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 €20.00 to €10.00, weekly sales change from 400 to 480. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €20.00P2 = €10.00Q1 = 400Q2 = 480
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 100 − 0.2Q, with P in euros. Find the price elasticity of demand E when 200 units are sold.
P = 100 − 0.2QQ = 200
E =
3.Economics conceptsMedium
Education generates benefits for society beyond the individual student. Without intervention, the market will likely:
- AUnder-provide education compared with the social optimum
- BStop providing education altogether
- CProvide exactly the efficient amount of education, as prices reflect all benefits
- DOver-provide education compared with the social optimum
4.Economics conceptsHard
The Lerner index (P − MC)/P for a profit-maximising monopolist equals 1/|PED|. If |PED| = 4, the price is:
- A4 times marginal cost
- BEqual to marginal cost
- C75% above marginal cost, as a share of price
- D25% above marginal cost, as a share of price
3Solutions
1.Price elasticity of demand
Answer: E = −0.2727
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
(480 − 400)/((400 + 480)/2) = 80/440 = 0.1818
Relative change in price
(10 − 20)/((20 + 10)/2) = −10/15 = −0.6667
Elasticity
E = 0.1818/−0.6667 = −0.2727
Answer
E = −0.2727
2.Price elasticity of demand
Answer: E = −1.5
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 = 100 − 0.2·200 = €60.00
Point elasticity
dQ/dP = −1/0.2 = −5
E = −5·60/200 = −1.5
Answer
E = −1.5
|E| > 1: demand is elastic.
3.Economics concepts
Answer: A · 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
A · Under-provide education compared with the social optimum
4.Economics concepts
Answer: D · 25% above marginal cost, as a share of price
Why this is the answer
The markup (P − MC)/P = 1/4 = 0.25, so a quarter of the price is a margin above MC; more elastic demand means less market power.
Answer
D · 25% above marginal cost, as a share of price
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