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 €35.00, weekly sales change from 100 to 70. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €35.00Q1 = 100Q2 = 70
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −2, so Q = A·P^−2. At a price of €10, 8 000 units are sold. How many units Q are sold at a price of €14.00?
E = −2P1 = €10Q1 = 8 000P2 = €14.00
Q = units
3.Economics conceptsMedium
The price of a good rises by 10% and quantity demanded falls by 20%. The price elasticity of demand is:
- A-0.5, so demand is elastic
- B-2, so demand is elastic
- C-0.5, so demand is inelastic
- D-2, so demand is inelastic
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:
- AAbout a 5% rise in the price level
- BA 5% fall in velocity
- CNo change in prices
- DAbout a 5% rise in real output
3Solutions
1.Price elasticity of demand
Answer: E = −1.059
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
(70 − 100)/((100 + 70)/2) = −30/85 = −0.3529
Relative change in price
(35 − 25)/((25 + 35)/2) = 10/30 = 0.3333
Elasticity
E = −0.3529/0.3333 = −1.059
Answer
E = −1.059
2.Price elasticity of demand
Answer: Q = 4082 units
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.
Ratio of the prices
P2/P1 = 14/10 = 1.4
New quantity
Q = 8 000·1.4−2 = 8 000·0.5102 = 4082
Answer
Q = 4082
3.Economics concepts
Answer: B · -2, so demand is elastic
Why this is the answer
PED = -20% / 10% = -2; since the absolute value is above 1, demand is elastic.
Answer
B · -2, so demand is elastic
4.Economics concepts
Answer: A · 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
A · About a 5% rise in the price level
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