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 5 000 units per month at €4. Its price elasticity of demand is −0.4. The firm changes the price by +5%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €4Q1 = 5 000E = −0.4%ΔP = +5%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 160 − 8P, with P in euros. At which price P is the price elasticity of demand equal to −4?
Q = 160 − 8PE = −4
P = €
3.Economics conceptsMedium
A per-unit tax is placed on a good with very inelastic demand and elastic supply. Who bears most of the tax burden?
- AIt is always split equally
- BConsumers
- CThe government
- DProducers
4.Economics conceptsHard
The "Taylor principle" says that, to stabilise inflation, a central bank should respond to a 1 percentage point rise in inflation by:
- ARaising the nominal interest rate, but by less than 1 percentage point
- BRaising the nominal interest rate by more than 1 percentage point
- CKeeping the nominal rate unchanged
- DCutting the nominal rate
3Solutions
1.Price elasticity of demand
Answer: ΔR = 580 €
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 = 4·1.05 = €4.20
Q2 = 5 000·0.98 = 4900
Change in revenue
ΔR = 4.2·4900 − 4·5 000 = 20 580.00 − 20 000 = €580.00
Answer
ΔR = €580.00
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: P = 16 €
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.
Elasticity as a function of price
E = −8P/(160 − 8P)
Solve for P
−8P = −4·(160 − 8P)
P·(−8 − 32) = −640 → P = €16.00
Answer
P = €16.00
Check: Q = 32, E = −8·16/32 = −4.
3.Economics concepts
Answer: B · Consumers
Why this is the answer
The tax burden falls mainly on the side of the market that is less elastic; here buyers cannot cut back, so the price they pay rises by most of the tax.
Answer
B · Consumers
4.Economics concepts
Answer: B · Raising the nominal interest rate by more than 1 percentage point
Why this is the answer
Only by raising nominal rates more than one-for-one does the real interest rate rise, cooling demand and bringing inflation back down.
Answer
B · Raising the nominal interest rate by more than 1 percentage point
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