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 €4.00 to €1.50, weekly sales change from 100 to 180. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €1.50Q1 = 100Q2 = 180
E =
2.Price elasticity of demandHard
The demand for a product is Q = 2000 − 20P, with P in euros. At which price P is total revenue as large as possible?
Q = 2000 − 20P
P = €
3.Economics conceptsMedium
A Gini coefficient of 0 indicates:
- APerfect equality of income
- BPerfect inequality of income
- CZero unemployment
- DZero economic growth
4.Economics conceptsHard
A monopolist maximises profit where:
- AMarginal revenue equals marginal cost
- BTotal revenue is at its maximum
- CPrice equals marginal cost
- DAverage cost is at its minimum
3Solutions
1.Price elasticity of demand
Answer: E = −0.6286
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
(180 − 100)/((100 + 180)/2) = 80/140 = 0.5714
Relative change in price
(1.5 − 4)/((4 + 1.5)/2) = −2.5/2.75 = −0.9091
Elasticity
E = 0.5714/−0.9091 = −0.6286
Answer
E = −0.6286
2.Price elasticity of demand
Answer: P = 50 €
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.
Revenue as a function of price
R = P·(2000 − 20P) = 2000P − 20P²
Set the derivative to zero
dR/dP = 2000 − 40P = 0
P = 2000/40 = €50.00
Answer
P = €50.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: A · Perfect equality of income
Why this is the answer
The Gini coefficient ranges from 0 (everyone has the same income) to 1 (one person has all income); higher values mean more inequality.
Answer
A · Perfect equality of income
4.Economics concepts
Answer: A · Marginal revenue equals marginal cost
Why this is the answer
Profit is maximised where MR = MC. For a monopolist, price is above MR, so P > MC, causing a deadweight loss.
Answer
A · Marginal revenue equals marginal cost
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