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
A product sells 10 000 units per month at €10. Its price elasticity of demand is −2.5. The firm changes the price by −5%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €10Q1 = 10 000E = −2.5%ΔP = −5%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 1500 − 50P, with P in euros. Find the price elasticity of demand E at a price of €18.
Q = 1500 − 50PP = €18
E =
3.Economics conceptsMedium
The marginal cost curve cuts the average total cost curve:
- AWhere average total cost equals zero
- BAt the minimum point of average total cost
- CAt the maximum point of average total cost
- DNever, as the two curves are parallel
4.Economics conceptsHard
The J-curve effect describes why, after a depreciation, the trade balance may:
- AImprove immediately and permanently
- BWorsen at first and then improve
- CRemain unchanged for many years
- DImprove at first and then worsen
3Solutions
1.Price elasticity of demand
Answer: ΔR = 6875 €
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.
New price and quantity
P2 = 10·0.95 = €9.50
Q2 = 10 000·1.125 = 11250
Change in revenue
ΔR = 9.5·11250 − 10·10 000 = 106 875.00 − 100 000 = €6 875.00
Answer
ΔR = €6 875.00
|E| > 1: demand is elastic.
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 = 1500 − 50·18 = 600
Point elasticity
dQ/dP = −50
E = (dQ/dP)·P/Q = −50·18/600 = −1.5
Answer
E = −1.5
|E| > 1: demand is elastic.
3.Economics concepts
Answer: B · At the minimum point of average total cost
Why this is the answer
When MC is below ATC it pulls the average down, and when it is above it pushes the average up, so MC crosses ATC at its minimum.
Answer
B · At the minimum point of average total cost
4.Economics concepts
Answer: B · Worsen at first and then improve
Why this is the answer
In the short run, volumes are slow to adjust while import prices rise immediately, so the balance worsens before the Marshall–Lerner condition takes hold.
Answer
B · Worsen at first and then improve
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