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
A product sells 2 500 units per month at €5. Its price elasticity of demand is −1.5. The firm changes the price by −20%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €5Q1 = 2 500E = −1.5%ΔP = −20%
ΔR = €
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 100 − 1Q, with P in euros. Find the price elasticity of demand E when 30 units are sold.
P = 100 − 1QQ = 30
E =
3.Economics conceptsMedium
A Gini coefficient of 0 indicates:
- APerfect inequality of income
- BZero economic growth
- CZero unemployment
- DPerfect equality of income
4.Economics conceptsHard
A monopolist faces demand P = 100 − Q and has constant marginal cost of 20. What are its profit-maximising output and price?
- AQ = 40, P = 20
- BQ = 40, P = 60
- CQ = 50, P = 50
- DQ = 80, P = 20
3Solutions
1.Price elasticity of demand
Answer: ΔR = 500 €
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.
New price and quantity
P2 = 5·0.8 = €4.00
Q2 = 2 500·1.3 = 3250
Change in revenue
ΔR = 4·3250 − 5·2 500 = 13 000.00 − 12 500 = €500.00
Answer
ΔR = €500.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: E = −2.333
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.
Price at this quantity
P = 100 − 1·30 = €70.00
Point elasticity
dQ/dP = −1/1 = −1
E = −1·70/30 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · 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
D · Perfect equality of income
4.Economics concepts
Answer: B · Q = 40, P = 60
Why this is the answer
Setting MR = MC gives 100 − 2Q = 20, so Q = 40; the price from the demand curve is 100 − 40 = 60.
Answer
B · Q = 40, P = 60
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