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 €8.00 to €7.50, weekly sales change from 500 to 530. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €8.00P2 = €7.50Q1 = 500Q2 = 530
E =
2.Price elasticity of demandHard
The demand for a product is Q = 240 − 8P, with P in euros. Find the price elasticity of demand E at a price of €12.
Q = 240 − 8PP = €12
E =
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic steel prices fall and imports rise
- BDomestic steel prices rise and domestic production increases
- CThe world price of steel rises sharply for all countries that trade it
- DDomestic consumers gain surplus
4.Economics conceptsHard
Why does the deadweight loss of a tax grow when the good's demand and supply are more elastic?
- APrices do not change, so consumers bear the whole burden of the tax instead
- BThe government collects more tax revenue
- CElastic markets have no consumer surplus
- DQuantity traded falls more, so more mutually beneficial trades are lost
3Solutions
1.Price elasticity of demand
Answer: E = −0.9029
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
(530 − 500)/((500 + 530)/2) = 30/515 = 0.05825
Relative change in price
(7.5 − 8)/((8 + 7.5)/2) = −0.5/7.75 = −0.06452
Elasticity
E = 0.05825/−0.06452 = −0.9029
Answer
E = −0.9029
2.Price elasticity of demand
Answer: E = −0.6667
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 = 240 − 8·12 = 144
Point elasticity
dQ/dP = −8
E = (dQ/dP)·P/Q = −8·12/144 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: B · Domestic steel prices rise and domestic production increases
Why this is the answer
The tariff raises the domestic price, increasing domestic output and government revenue but reducing consumer surplus and creating deadweight losses.
Answer
B · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: D · Quantity traded falls more, so more mutually beneficial trades are lost
Why this is the answer
The more responsive buyers and sellers are, the more the tax reduces quantity, and the bigger the triangle of lost surplus; DWL also rises roughly with the square of the tax.
Answer
D · Quantity traded falls more, so more mutually beneficial trades are lost
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