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 €4.50, weekly sales change from 1000 to 1200. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €4.50Q1 = 1000Q2 = 1200
E =
2.Price elasticity of demandHard
The demand for a product is Q = 600 − 20P, with P in euros. Find the price elasticity of demand E at a price of €12.
Q = 600 − 20PP = €12
E =
3.Economics conceptsMedium
Education generates benefits for society beyond the individual student. Without intervention, the market will likely:
- AProvide exactly the efficient amount of education, as prices reflect all benefits
- BOver-provide education compared with the social optimum
- CStop providing education altogether
- DUnder-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:
- A75% above marginal cost, as a share of price
- B25% above marginal cost, as a share of price
- C4 times marginal cost
- DEqual to marginal cost
3Solutions
1.Price elasticity of demand
Answer: E = −1.727
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
(1200 − 1000)/((1000 + 1200)/2) = 200/1100 = 0.1818
Relative change in price
(4.5 − 5)/((5 + 4.5)/2) = −0.5/4.75 = −0.1053
Elasticity
E = 0.1818/−0.1053 = −1.727
Answer
E = −1.727
2.Price elasticity of demand
Answer: E = −0.6667
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 = 600 − 20·12 = 360
Point elasticity
dQ/dP = −20
E = (dQ/dP)·P/Q = −20·12/360 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
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: B · 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
B · 25% above marginal cost, as a share of price
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