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 €25.00 to €21.00, weekly sales change from 1000 to 1060. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €21.00Q1 = 1000Q2 = 1060
E =
2.Price elasticity of demandHard
The demand for a product is Q = 120 − 2P, with P in euros. At which price P is the price elasticity of demand equal to −4?
Q = 120 − 2PE = −4
P = €
3.Economics conceptsMedium
A country has 950 employed people and 50 unemployed people seeking work. Its unemployment rate is:
- A95%
- B5.3%
- C5%
- D50%
4.Economics conceptsHard
A regulator forces a natural monopoly to set price equal to marginal cost. The likely problem is that:
- AOutput falls below the monopoly level
- BConsumers face a shortage, because demand exceeds supply at that price
- CThe firm makes very large profits
- DThe firm makes a loss because average cost is above marginal cost
3Solutions
1.Price elasticity of demand
Answer: E = −0.335
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
(1060 − 1000)/((1000 + 1060)/2) = 60/1030 = 0.05825
Relative change in price
(21 − 25)/((25 + 21)/2) = −4/23 = −0.1739
Elasticity
E = 0.05825/−0.1739 = −0.335
Answer
E = −0.335
2.Price elasticity of demand
Answer: P = 48 €
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/(120 − 2P)
Solve for P
−2P = −4·(120 − 2P)
P·(−2 − 8) = −480 → P = €48.00
Answer
P = €48.00
Check: Q = 24, E = −2·48/24 = −4.
3.Economics concepts
Answer: C · 5%
Why this is the answer
The labour force is 950 + 50 = 1,000, so the rate is 50 / 1,000 = 5%.
Answer
C · 5%
4.Economics concepts
Answer: D · The firm makes a loss because average cost is above marginal cost
Why this is the answer
With falling average cost, marginal cost is below average cost, so marginal cost pricing does not cover total costs; subsidies or average cost pricing are alternatives.
Answer
D · The firm makes a loss because average cost is above marginal cost
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