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 €5.00 to €6.00, weekly sales change from 1200 to 1010. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €6.00Q1 = 1200Q2 = 1010
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1000 − 20P, with P in euros. At which price P is total revenue as large as possible?
Q = 1000 − 20P
P = €
3.Economics conceptsMedium
Unemployment benefits and progressive income taxes are called automatic stabilisers because they:
- AFix the exchange rate automatically
- BPrevent all recessions from happening
- CKeep the government budget balanced in every year of the business cycle
- DReduce fluctuations in demand without new government decisions
4.Economics conceptsHard
Using the "rule of 70", an economy growing at 7% per year will double its real GDP in about:
- A70 years
- B10 years
- C49 years
- D7 years
3Solutions
1.Price elasticity of demand
Answer: E = −0.9457
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
(1010 − 1200)/((1200 + 1010)/2) = −190/1105 = −0.1719
Relative change in price
(6 − 5)/((5 + 6)/2) = 1/5.5 = 0.1818
Elasticity
E = −0.1719/0.1818 = −0.9457
Answer
E = −0.9457
2.Price elasticity of demand
Answer: P = 25 €
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·(1000 − 20P) = 1000P − 20P²
Set the derivative to zero
dR/dP = 1000 − 40P = 0
P = 1000/40 = €25.00
Answer
P = €25.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · Reduce fluctuations in demand without new government decisions
Why this is the answer
In a downturn tax revenue falls and benefit payments rise automatically, supporting incomes and spending; the reverse happens in a boom.
Answer
D · Reduce fluctuations in demand without new government decisions
4.Economics concepts
Answer: B · 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
B · 10 years
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