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 10 000 units per month at €12. Its price elasticity of demand is −0.3. The firm changes the price by −20%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €12Q1 = 10 000E = −0.3%ΔP = −20%
ΔR = €
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 50 − 0.05Q, with P in euros. Find the price elasticity of demand E when 300 units are sold.
P = 50 − 0.05QQ = 300
E =
3.Economics conceptsMedium
A country has 950 employed people and 50 unemployed people seeking work. Its unemployment rate is:
- A50%
- B5%
- C95%
- D5.3%
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 = −18240 €
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 = 12·0.8 = €9.60
Q2 = 10 000·1.06 = 10600
Change in revenue
ΔR = 9.6·10600 − 12·10 000 = 101 760.00 − 120 000 = −€18 240.00
Answer
ΔR = −€18 240.00
|E| < 1: demand is inelastic.
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 = 50 − 0.05·300 = €35.00
Point elasticity
dQ/dP = −1/0.05 = −20
E = −20·35/300 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: B · 5%
Why this is the answer
The labour force is 950 + 50 = 1,000, so the rate is 50 / 1,000 = 5%.
Answer
B · 5%
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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