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 4 000 units per month at €10. Its price elasticity of demand is −2. The firm changes the price by +5%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €10Q1 = 4 000E = −2%ΔP = +5%
ΔR = €
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 80 − 0.5Q, with P in euros. Find the price elasticity of demand E when 64 units are sold.
P = 80 − 0.5QQ = 64
E =
3.Economics conceptsMedium
Using the expenditure approach, GDP equals:
- AC + I + G + (X − M)
- BC − I + G − (X + M)
- CC + I + G + X + M
- DWages + profits − taxes
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:
- AEqual to marginal cost
- BHalfway between monopoly price and marginal cost
- CThe monopoly price
- DZero
3Solutions
1.Price elasticity of demand
Answer: ΔR = −2200 €
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 = 10·1.05 = €10.50
Q2 = 4 000·0.9 = 3600
Change in revenue
ΔR = 10.5·3600 − 10·4 000 = 37 800.00 − 40 000 = −€2 200.00
Answer
ΔR = −€2 200.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: E = −1.5
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 = 80 − 0.5·64 = €48.00
Point elasticity
dQ/dP = −1/0.5 = −2
E = −2·48/64 = −1.5
Answer
E = −1.5
|E| > 1: demand is elastic.
3.Economics concepts
Answer: A · C + I + G + (X − M)
Why this is the answer
GDP is consumption plus investment plus government purchases plus net exports (exports minus imports).
Answer
A · C + I + G + (X − M)
4.Economics concepts
Answer: A · 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
A · Equal to marginal cost
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