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 €12.00 to €8.00, weekly sales change from 1200 to 1360. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €12.00P2 = €8.00Q1 = 1200Q2 = 1360
E =
2.Price elasticity of demandHard
The demand for a product is Q = 200 − 2P, with P in euros. Find the price elasticity of demand E at a price of €40.
Q = 200 − 2PP = €40
E =
3.Economics conceptsMedium
In a simple closed economy without taxes, the MPC is 0.8. The Keynesian spending multiplier is:
- A1.25
- B8
- C5
- D0.8
4.Economics conceptsHard
Ricardian equivalence suggests that a debt-financed tax cut will:
- AHave little effect on spending, because households save to pay expected future taxes
- BAlways cause inflation
- CReduce interest rates sharply
- DStrongly increase consumption, because households spend most of the tax cut through the multiplier
3Solutions
1.Price elasticity of demand
Answer: E = −0.3125
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
(1360 − 1200)/((1200 + 1360)/2) = 160/1280 = 0.125
Relative change in price
(8 − 12)/((12 + 8)/2) = −4/10 = −0.4
Elasticity
E = 0.125/−0.4 = −0.3125
Answer
E = −0.3125
2.Price elasticity of demand
Answer: E = −0.6667
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 − 2·40 = 120
Point elasticity
dQ/dP = −2
E = (dQ/dP)·P/Q = −2·40/120 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · 5
Why this is the answer
1 / (1 − 0.8) = 1 / 0.2 = 5, so an extra €1 of spending can raise income by up to €5.
Answer
C · 5
4.Economics concepts
Answer: A · 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
A · Have little effect on spending, because households save to pay expected future taxes
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