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 2 500 units per month at €10. Its price elasticity of demand is −2.5. The firm changes the price by −10%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €10Q1 = 2 500E = −2.5%ΔP = −10%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 200 − 10P, with P in euros. At which price P is total revenue as large as possible?
Q = 200 − 10P
P = €
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AAverage variable cost
- BAverage fixed cost
- CMarginal revenue
- DAverage total cost
4.Economics conceptsHard
In the Mundell–Fleming model with perfect capital mobility and a floating exchange rate:
- AMonetary policy is effective but fiscal policy is largely ineffective
- BFiscal policy is effective, but monetary policy is largely ineffective
- CBoth policies are equally effective
- DBoth policies have no effect on output
3Solutions
1.Price elasticity of demand
Answer: ΔR = 3125 €
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 = 10·0.9 = €9.00
Q2 = 2 500·1.25 = 3125
Change in revenue
ΔR = 9·3125 − 10·2 500 = 28 125.00 − 25 000 = €3 125.00
Answer
ΔR = €3 125.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: P = 10 €
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·(200 − 10P) = 200P − 10P²
Set the derivative to zero
dR/dP = 200 − 20P = 0
P = 200/20 = €10.00
Answer
P = €10.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: A · Average variable cost
Why this is the answer
If price covers average variable cost, producing reduces losses by contributing to fixed costs; below AVC, shutting down loses less.
Answer
A · Average variable cost
4.Economics concepts
Answer: A · Monetary policy is effective but fiscal policy is largely ineffective
Why this is the answer
Under floating rates, fiscal expansion causes appreciation that crowds out net exports, while monetary expansion causes depreciation that boosts output; under fixed rates the result is reversed.
Answer
A · Monetary policy is effective but fiscal policy is largely ineffective
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