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 €25. 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 = €25Q1 = 10 000E = −2.5%ΔP = −10%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 2000 − 20P, with P in euros. Find the price elasticity of demand E at a price of €70.
Q = 2000 − 20PP = €70
E =
3.Economics conceptsMedium
A minimum wage set above the equilibrium wage in a competitive labour market is predicted to cause:
- AA shortage of labour
- BA surplus of labour (unemployment)
- CNo change in employment
- DA fall in the wage rate
4.Economics conceptsHard
The Laffer curve illustrates that:
- ALower tax rates always reduce tax revenue, whatever the starting rate
- BBeyond some point, raising tax rates can reduce total tax revenue
- CTax revenue is unrelated to tax rates
- DHigher tax rates always increase tax revenue
3Solutions
1.Price elasticity of demand
Answer: ΔR = 31250 €
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 = 25·0.9 = €22.50
Q2 = 10 000·1.25 = 12500
Change in revenue
ΔR = 22.5·12500 − 25·10 000 = 281 250.00 − 250 000 = €31 250.00
Answer
ΔR = €31 250.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: E = −2.333
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 = 2000 − 20·70 = 600
Point elasticity
dQ/dP = −20
E = (dQ/dP)·P/Q = −20·70/600 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: B · A surplus of labour (unemployment)
Why this is the answer
At the higher wage more people want to work and firms hire fewer, so labour supplied exceeds labour demanded in the simple competitive model.
Answer
B · A surplus of labour (unemployment)
4.Economics concepts
Answer: B · 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
B · Beyond some point, raising tax rates can reduce total tax revenue
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