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
A product sells 5 000 units per month at €12. Its price elasticity of demand is −0.4. The firm changes the price by −10%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €12Q1 = 5 000E = −0.4%ΔP = −10%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 240 − 4P, with P in euros. At which price P is the price elasticity of demand equal to −3?
Q = 240 − 4PE = −3
P = €
3.Economics conceptsMedium
The law of diminishing marginal returns states that:
- ALong-run average costs always fall as output rises
- BAdding more of a variable input to a fixed input eventually lowers the extra output per unit added
- CTotal output always falls as more workers are hired
- DConsumers get less satisfaction as prices rise
4.Economics conceptsHard
Moral hazard arises when:
- AOne party changes behaviour after a contract because they do not bear the full consequences
- BA buyer cannot observe product quality before buying, so low-quality sellers dominate the market
- CPrices are too high for poor consumers
- DTwo firms collude on price
3Solutions
1.Price elasticity of demand
Answer: ΔR = −3840 €
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.
New price and quantity
P2 = 12·0.9 = €10.80
Q2 = 5 000·1.04 = 5200
Change in revenue
ΔR = 10.8·5200 − 12·5 000 = 56 160.00 − 60 000 = −€3 840.00
Answer
ΔR = −€3 840.00
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: P = 45 €
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 = −4P/(240 − 4P)
Solve for P
−4P = −3·(240 − 4P)
P·(−4 − 12) = −720 → P = €45.00
Answer
P = €45.00
Check: Q = 60, E = −4·45/60 = −3.
3.Economics concepts
Answer: B · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
Why this is the answer
In the short run, with at least one fixed factor, marginal product eventually falls, which makes marginal cost rise.
Answer
B · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
4.Economics concepts
Answer: A · One party changes behaviour after a contract because they do not bear the full consequences
Why this is the answer
Moral hazard is hidden action after the contract, such as an insured driver taking more risks. Adverse selection is hidden information before the contract.
Answer
A · One party changes behaviour after a contract because they do not bear the full consequences
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