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 €20.00 to €22.00, weekly sales change from 500 to 480. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €20.00P2 = €22.00Q1 = 500Q2 = 480
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 120 − 0.05Q, with P in euros. Find the price elasticity of demand E when 720 units are sold.
P = 120 − 0.05QQ = 720
E =
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
- BNo change in employment
- CA shortage of labour
- DA surplus of labour (unemployment)
4.Economics conceptsHard
The "Taylor principle" says that, to stabilise inflation, a central bank should respond to a 1 percentage point rise in inflation by:
- ARaising the nominal interest rate, but by less than 1 percentage point
- BRaising the nominal interest rate by more than 1 percentage point
- CCutting the nominal rate
- DKeeping the nominal rate unchanged
3Solutions
1.Price elasticity of demand
Answer: E = −0.4286
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
(480 − 500)/((500 + 480)/2) = −20/490 = −0.04082
Relative change in price
(22 − 20)/((20 + 22)/2) = 2/21 = 0.09524
Elasticity
E = −0.04082/0.09524 = −0.4286
Answer
E = −0.4286
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.
Price at this quantity
P = 120 − 0.05·720 = €84.00
Point elasticity
dQ/dP = −1/0.05 = −20
E = −20·84/720 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · 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
D · A surplus of labour (unemployment)
4.Economics concepts
Answer: B · Raising the nominal interest rate by more than 1 percentage point
Why this is the answer
Only by raising nominal rates more than one-for-one does the real interest rate rise, cooling demand and bringing inflation back down.
Answer
B · Raising the nominal interest rate by more than 1 percentage point
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