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 €12.00 to €16.00, weekly sales change from 800 to 270. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €12.00P2 = €16.00Q1 = 800Q2 = 270
E =
2.Price elasticity of demandHard
The demand for a product is Q = 320 − 4P, with P in euros. Find the price elasticity of demand E at a price of €48.
Q = 320 − 4PP = €48
E =
3.Economics conceptsMedium
Comparative advantage means a country should specialise in goods it can produce:
- AOnly for its own consumption
- BMore cheaply in absolute terms than every other country
- CWith the most workers
- DAt a lower opportunity cost than other countries
4.Economics conceptsHard
A monopolist faces demand P = 100 − Q and has constant marginal cost of 20. What are its profit-maximising output and price?
- AQ = 50, P = 50
- BQ = 80, P = 20
- CQ = 40, P = 60
- DQ = 40, P = 20
3Solutions
1.Price elasticity of demand
Answer: E = −3.467
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
(270 − 800)/((800 + 270)/2) = −530/535 = −0.9907
Relative change in price
(16 − 12)/((12 + 16)/2) = 4/14 = 0.2857
Elasticity
E = −0.9907/0.2857 = −3.467
Answer
E = −3.467
2.Price elasticity of demand
Answer: E = −1.5
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.
Quantity at this price
Q = 320 − 4·48 = 128
Point elasticity
dQ/dP = −4
E = (dQ/dP)·P/Q = −4·48/128 = −1.5
Answer
E = −1.5
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · 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
D · At a lower opportunity cost than other countries
4.Economics concepts
Answer: C · Q = 40, P = 60
Why this is the answer
Setting MR = MC gives 100 − 2Q = 20, so Q = 40; the price from the demand curve is 100 − 40 = 60.
Answer
C · Q = 40, P = 60
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