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
When the price of a ticket changes from €20.00 to €30.00, weekly sales change from 800 to 640. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €20.00P2 = €30.00Q1 = 800Q2 = 640
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −0.8, so Q = A·P^−0.8. At a price of €10, 2 000 units are sold. How many units Q are sold at a price of €6.00?
E = −0.8P1 = €10Q1 = 2 000P2 = €6.00
Q = units
3.Economics conceptsMedium
Nominal GDP grew by 5% and the GDP deflator rose by 2%. Real GDP grew by approximately:
- A2.5%
- B7%
- C3%
- D10%
4.Economics conceptsHard
A liquidity trap is a situation where:
- AInflation is very high and rising
- BThe central bank raises interest rates sharply to fight high and rapidly rising inflation
- CBanks have no money left to lend
- DInterest rates are near zero and further monetary expansion has little effect on demand
3Solutions
1.Price elasticity of demand
Answer: E = −0.5556
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.
Relative change in quantity
(640 − 800)/((800 + 640)/2) = −160/720 = −0.2222
Relative change in price
(30 − 20)/((20 + 30)/2) = 10/25 = 0.4
Elasticity
E = −0.2222/0.4 = −0.5556
Answer
E = −0.5556
2.Price elasticity of demand
Answer: Q = 3010 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 = 6/10 = 0.6
New quantity
Q = 2 000·0.6−0.8 = 2 000·1.505 = 3010
Answer
Q = 3010
3.Economics concepts
Answer: C · 3%
Why this is the answer
Subtracting the rise in prices from nominal growth gives real growth of roughly 5% − 2% = 3%.
Answer
C · 3%
4.Economics concepts
Answer: D · 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
D · Interest rates are near zero and further monetary expansion has little effect on demand
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