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 €2.00 to €1.00, weekly sales change from 200 to 400. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €2.00P2 = €1.00Q1 = 200Q2 = 400
E =
2.Price elasticity of demandHard
The demand for a product is Q = 400 − 10P, with P in euros. Find the price elasticity of demand E at a price of €24.
Q = 400 − 10PP = €24
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 shortage of labour
- DA fall in the wage rate
4.Economics conceptsHard
The time-inconsistency problem in monetary policy (Kydland and Prescott) is a key argument for:
- AGovernments setting interest rates directly, especially before elections
- BIndependent central banks with a credible commitment to low inflation
- CAbolishing central banks entirely
- DFixing the money supply at zero growth
3Solutions
1.Price elasticity of demand
Answer: E = −1
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
(400 − 200)/((200 + 400)/2) = 200/300 = 0.6667
Relative change in price
(1 − 2)/((2 + 1)/2) = −1/1.5 = −0.6667
Elasticity
E = 0.6667/−0.6667 = −1
Answer
E = −1
2.Price elasticity of demand
Answer: E = −1.5
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 = 400 − 10·24 = 160
Point elasticity
dQ/dP = −10
E = (dQ/dP)·P/Q = −10·24/160 = −1.5
Answer
E = −1.5
|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: B · Independent central banks with a credible commitment to low inflation
Why this is the answer
If the public expects policymakers to inflate later, expectations and inflation rise; delegating policy to an independent, credible central bank reduces this bias.
Answer
B · Independent central banks with a credible commitment to low inflation
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