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 €12. Its price elasticity of demand is −0.6. The firm changes the price by −5%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €12Q1 = 10 000E = −0.6%ΔP = −5%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 200 − 5P, with P in euros. Find the price elasticity of demand E at a price of €28.
Q = 200 − 5PP = €28
E =
3.Economics conceptsMedium
The income elasticity of demand for a good is -0.4. The good is:
- AA luxury good
- BAn inferior good
- CA complement
- DA normal necessity
4.Economics conceptsHard
For a normal good, when its price falls, the substitution effect and income effect:
- ABoth increase the quantity demanded
- BBoth decrease the quantity demanded
- CCancel out exactly
- DWork in opposite directions
3Solutions
1.Price elasticity of demand
Answer: ΔR = −2580 €
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 = 12·0.95 = €11.40
Q2 = 10 000·1.03 = 10300
Change in revenue
ΔR = 11.4·10300 − 12·10 000 = 117 420.00 − 120 000 = −€2 580.00
Answer
ΔR = −€2 580.00
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: E = −2.333
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 = 200 − 5·28 = 60
Point elasticity
dQ/dP = −5
E = (dQ/dP)·P/Q = −5·28/60 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: B · An inferior good
Why this is the answer
A negative income elasticity means demand falls as income rises, which defines an inferior good; luxuries have income elasticity above 1.
Answer
B · An inferior good
4.Economics concepts
Answer: A · Both increase the quantity demanded
Why this is the answer
The substitution effect always favours the cheaper good, and for a normal good the higher real income also raises demand, so both effects reinforce each other.
Answer
A · Both increase the quantity demanded
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