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 €4.00, weekly sales change from 400 to 530. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €4.00Q1 = 400Q2 = 530
E =
2.Price elasticity of demandHard
The demand for a product is Q = 160 − 8P, with P in euros. At which price P is total revenue as large as possible?
Q = 160 − 8P
P = €
3.Economics conceptsMedium
A minimum wage set above the equilibrium wage in a competitive labour market is predicted to cause:
- AA fall in the wage rate
- BA surplus of labour (unemployment)
- CA shortage of labour
- DNo change in employment
4.Economics conceptsHard
The Coase theorem states that, if property rights are clearly defined and transaction costs are low:
- AThe polluter must always compensate the victim
- BGovernments must always tax externalities
- CExternalities cannot be corrected without direct government regulation or a Pigouvian tax
- DPrivate bargaining can reach an efficient outcome regardless of who holds the rights
3Solutions
1.Price elasticity of demand
Answer: E = −1.258
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
(530 − 400)/((400 + 530)/2) = 130/465 = 0.2796
Relative change in price
(4 − 5)/((5 + 4)/2) = −1/4.5 = −0.2222
Elasticity
E = 0.2796/−0.2222 = −1.258
Answer
E = −1.258
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·(160 − 8P) = 160P − 8P²
Set the derivative to zero
dR/dP = 160 − 16P = 0
P = 160/16 = €10.00
Answer
P = €10.00
At this price E = −1: demand is unit 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: D · Private bargaining can reach an efficient outcome regardless of who holds the rights
Why this is the answer
With costless bargaining, parties will negotiate to the efficient level of the externality; who holds the rights only decides who pays whom.
Answer
D · Private bargaining can reach an efficient outcome regardless of who holds the rights
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