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 800 to 200. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €5.50Q1 = 800Q2 = 200
E =
2.Price elasticity of demandHard
The demand for a product is Q = 60 − 2P, with P in euros. Find the price elasticity of demand E at a price of €23.
Q = 60 − 2PP = €23
E =
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- AThe world price of steel rises sharply for all countries that trade it
- BDomestic consumers gain surplus
- CDomestic steel prices fall and imports rise
- DDomestic steel prices rise and domestic production increases
4.Economics conceptsHard
The "Taylor principle" says that, to stabilise inflation, a central bank should respond to a 1 percentage point rise in inflation by:
- ACutting the nominal rate
- BKeeping the nominal rate unchanged
- CRaising the nominal interest rate by more than 1 percentage point
- DRaising the nominal interest rate, but by less than 1 percentage point
3Solutions
1.Price elasticity of demand
Answer: E = −3.8
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
(200 − 800)/((800 + 200)/2) = −600/500 = −1.2
Relative change in price
(5.5 − 4)/((4 + 5.5)/2) = 1.5/4.75 = 0.3158
Elasticity
E = −1.2/0.3158 = −3.8
Answer
E = −3.8
2.Price elasticity of demand
Answer: E = −3.286
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 = 60 − 2·23 = 14
Point elasticity
dQ/dP = −2
E = (dQ/dP)·P/Q = −2·23/14 = −3.286
Answer
E = −3.286
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · 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
D · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: C · Raising the nominal interest rate by more than 1 percentage point
Why this is the answer
Only by raising nominal rates more than one-for-one does the real interest rate rise, cooling demand and bringing inflation back down.
Answer
C · Raising the nominal interest rate by more than 1 percentage point
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