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 €12. Its price elasticity of demand is −0.6. The firm changes the price by −15%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €12Q1 = 10 000E = −0.6%ΔP = −15%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 400 − 10P, with P in euros. At which price P is total revenue as large as possible?
Q = 400 − 10P
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?
- AConsumers
- BIt is always split equally
- CThe government
- DProducers
4.Economics conceptsHard
Purchasing power parity (PPP) suggests that, in the long run, exchange rates adjust so that:
- ATrade balances are always zero
- BThe same basket of goods costs the same in different countries
- CEvery currency ends up having the same nominal value as the US dollar
- DInterest rates are equal in all countries
3Solutions
1.Price elasticity of demand
Answer: ΔR = −8820 €
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 = 12·0.85 = €10.20
Q2 = 10 000·1.09 = 10900
Change in revenue
ΔR = 10.2·10900 − 12·10 000 = 111 180.00 − 120 000 = −€8 820.00
Answer
ΔR = −€8 820.00
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: P = 20 €
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·(400 − 10P) = 400P − 10P²
Set the derivative to zero
dR/dP = 400 − 20P = 0
P = 400/20 = €20.00
Answer
P = €20.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: A · 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
A · Consumers
4.Economics concepts
Answer: B · The same basket of goods costs the same in different countries
Why this is the answer
PPP is based on the law of one price: if a good is cheaper in one country, arbitrage should push exchange rates towards equalising prices, though transport costs and non-traded goods limit this.
Answer
B · The same basket of goods costs the same in different countries
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