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 €4.50, weekly sales change from 800 to 640. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €4.50Q1 = 800Q2 = 640
E =
2.Price elasticity of demandHard
The demand for a product is Q = 240 − 8P, with P in euros. At which price P is the price elasticity of demand equal to −2?
Q = 240 − 8PE = −2
P = €
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
According to the quantity theory of money (MV = PY), if velocity and real output are constant, a 5% rise in the money supply leads to:
- AA 5% fall in velocity
- BNo change in prices
- CAbout a 5% rise in the price level
- DAbout a 5% rise in real output
3Solutions
1.Price elasticity of demand
Answer: E = −1.889
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
(640 − 800)/((800 + 640)/2) = −160/720 = −0.2222
Relative change in price
(4.5 − 4)/((4 + 4.5)/2) = 0.5/4.25 = 0.1176
Elasticity
E = −0.2222/0.1176 = −1.889
Answer
E = −1.889
2.Price elasticity of demand
Answer: P = 20 €
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 = −8P/(240 − 8P)
Solve for P
−8P = −2·(240 − 8P)
P·(−8 − 16) = −480 → P = €20.00
Answer
P = €20.00
Check: Q = 80, E = −8·20/80 = −2.
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: C · About a 5% rise in the price level
Why this is the answer
With V and Y constant, M and P move proportionally, so prices rise about 5%. This is the classical view of money neutrality in the long run.
Answer
C · About a 5% rise in the price level
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