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 1 000 units per month at €5. Its price elasticity of demand is −0.4. The firm changes the price by −20%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €5Q1 = 1 000E = −0.4%ΔP = −20%
ΔR = €
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 30 − 0.1Q, with P in euros. Find the price elasticity of demand E when 90 units are sold.
P = 30 − 0.1QQ = 90
E =
3.Economics conceptsMedium
Comparative advantage means a country should specialise in goods it can produce:
- AWith the most workers
- BMore cheaply in absolute terms than every other country
- COnly for its own consumption
- DAt a lower opportunity cost than other countries
4.Economics conceptsHard
The Fisher effect predicts that, in the long run, a permanent 2 percentage point rise in expected inflation will:
- ARaise nominal interest rates by about 2 points, leaving real rates unchanged
- BHave no effect on nominal interest rates, so real interest rates fall by about 2 points
- CRaise real interest rates by about 2 points
- DLower nominal interest rates by about 2 points
3Solutions
1.Price elasticity of demand
Answer: ΔR = −680 €
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 = 5·0.8 = €4.00
Q2 = 1 000·1.08 = 1080
Change in revenue
ΔR = 4·1080 − 5·1 000 = 4 320.00 − 5 000 = −€680.00
Answer
ΔR = −€680.00
|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.
Price at this quantity
P = 30 − 0.1·90 = €21.00
Point elasticity
dQ/dP = −1/0.1 = −10
E = −10·21/90 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · At a lower opportunity cost than other countries
Why this is the answer
Even a country that is less efficient at everything gains from trade by specialising where its opportunity cost is lowest.
Answer
D · At a lower opportunity cost than other countries
4.Economics concepts
Answer: A · Raise nominal interest rates by about 2 points, leaving real rates unchanged
Why this is the answer
Lenders demand compensation for expected inflation, so nominal rates move one-for-one with it in the long run while the real rate is set by real factors.
Answer
A · Raise nominal interest rates by about 2 points, leaving real rates unchanged
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