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
When the price of a ticket changes from €5.00 to €6.00, weekly sales change from 500 to 460. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €6.00Q1 = 500Q2 = 460
E =
2.Price elasticity of demandHard
The demand for a product is Q = 200 − 10P, with P in euros. Find the price elasticity of demand E at a price of €15.
Q = 200 − 10PP = €15
E =
3.Economics conceptsMedium
A minimum wage set above the equilibrium wage in a competitive labour market is predicted to cause:
- AA surplus of labour (unemployment)
- BNo change in employment
- CA fall in the wage rate
- DA shortage of labour
4.Economics conceptsHard
In Spence's job market signalling model, education can be valuable to employers even if it does not raise productivity because:
- AEmployers are required by law to hire graduates
- BIt reduces the wages employers must pay
- CIt is less costly for high-ability workers to acquire, so it reveals their type
- DIt guarantees that every graduate is highly productive
3Solutions
1.Price elasticity of demand
Answer: E = −0.4583
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.
Relative change in quantity
(460 − 500)/((500 + 460)/2) = −40/480 = −0.08333
Relative change in price
(6 − 5)/((5 + 6)/2) = 1/5.5 = 0.1818
Elasticity
E = −0.08333/0.1818 = −0.4583
Answer
E = −0.4583
2.Price elasticity of demand
Answer: E = −3
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 = 200 − 10·15 = 50
Point elasticity
dQ/dP = −10
E = (dQ/dP)·P/Q = −10·15/50 = −3
Answer
E = −3
|E| > 1: demand is elastic.
3.Economics concepts
Answer: A · 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
A · A surplus of labour (unemployment)
4.Economics concepts
Answer: C · It is less costly for high-ability workers to acquire, so it reveals their type
Why this is the answer
If acquiring education costs less for able workers, only they find it worth getting, so it separates types and solves the hidden information problem.
Answer
C · It is less costly for high-ability workers to acquire, so it reveals their type
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