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 €26.00, weekly sales change from 1000 to 640. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €20.00P2 = €26.00Q1 = 1000Q2 = 640
E =
2.Price elasticity of demandHard
The demand for a product is Q = 60 − 2P, with P in euros. At which price P is the price elasticity of demand equal to −0.5?
Q = 60 − 2PE = −0.5
P = €
3.Economics conceptsMedium
Rising consumer confidence would most likely:
- AHave no effect on the economy
- BShift aggregate supply to the left
- CShift aggregate demand to the left
- DShift aggregate demand to the right
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
- BFall to zero
- CStay the same, because MR and MC do not change
- DRise to make up for the tax
3Solutions
1.Price elasticity of demand
Answer: E = −1.683
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
(640 − 1000)/((1000 + 640)/2) = −360/820 = −0.439
Relative change in price
(26 − 20)/((20 + 26)/2) = 6/23 = 0.2609
Elasticity
E = −0.439/0.2609 = −1.683
Answer
E = −1.683
2.Price elasticity of demand
Answer: P = 10 €
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 = −2P/(60 − 2P)
Solve for P
−2P = −0.5·(60 − 2P)
P·(−2 − 1) = −30 → P = €10.00
Answer
P = €10.00
Check: Q = 40, E = −2·10/40 = −0.5.
3.Economics concepts
Answer: D · Shift aggregate demand to the right
Why this is the answer
Higher confidence raises consumption at every price level, shifting AD right and raising output and, possibly, prices in the short run.
Answer
D · Shift aggregate demand to the right
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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