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 €8.00 to €10.50, weekly sales change from 500 to 380. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €8.00P2 = €10.50Q1 = 500Q2 = 380
E =
2.Price elasticity of demandHard
The demand for a product is Q = 320 − 8P, with P in euros. Find the price elasticity of demand E at a price of €28.
Q = 320 − 8PP = €28
E =
3.Economics conceptsMedium
The principle of diminishing marginal utility states that:
- ASatisfaction rises as income falls
- BTotal satisfaction falls with each additional unit of the good that is consumed
- CConsumers always prefer more expensive goods
- DExtra satisfaction from each additional unit consumed tends to fall
4.Economics conceptsHard
According to the quantity theory of money (MV = PY), if velocity and real output are constant, a 5% rise in the money supply leads to:
- ANo change in prices
- BAbout a 5% rise in the price level
- CA 5% fall in velocity
- DAbout a 5% rise in real output
3Solutions
1.Price elasticity of demand
Answer: E = −1.009
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
(380 − 500)/((500 + 380)/2) = −120/440 = −0.2727
Relative change in price
(10.5 − 8)/((8 + 10.5)/2) = 2.5/9.25 = 0.2703
Elasticity
E = −0.2727/0.2703 = −1.009
Answer
E = −1.009
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.
Quantity at this price
Q = 320 − 8·28 = 96
Point elasticity
dQ/dP = −8
E = (dQ/dP)·P/Q = −8·28/96 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · Extra satisfaction from each additional unit consumed tends to fall
Why this is the answer
As consumption of a good increases, the marginal utility of each extra unit usually declines, which helps explain downward-sloping demand.
Answer
D · Extra satisfaction from each additional unit consumed tends to fall
4.Economics concepts
Answer: B · About a 5% rise in the price level
Why this is the answer
With V and Y constant, M and P move proportionally, so prices rise about 5%. This is the classical view of money neutrality in the long run.
Answer
B · About a 5% rise in the price level
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