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 10 000 units per month at €15. Its price elasticity of demand is −2. The firm changes the price by +10%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €15Q1 = 10 000E = −2%ΔP = +10%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 2000 − 50P, with P in euros. At which price P is the price elasticity of demand equal to −0.25?
Q = 2000 − 50PE = −0.25
P = €
3.Economics conceptsMedium
A per-unit tax is placed on a good with very inelastic demand and elastic supply. Who bears most of the tax burden?
- AProducers
- BConsumers
- CThe government
- DIt is always split equally
4.Economics conceptsHard
According to prospect theory (Kahneman and Tversky), people typically:
- APrefer risk when facing gains of any size
- BTreat losses and gains of the same size as equally important
- CAlways maximise expected monetary value
- DFeel losses more strongly than equal-sized gains
3Solutions
1.Price elasticity of demand
Answer: ΔR = −18000 €
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 = 15·1.1 = €16.50
Q2 = 10 000·0.8 = 8000
Change in revenue
ΔR = 16.5·8000 − 15·10 000 = 132 000.00 − 150 000 = −€18 000.00
Answer
ΔR = −€18 000.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: P = 8 €
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/(2000 − 50P)
Solve for P
−50P = −0.25·(2000 − 50P)
P·(−50 − 12.5) = −500 → P = €8.00
Answer
P = €8.00
Check: Q = 1600, E = −50·8/1600 = −0.25.
3.Economics concepts
Answer: B · Consumers
Why this is the answer
The tax burden falls mainly on the side of the market that is less elastic; here buyers cannot cut back, so the price they pay rises by most of the tax.
Answer
B · Consumers
4.Economics concepts
Answer: D · Feel losses more strongly than equal-sized gains
Why this is the answer
The value function is steeper for losses than for gains and is measured relative to a reference point, explaining behaviour that expected utility theory struggles with.
Answer
D · Feel losses more strongly than equal-sized gains
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