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 −2.5. The firm changes the price by +10%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €10Q1 = 10 000E = −2.5%ΔP = +10%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 640 − 8P, with P in euros. At which price P is total revenue as large as possible?
Q = 640 − 8P
P = €
3.Economics conceptsMedium
A currency depreciation tends to:
- AMake exports cheaper abroad and imports more expensive
- BReduce the price of all domestic goods and make imports cheaper
- CMake imports cheaper
- DHave no effect on trade
4.Economics conceptsHard
For a normal good, when its price falls, the substitution effect and income effect:
- ABoth decrease the quantity demanded
- BWork in opposite directions
- CBoth increase the quantity demanded
- DCancel out exactly
3Solutions
1.Price elasticity of demand
Answer: ΔR = −17500 €
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 = 10·1.1 = €11.00
Q2 = 10 000·0.75 = 7500
Change in revenue
ΔR = 11·7500 − 10·10 000 = 82 500.00 − 100 000 = −€17 500.00
Answer
ΔR = −€17 500.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: P = 40 €
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·(640 − 8P) = 640P − 8P²
Set the derivative to zero
dR/dP = 640 − 16P = 0
P = 640/16 = €40.00
Answer
P = €40.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: A · Make exports cheaper abroad and imports more expensive
Why this is the answer
A weaker currency improves export competitiveness and raises import prices, which can increase inflation.
Answer
A · Make exports cheaper abroad and imports more expensive
4.Economics concepts
Answer: C · 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
C · Both increase the quantity demanded
ExamProblems · examproblems.com/courses/microeconomics