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 €40.00 to €34.00, weekly sales change from 800 to 870. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €34.00Q1 = 800Q2 = 870
E =
2.Price elasticity of demandHard
The demand for a product is Q = 600 − 10P, with P in euros. At which price P is the price elasticity of demand equal to −2?
Q = 600 − 10PE = −2
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 elastic
- C-0.5, so demand is inelastic
- D-2, so demand is elastic
4.Economics conceptsHard
Purchasing power parity (PPP) suggests that, in the long run, exchange rates adjust so that:
- ATrade balances are always zero
- BInterest rates are equal in all countries
- CEvery currency ends up having the same nominal value as the US dollar
- DThe same basket of goods costs the same in different countries
3Solutions
1.Price elasticity of demand
Answer: E = −0.517
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
(870 − 800)/((800 + 870)/2) = 70/835 = 0.08383
Relative change in price
(34 − 40)/((40 + 34)/2) = −6/37 = −0.1622
Elasticity
E = 0.08383/−0.1622 = −0.517
Answer
E = −0.517
2.Price elasticity of demand
Answer: P = 40 €
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 = −10P/(600 − 10P)
Solve for P
−10P = −2·(600 − 10P)
P·(−10 − 20) = −1200 → P = €40.00
Answer
P = €40.00
Check: Q = 200, E = −10·40/200 = −2.
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: D · 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
D · The same basket of goods costs the same in different countries
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