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 €10. Its price elasticity of demand is −1.5. The firm changes the price by −5%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €10Q1 = 5 000E = −1.5%ΔP = −5%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 480 − 8P, with P in euros. At which price P is total revenue as large as possible?
Q = 480 − 8P
P = €
3.Economics conceptsMedium
A public good is:
- AProvided only by private firms
- BAny good bought by the government
- CRival and excludable
- DNon-rival and non-excludable
4.Economics conceptsHard
In the Solow growth model, sustained long-run growth in output per worker comes from:
- AA higher saving rate alone
- BPopulation growth
- CGovernment budget deficits
- DTechnological progress
3Solutions
1.Price elasticity of demand
Answer: ΔR = 1063 €
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 = 10·0.95 = €9.50
Q2 = 5 000·1.075 = 5375
Change in revenue
ΔR = 9.5·5375 − 10·5 000 = 51 062.50 − 50 000 = €1 062.50
Answer
ΔR = €1 062.50
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: P = 30 €
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.
Revenue as a function of price
R = P·(480 − 8P) = 480P − 8P²
Set the derivative to zero
dR/dP = 480 − 16P = 0
P = 480/16 = €30.00
Answer
P = €30.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · Non-rival and non-excludable
Why this is the answer
Public goods can be used by many at once and people cannot easily be excluded, leading to free-riding and under-provision by markets.
Answer
D · Non-rival and non-excludable
4.Economics concepts
Answer: D · Technological progress
Why this is the answer
A higher saving rate raises the steady-state level of output per worker but not its long-run growth rate; only technological progress produces continuous growth.
Answer
D · Technological progress
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