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 10 000 units per month at €10. Its price elasticity of demand is −0.5. The firm changes the price by −15%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €10Q1 = 10 000E = −0.5%ΔP = −15%
ΔR = €
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 60 − 0.05Q, with P in euros. Find the price elasticity of demand E when 960 units are sold.
P = 60 − 0.05QQ = 960
E =
3.Economics conceptsMedium
The principle of diminishing marginal utility states that:
- ASatisfaction rises as income falls
- BTotal satisfaction falls with each additional unit of the good that is consumed
- CExtra satisfaction from each additional unit consumed tends to fall
- DConsumers always prefer more expensive goods
4.Economics conceptsHard
A Giffen good is one where:
- AThe price never changes
- BDemand rises with income, like most goods
- CDemand rises because the good is a status symbol
- DQuantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
3Solutions
1.Price elasticity of demand
Answer: ΔR = −8625 €
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 = 10·0.85 = €8.50
Q2 = 10 000·1.075 = 10750
Change in revenue
ΔR = 8.5·10750 − 10·10 000 = 91 375.00 − 100 000 = −€8 625.00
Answer
ΔR = −€8 625.00
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: E = −0.25
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 = 60 − 0.05·960 = €12.00
Point elasticity
dQ/dP = −1/0.05 = −20
E = −20·12/960 = −0.25
Answer
E = −0.25
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · Extra satisfaction from each additional unit consumed tends to fall
Why this is the answer
As consumption of a good increases, the marginal utility of each extra unit usually declines, which helps explain downward-sloping demand.
Answer
C · Extra satisfaction from each additional unit consumed tends to fall
4.Economics concepts
Answer: D · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
Why this is the answer
For a Giffen good the income effect of a price rise (feeling poorer, buying more of the cheap staple) dominates the substitution effect, so demand slopes upward.
Answer
D · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
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