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 €15. 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 = €15Q1 = 2 500E = −1.5%ΔP = +20%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 1000 − 50P, with P in euros. Find the price elasticity of demand E at a price of €6.
Q = 1000 − 50PP = €6
E =
3.Economics conceptsMedium
A price ceiling set below the equilibrium price typically causes:
- ANo change in the market
- BA surplus
- CAn increase in supply
- DA shortage
4.Economics conceptsHard
In the Bertrand model, two firms sell identical products with the same constant marginal cost and compete on price. The equilibrium price is:
- AHalfway between monopoly price and marginal cost
- BEqual to marginal cost
- CThe monopoly price
- DZero
3Solutions
1.Price elasticity of demand
Answer: ΔR = −6000 €
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 = 15·1.2 = €18.00
Q2 = 2 500·0.7 = 1750
Change in revenue
ΔR = 18·1750 − 15·2 500 = 31 500.00 − 37 500 = −€6 000.00
Answer
ΔR = −€6 000.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: E = −0.4286
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 = 1000 − 50·6 = 700
Point elasticity
dQ/dP = −50
E = (dQ/dP)·P/Q = −50·6/700 = −0.4286
Answer
E = −0.4286
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: D · A shortage
Why this is the answer
A binding maximum price raises quantity demanded and lowers quantity supplied, creating excess demand, as with rent control.
Answer
D · A shortage
4.Economics concepts
Answer: B · Equal to marginal cost
Why this is the answer
Undercutting continues until price equals marginal cost, so even two firms reach the competitive outcome; in Cournot quantity competition, price stays above MC.
Answer
B · Equal to marginal cost
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