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 4 000 units per month at €12. Its price elasticity of demand is −0.5. The firm changes the price by +5%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €12Q1 = 4 000E = −0.5%ΔP = +5%
ΔR = €
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −2, so Q = A·P^−2. At a price of €12, 2 000 units are sold. How many units Q are sold at a price of €10.80?
E = −2P1 = €12Q1 = 2 000P2 = €10.80
Q = units
3.Economics conceptsMedium
The income elasticity of demand for a good is -0.4. The good is:
- AA normal necessity
- BA complement
- CAn inferior good
- DA luxury good
4.Economics conceptsHard
A liquidity trap is a situation where:
- AThe central bank raises interest rates sharply to fight high and rapidly rising inflation
- BInterest rates are near zero and further monetary expansion has little effect on demand
- CBanks have no money left to lend
- DInflation is very high and rising
3Solutions
1.Price elasticity of demand
Answer: ΔR = 1140 €
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 = 12·1.05 = €12.60
Q2 = 4 000·0.975 = 3900
Change in revenue
ΔR = 12.6·3900 − 12·4 000 = 49 140.00 − 48 000 = €1 140.00
Answer
ΔR = €1 140.00
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: Q = 2469 units
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.
Ratio of the prices
P2/P1 = 10.8/12 = 0.9
New quantity
Q = 2 000·0.9−2 = 2 000·1.235 = 2469
Answer
Q = 2469
3.Economics concepts
Answer: C · 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
C · An inferior good
4.Economics concepts
Answer: B · Interest rates are near zero and further monetary expansion has little effect on demand
Why this is the answer
When nominal rates are near their lower bound, people hold extra money rather than spend it, so conventional monetary policy loses power and fiscal policy or unconventional tools matter more.
Answer
B · Interest rates are near zero and further monetary expansion has little effect on demand
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