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 €10.00 to €4.00, weekly sales change from 800 to 1090. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €4.00Q1 = 800Q2 = 1090
E =
2.Price elasticity of demandHard
The demand for a product is Q = 400 − 8P, with P in euros. Find the price elasticity of demand E at a price of €10.
Q = 400 − 8PP = €10
E =
3.Economics conceptsMedium
A country has 950 employed people and 50 unemployed people seeking work. Its unemployment rate is:
- A5.3%
- B50%
- C5%
- D95%
4.Economics conceptsHard
A monopolist maximises profit where:
- AAverage cost is at its minimum
- BPrice equals marginal cost
- CTotal revenue is at its maximum
- DMarginal revenue equals marginal cost
3Solutions
1.Price elasticity of demand
Answer: E = −0.358
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
(1090 − 800)/((800 + 1090)/2) = 290/945 = 0.3069
Relative change in price
(4 − 10)/((10 + 4)/2) = −6/7 = −0.8571
Elasticity
E = 0.3069/−0.8571 = −0.358
Answer
E = −0.358
2.Price elasticity of demand
Answer: E = −0.25
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.
Quantity at this price
Q = 400 − 8·10 = 320
Point elasticity
dQ/dP = −8
E = (dQ/dP)·P/Q = −8·10/320 = −0.25
Answer
E = −0.25
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · 5%
Why this is the answer
The labour force is 950 + 50 = 1,000, so the rate is 50 / 1,000 = 5%.
Answer
C · 5%
4.Economics concepts
Answer: D · Marginal revenue equals marginal cost
Why this is the answer
Profit is maximised where MR = MC. For a monopolist, price is above MR, so P > MC, causing a deadweight loss.
Answer
D · Marginal revenue equals marginal cost
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