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 1 000 units per month at €20. Its price elasticity of demand is −0.5. The firm changes the price by −20%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €20Q1 = 1 000E = −0.5%ΔP = −20%
ΔR = €
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −0.5, so Q = A·P^−0.5. At a price of €25, 2 000 units are sold. How many units Q are sold at a price of €27.50?
E = −0.5P1 = €25Q1 = 2 000P2 = €27.50
Q = units
3.Economics conceptsMedium
A sharp rise in world oil prices leading to higher inflation is an example of:
- ADeflation
- BDemand-pull inflation
- CDisinflation
- DCost-push inflation
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACreates the largest possible deadweight loss
- BProduces less than a single-price monopolist, creating a larger deadweight loss
- CCaptures all consumer surplus and produces the efficient output
- DCharges every consumer the same price
3Solutions
1.Price elasticity of demand
Answer: ΔR = −2400 €
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 = 20·0.8 = €16.00
Q2 = 1 000·1.1 = 1100
Change in revenue
ΔR = 16·1100 − 20·1 000 = 17 600.00 − 20 000 = −€2 400.00
Answer
ΔR = −€2 400.00
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: Q = 1907 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 = 27.5/25 = 1.1
New quantity
Q = 2 000·1.1−0.5 = 2 000·0.9535 = 1907
Answer
Q = 1907
3.Economics concepts
Answer: D · Cost-push inflation
Why this is the answer
Higher input costs shift aggregate supply to the left, raising prices and possibly lowering output; demand-pull inflation comes from excess aggregate demand.
Answer
D · Cost-push inflation
4.Economics concepts
Answer: C · Captures all consumer surplus and produces the efficient output
Why this is the answer
Charging each buyer their reservation price means it sells until price equals MC, so there is no deadweight loss, but all surplus goes to the producer.
Answer
C · Captures all consumer surplus and produces the efficient output
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