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 2 000 units per month at €25. Its price elasticity of demand is −0.5. The firm changes the price by −20%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €25Q1 = 2 000E = −0.5%ΔP = −20%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 2000 − 50P, with P in euros. At which price P is total revenue as large as possible?
Q = 2000 − 50P
P = €
3.Economics conceptsMedium
In an oligopoly, firms are typically:
- AFew and interdependent in their decisions
- BA single seller in the market
- CMany and too small to affect the price
- DCompletely unregulated by competition law
4.Economics conceptsHard
The Fisher effect predicts that, in the long run, a permanent 2 percentage point rise in expected inflation will:
- AHave no effect on nominal interest rates, so real interest rates fall by about 2 points
- BRaise real interest rates by about 2 points
- CLower nominal interest rates by about 2 points
- DRaise nominal interest rates by about 2 points, leaving real rates unchanged
3Solutions
1.Price elasticity of demand
Answer: ΔR = −6000 €
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 = 25·0.8 = €20.00
Q2 = 2 000·1.1 = 2200
Change in revenue
ΔR = 20·2200 − 25·2 000 = 44 000.00 − 50 000 = −€6 000.00
Answer
ΔR = −€6 000.00
|E| < 1: demand is inelastic.
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.
Revenue as a function of price
R = P·(2000 − 50P) = 2000P − 50P²
Set the derivative to zero
dR/dP = 2000 − 100P = 0
P = 2000/100 = €20.00
Answer
P = €20.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: A · Few and interdependent in their decisions
Why this is the answer
Oligopolies have a few large firms whose pricing and output decisions affect each other, often analysed with game theory.
Answer
A · Few and interdependent in their decisions
4.Economics concepts
Answer: D · Raise nominal interest rates by about 2 points, leaving real rates unchanged
Why this is the answer
Lenders demand compensation for expected inflation, so nominal rates move one-for-one with it in the long run while the real rate is set by real factors.
Answer
D · Raise nominal interest rates by about 2 points, leaving real rates unchanged
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