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 200 to 230. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €4.50Q1 = 200Q2 = 230
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1000 − 25P, with P in euros. Find the price elasticity of demand E at a price of €30.
Q = 1000 − 25PP = €30
E =
3.Economics conceptsMedium
A Gini coefficient of 0 indicates:
- AZero unemployment
- BPerfect equality of income
- CZero economic growth
- DPerfect inequality of income
4.Economics conceptsHard
A lump-sum tax (a fixed amount, independent of output) is imposed on a profit-maximising monopolist. In the short run, its output will:
- AFall, because the tax raises the firm's average cost
- BRise to make up for the tax
- CStay the same, because MR and MC do not change
- DFall to zero
3Solutions
1.Price elasticity of demand
Answer: E = −1.326
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
(230 − 200)/((200 + 230)/2) = 30/215 = 0.1395
Relative change in price
(4.5 − 5)/((5 + 4.5)/2) = −0.5/4.75 = −0.1053
Elasticity
E = 0.1395/−0.1053 = −1.326
Answer
E = −1.326
2.Price elasticity of demand
Answer: E = −3
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 = 1000 − 25·30 = 250
Point elasticity
dQ/dP = −25
E = (dQ/dP)·P/Q = −25·30/250 = −3
Answer
E = −3
|E| > 1: demand is elastic.
3.Economics concepts
Answer: B · 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
B · Perfect equality of income
4.Economics concepts
Answer: C · Stay the same, because MR and MC do not change
Why this is the answer
A lump-sum tax is like a fixed cost: it lowers profit but does not change MR or MC, so the optimal quantity and price stay the same (unless the firm exits).
Answer
C · Stay the same, because MR and MC do not change
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