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 €5.00 to €3.50, weekly sales change from 100 to 160. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €3.50Q1 = 100Q2 = 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 −0.25?
Q = 5000 − 50PE = −0.25
P = €
3.Economics conceptsMedium
Crowding out refers to:
- AOvercrowded public services
- BImports replacing domestic production
- CHigher government borrowing raising interest rates and reducing private investment
- DToo many firms entering a market
4.Economics conceptsHard
The Marshall–Lerner condition states that a currency depreciation improves the trade balance if:
- AInterest rates rise at the same time
- BThe country has a budget surplus
- CExports and imports have zero price elasticity
- DThe sum of the price elasticities of demand for exports and imports exceeds 1
3Solutions
1.Price elasticity of demand
Answer: E = −1.308
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 − 100)/((100 + 160)/2) = 60/130 = 0.4615
Relative change in price
(3.5 − 5)/((5 + 3.5)/2) = −1.5/4.25 = −0.3529
Elasticity
E = 0.4615/−0.3529 = −1.308
Answer
E = −1.308
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 = −50P/(5000 − 50P)
Solve for P
−50P = −0.25·(5000 − 50P)
P·(−50 − 12.5) = −1250 → P = €20.00
Answer
P = €20.00
Check: Q = 4000, E = −50·20/4000 = −0.25.
3.Economics concepts
Answer: C · Higher government borrowing raising interest rates and reducing private investment
Why this is the answer
When government borrowing raises interest rates, some private investment is no longer profitable, reducing the net effect of fiscal expansion.
Answer
C · Higher government borrowing raising interest rates and reducing private investment
4.Economics concepts
Answer: D · The sum of the price elasticities of demand for exports and imports exceeds 1
Why this is the answer
If export and import demand are elastic enough (absolute values summing to more than 1), volume effects outweigh the higher import prices and the balance improves.
Answer
D · The sum of the price elasticities of demand for exports and imports exceeds 1
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