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 €40.00 to €34.00, weekly sales change from 800 to 940. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €34.00Q1 = 800Q2 = 940
E =
2.Price elasticity of demandHard
The demand for a product is Q = 5000 − 50P, with P in euros. At which price P is the price elasticity of demand equal to −0.25?
Q = 5000 − 50PE = −0.25
P = €
3.Economics conceptsMedium
The income elasticity of demand for a good is -0.4. The good is:
- AAn inferior good
- BA complement
- CA normal necessity
- DA luxury good
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:
- ARise to make up for the tax
- BStay the same, because MR and MC do not change
- CFall to zero
- DFall, because the tax raises the firm's average cost
3Solutions
1.Price elasticity of demand
Answer: E = −0.9923
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
(940 − 800)/((800 + 940)/2) = 140/870 = 0.1609
Relative change in price
(34 − 40)/((40 + 34)/2) = −6/37 = −0.1622
Elasticity
E = 0.1609/−0.1622 = −0.9923
Answer
E = −0.9923
2.Price elasticity of demand
Answer: P = 20 €
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 = −50P/(5000 − 50P)
Solve for P
−50P = −0.25·(5000 − 50P)
P·(−50 − 12.5) = −1250 → P = €20.00
Answer
P = €20.00
Check: Q = 4000, E = −50·20/4000 = −0.25.
3.Economics concepts
Answer: A · An inferior good
Why this is the answer
A negative income elasticity means demand falls as income rises, which defines an inferior good; luxuries have income elasticity above 1.
Answer
A · An inferior good
4.Economics concepts
Answer: B · 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
B · Stay the same, because MR and MC do not change
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