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 €10.00 to €4.00, weekly sales change from 400 to 500. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €4.00Q1 = 400Q2 = 500
E =
2.Price elasticity of demandHard
The demand for a product is Q = 120 − 2P, with P in euros. At which price P is total revenue as large as possible?
Q = 120 − 2P
P = €
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 inelastic
- C-2, so demand is elastic
- D-0.5, 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 real output
- BNo change in prices
- CA 5% fall in velocity
- DAbout a 5% rise in the price level
3Solutions
1.Price elasticity of demand
Answer: E = −0.2593
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
(500 − 400)/((400 + 500)/2) = 100/450 = 0.2222
Relative change in price
(4 − 10)/((10 + 4)/2) = −6/7 = −0.8571
Elasticity
E = 0.2222/−0.8571 = −0.2593
Answer
E = −0.2593
2.Price elasticity of demand
Answer: P = 30 €
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.
Revenue as a function of price
R = P·(120 − 2P) = 120P − 2P²
Set the derivative to zero
dR/dP = 120 − 4P = 0
P = 120/4 = €30.00
Answer
P = €30.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: C · -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
C · -2, so demand is elastic
4.Economics concepts
Answer: D · 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
D · About a 5% rise in the price level
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