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 €5.50, weekly sales change from 1200 to 1500. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €8.00P2 = €5.50Q1 = 1200Q2 = 1500
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 80 − 0.02Q, with P in euros. Find the price elasticity of demand E when 800 units are sold.
P = 80 − 0.02QQ = 800
E =
3.Economics conceptsMedium
Overfishing in international waters is an example of:
- AA natural monopoly
- BA Giffen good
- CPrice discrimination
- DThe tragedy of the commons
4.Economics conceptsHard
According to the quantity theory of money (MV = PY), if velocity and real output are constant, a 5% rise in the money supply leads to:
- AAbout a 5% rise in real output
- BA 5% fall in velocity
- CNo change in prices
- DAbout a 5% rise in the price level
3Solutions
1.Price elasticity of demand
Answer: E = −0.6
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
(1500 − 1200)/((1200 + 1500)/2) = 300/1350 = 0.2222
Relative change in price
(5.5 − 8)/((8 + 5.5)/2) = −2.5/6.75 = −0.3704
Elasticity
E = 0.2222/−0.3704 = −0.6
Answer
E = −0.6
2.Price elasticity of demand
Answer: E = −4
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.
Price at this quantity
P = 80 − 0.02·800 = €64.00
Point elasticity
dQ/dP = −1/0.02 = −50
E = −50·64/800 = −4
Answer
E = −4
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · The tragedy of the commons
Why this is the answer
When a common resource is rival but people cannot be excluded, each user ignores the cost they impose on others, leading to overuse.
Answer
D · The tragedy of the commons
4.Economics concepts
Answer: D · About a 5% rise in the price level
Why this is the answer
With V and Y constant, M and P move proportionally, so prices rise about 5%. This is the classical view of money neutrality in the long run.
Answer
D · About a 5% rise in the price level
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