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 €25.00 to €27.00, weekly sales change from 200 to 170. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €27.00Q1 = 200Q2 = 170
E =
2.Price elasticity of demandHard
The demand for a product is Q = 200 − 4P, with P in euros. Find the price elasticity of demand E at a price of €30.
Q = 200 − 4PP = €30
E =
3.Economics conceptsMedium
A country has 950 employed people and 50 unemployed people seeking work. Its unemployment rate is:
- A5.3%
- B95%
- C5%
- D50%
4.Economics conceptsHard
Ricardian equivalence suggests that a debt-financed tax cut will:
- AStrongly increase consumption, because households spend most of the tax cut through the multiplier
- BAlways cause inflation
- CReduce interest rates sharply
- DHave little effect on spending, because households save to pay expected future taxes
3Solutions
1.Price elasticity of demand
Answer: E = −2.108
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
(170 − 200)/((200 + 170)/2) = −30/185 = −0.1622
Relative change in price
(27 − 25)/((25 + 27)/2) = 2/26 = 0.07692
Elasticity
E = −0.1622/0.07692 = −2.108
Answer
E = −2.108
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 = 200 − 4·30 = 80
Point elasticity
dQ/dP = −4
E = (dQ/dP)·P/Q = −4·30/80 = −1.5
Answer
E = −1.5
|E| > 1: demand is elastic.
3.Economics concepts
Answer: C · 5%
Why this is the answer
The labour force is 950 + 50 = 1,000, so the rate is 50 / 1,000 = 5%.
Answer
C · 5%
4.Economics concepts
Answer: D · Have little effect on spending, because households save to pay expected future taxes
Why this is the answer
If consumers are forward-looking and see that government borrowing means higher taxes later, they save the tax cut, so aggregate demand barely changes.
Answer
D · Have little effect on spending, because households save to pay expected future taxes
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