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 €4.00 to €5.00, weekly sales change from 1200 to 840. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €5.00Q1 = 1200Q2 = 840
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −2.5, so Q = A·P^−2.5. At a price of €4, 2 000 units are sold. How many units Q are sold at a price of €2.40?
E = −2.5P1 = €4Q1 = 2 000P2 = €2.40
Q = units
3.Economics conceptsMedium
Overfishing in international waters is an example of:
- AThe tragedy of the commons
- BA Giffen good
- CA natural monopoly
- DPrice discrimination
4.Economics conceptsHard
Price discrimination by a firm requires that:
- AIt operates in perfect competition
- BIts costs differ for each customer
- CIt has market power, can separate markets and prevent resale
- DAll consumers have identical elasticity of demand and buy the same amount
3Solutions
1.Price elasticity of demand
Answer: E = −1.588
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
(840 − 1200)/((1200 + 840)/2) = −360/1020 = −0.3529
Relative change in price
(5 − 4)/((4 + 5)/2) = 1/4.5 = 0.2222
Elasticity
E = −0.3529/0.2222 = −1.588
Answer
E = −1.588
2.Price elasticity of demand
Answer: Q = 7172 units
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.
Ratio of the prices
P2/P1 = 2.4/4 = 0.6
New quantity
Q = 2 000·0.6−2.5 = 2 000·3.586 = 7172
Answer
Q = 7172
3.Economics concepts
Answer: A · The tragedy of the commons
Why this is the answer
When a common resource is rival but people cannot be excluded, each user ignores the cost they impose on others, leading to overuse.
Answer
A · The tragedy of the commons
4.Economics concepts
Answer: C · It has market power, can separate markets and prevent resale
Why this is the answer
To charge different prices for the same good, the firm needs market power, the ability to identify groups with different elasticities and to prevent arbitrage.
Answer
C · It has market power, can separate markets and prevent resale
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