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 500 to 690. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €19.00Q1 = 500Q2 = 690
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1250 − 25P, with P in euros. At which price P is the price elasticity of demand equal to −0.25?
Q = 1250 − 25PE = −0.25
P = €
3.Economics conceptsMedium
Education generates benefits for society beyond the individual student. Without intervention, the market will likely:
- AOver-provide education compared with the social optimum
- BStop providing education altogether
- CProvide exactly the efficient amount of education, as prices reflect all benefits
- DUnder-provide education compared with the social optimum
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 = −1.171
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
(690 − 500)/((500 + 690)/2) = 190/595 = 0.3193
Relative change in price
(19 − 25)/((25 + 19)/2) = −6/22 = −0.2727
Elasticity
E = 0.3193/−0.2727 = −1.171
Answer
E = −1.171
2.Price elasticity of demand
Answer: P = 10 €
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.
Elasticity as a function of price
E = −25P/(1250 − 25P)
Solve for P
−25P = −0.25·(1250 − 25P)
P·(−25 − 6.25) = −312.5 → P = €10.00
Answer
P = €10.00
Check: Q = 1000, E = −25·10/1000 = −0.25.
3.Economics concepts
Answer: D · Under-provide education compared with the social optimum
Why this is the answer
Private decisions ignore external benefits, so output is below the socially optimal level; subsidies or public provision can raise it.
Answer
D · Under-provide education compared with the social optimum
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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