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 €10.00 to €8.00, weekly sales change from 800 to 900. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €8.00Q1 = 800Q2 = 900
E =
2.Price elasticity of demandHard
The demand for a product is Q = 600 − 20P, with P in euros. At which price P is total revenue as large as possible?
Q = 600 − 20P
P = €
3.Economics conceptsMedium
The price of a good rises by 10% and quantity demanded falls by 20%. The price elasticity of demand is:
- A-2, so demand is inelastic
- B-0.5, so demand is inelastic
- C-0.5, so demand is elastic
- D-2, so demand is elastic
4.Economics conceptsHard
Moral hazard arises when:
- AA buyer cannot observe product quality before buying, so low-quality sellers dominate the market
- BOne party changes behaviour after a contract because they do not bear the full consequences
- CPrices are too high for poor consumers
- DTwo firms collude on price
3Solutions
1.Price elasticity of demand
Answer: E = −0.5294
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
(900 − 800)/((800 + 900)/2) = 100/850 = 0.1176
Relative change in price
(8 − 10)/((10 + 8)/2) = −2/9 = −0.2222
Elasticity
E = 0.1176/−0.2222 = −0.5294
Answer
E = −0.5294
2.Price elasticity of demand
Answer: P = 15 €
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.
Revenue as a function of price
R = P·(600 − 20P) = 600P − 20P²
Set the derivative to zero
dR/dP = 600 − 40P = 0
P = 600/40 = €15.00
Answer
P = €15.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · -2, so demand is elastic
Why this is the answer
PED = -20% / 10% = -2; since the absolute value is above 1, demand is elastic.
Answer
D · -2, so demand is elastic
4.Economics concepts
Answer: B · 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
B · One party changes behaviour after a contract because they do not bear the full consequences
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