative for normal goods. |E| > 1 is elastic (revenue falls when price rises), |E| < 1 is inelastic.
Elasticity as a function of price
E = −25P/(1250 − 25P)
Solve for P
−25P = −0.25·(1250 − 25P)
P·(−25 − 6.25) = −312.5 → P = €10.00
Answer
P = €10.00
Check: Q = 1000, E = −25·10/1000 = −0.25.
3.Economics concepts
Answer: C · Perfect equality of income
Why this is the answer
The Gini coefficient ranges from 0 (everyone has the same income) to 1 (one person has all income); higher values mean more inequality.
Answer
C · Perfect equality of income
4.Economics concepts
Answer: A · A trade-off between inflation and unemployment in the short run
Why this is the answer
Phillips found an inverse relationship between wage inflation and unemployment; expectations-augmented versions show no long-run trade-off at the natural rate.
Answer
A · A trade-off between inflation and unemployment in the short run
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