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 €8.00 to €6.50, weekly sales change from 400 to 490. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €8.00P2 = €6.50Q1 = 400Q2 = 490
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −2.5, so Q = A·P^−2.5. At a price of €25, 10 000 units are sold. How many units Q are sold at a price of €32.50?
E = −2.5P1 = €25Q1 = 10 000P2 = €32.50
Q = units
3.Economics conceptsMedium
If the ECB raises its main interest rate, the most likely short-term effect is:
- ALower borrowing and spending, reducing inflationary pressure
- BHigher borrowing and spending, which adds to inflationary pressure
- CA fall in the value of the euro
- DAn immediate rise in GDP
4.Economics conceptsHard
Using the "rule of 70", an economy growing at 7% per year will double its real GDP in about:
- A70 years
- B49 years
- C7 years
- D10 years
3Solutions
1.Price elasticity of demand
Answer: E = −0.9775
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
(490 − 400)/((400 + 490)/2) = 90/445 = 0.2022
Relative change in price
(6.5 − 8)/((8 + 6.5)/2) = −1.5/7.25 = −0.2069
Elasticity
E = 0.2022/−0.2069 = −0.9775
Answer
E = −0.9775
2.Price elasticity of demand
Answer: Q = 5190 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 = 32.5/25 = 1.3
New quantity
Q = 10 000·1.3−2.5 = 10 000·0.519 = 5190
Answer
Q = 5190
3.Economics concepts
Answer: A · Lower borrowing and spending, reducing inflationary pressure
Why this is the answer
Higher rates make credit more expensive and saving more attractive, reducing demand and inflation; they also tend to strengthen the currency.
Answer
A · Lower borrowing and spending, reducing inflationary pressure
4.Economics concepts
Answer: D · 10 years
Why this is the answer
The doubling time is approximately 70 divided by the percentage growth rate, so 70 / 7 = 10 years, showing the power of compound growth.
Answer
D · 10 years
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