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 €25.00 to €19.00, weekly sales change from 400 to 550. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €19.00Q1 = 400Q2 = 550
E =
2.Price elasticity of demandHard
The demand for a product is Q = 160 − 8P, with P in euros. Find the price elasticity of demand E at a price of €6.
Q = 160 − 8PP = €6
E =
3.Economics conceptsMedium
Comparative advantage means a country should specialise in goods it can produce:
- AAt a lower opportunity cost than other countries
- BOnly for its own consumption
- CWith the most workers
- DMore cheaply in absolute terms than every other country
4.Economics conceptsHard
Using the "rule of 70", an economy growing at 7% per year will double its real GDP in about:
- A70 years
- B7 years
- C49 years
- D10 years
3Solutions
1.Price elasticity of demand
Answer: E = −1.158
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
(550 − 400)/((400 + 550)/2) = 150/475 = 0.3158
Relative change in price
(19 − 25)/((25 + 19)/2) = −6/22 = −0.2727
Elasticity
E = 0.3158/−0.2727 = −1.158
Answer
E = −1.158
2.Price elasticity of demand
Answer: E = −0.4286
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.
Quantity at this price
Q = 160 − 8·6 = 112
Point elasticity
dQ/dP = −8
E = (dQ/dP)·P/Q = −8·6/112 = −0.4286
Answer
E = −0.4286
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: A · 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
A · At a lower opportunity cost than other countries
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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