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 €8. Its price elasticity of demand is −1.5. The firm changes the price by +10%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €8Q1 = 2 000E = −1.5%ΔP = +10%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 5000 − 50P, with P in euros. At which price P is total revenue as large as possible?
Q = 5000 − 50P
P = €
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- AThe world price of steel rises sharply for all countries that trade it
- BDomestic steel prices fall and imports rise
- CDomestic consumers gain surplus
- DDomestic steel prices rise and domestic production increases
4.Economics conceptsHard
The Laffer curve illustrates that:
- AHigher tax rates always increase tax revenue
- BLower tax rates always reduce tax revenue, whatever the starting rate
- CTax revenue is unrelated to tax rates
- DBeyond some point, raising tax rates can reduce total tax revenue
3Solutions
1.Price elasticity of demand
Answer: ΔR = −1040 €
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 = 8·1.1 = €8.80
Q2 = 2 000·0.85 = 1700
Change in revenue
ΔR = 8.8·1700 − 8·2 000 = 14 960.00 − 16 000 = −€1 040.00
Answer
ΔR = −€1 040.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: P = 50 €
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·(5000 − 50P) = 5000P − 50P²
Set the derivative to zero
dR/dP = 5000 − 100P = 0
P = 5000/100 = €50.00
Answer
P = €50.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · 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
D · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: D · Beyond some point, raising tax rates can reduce total tax revenue
Why this is the answer
Very high rates discourage taxed activity or encourage avoidance, so revenue peaks at some rate between 0 and 100%; where that peak lies is debated.
Answer
D · Beyond some point, raising tax rates can reduce total tax revenue
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