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 €4.00 to €5.50, weekly sales change from 400 to 160. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €5.50Q1 = 400Q2 = 160
E =
2.Price elasticity of demandHard
The demand for a product is Q = 5000 − 50P, with P in euros. At which price P is the price elasticity of demand equal to −4?
Q = 5000 − 50PE = −4
P = €
3.Economics conceptsMedium
Comparative advantage means a country should specialise in goods it can produce:
- AOnly for its own consumption
- BWith the most workers
- CAt a lower opportunity cost than other countries
- DMore cheaply in absolute terms than every other country
4.Economics conceptsHard
Price discrimination by a firm requires that:
- AAll consumers have identical elasticity of demand and buy the same amount
- BIt has market power, can separate markets and prevent resale
- CIt operates in perfect competition
- DIts costs differ for each customer
3Solutions
1.Price elasticity of demand
Answer: E = −2.714
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
(160 − 400)/((400 + 160)/2) = −240/280 = −0.8571
Relative change in price
(5.5 − 4)/((4 + 5.5)/2) = 1.5/4.75 = 0.3158
Elasticity
E = −0.8571/0.3158 = −2.714
Answer
E = −2.714
2.Price elasticity of demand
Answer: P = 80 €
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/(5000 − 50P)
Solve for P
−50P = −4·(5000 − 50P)
P·(−50 − 200) = −20000 → P = €80.00
Answer
P = €80.00
Check: Q = 1000, E = −50·80/1000 = −4.
3.Economics concepts
Answer: C · At a lower opportunity cost than other countries
Why this is the answer
Even a country that is less efficient at everything gains from trade by specialising where its opportunity cost is lowest.
Answer
C · At a lower opportunity cost than other countries
4.Economics concepts
Answer: B · It has market power, can separate markets and prevent resale
Why this is the answer
To charge different prices for the same good, the firm needs market power, the ability to identify groups with different elasticities and to prevent arbitrage.
Answer
B · It has market power, can separate markets and prevent resale
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