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 €5. 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 = €5Q1 = 10 000E = −0.5%ΔP = +15%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 300 − 10P, with P in euros. At which price P is total revenue as large as possible?
Q = 300 − 10P
P = €
3.Economics conceptsMedium
A currency depreciation tends to:
- AReduce the price of all domestic goods and make imports cheaper
- BMake imports cheaper
- CMake exports cheaper abroad and imports more expensive
- DHave no effect on trade
4.Economics conceptsHard
According to the quantity theory of money (MV = PY), if velocity and real output are constant, a 5% rise in the money supply leads to:
- ANo change in prices
- BAbout a 5% rise in the price level
- CA 5% fall in velocity
- DAbout a 5% rise in real output
3Solutions
1.Price elasticity of demand
Answer: ΔR = 3188 €
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 = 5·1.15 = €5.75
Q2 = 10 000·0.925 = 9250
Change in revenue
ΔR = 5.75·9250 − 5·10 000 = 53 187.50 − 50 000 = €3 187.50
Answer
ΔR = €3 187.50
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: P = 15 €
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·(300 − 10P) = 300P − 10P²
Set the derivative to zero
dR/dP = 300 − 20P = 0
P = 300/20 = €15.00
Answer
P = €15.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: C · 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
C · Make exports cheaper abroad and imports more expensive
4.Economics concepts
Answer: B · About a 5% rise in the price level
Why this is the answer
With V and Y constant, M and P move proportionally, so prices rise about 5%. This is the classical view of money neutrality in the long run.
Answer
B · About a 5% rise in the price level
ExamProblems · examproblems.com/courses/microeconomics