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 €15.00 to €11.00, weekly sales change from 1200 to 1390. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €15.00P2 = €11.00Q1 = 1200Q2 = 1390
E =
2.Price elasticity of demandHard
The demand for a product is Q = 400 − 10P, with P in euros. At which price P is total revenue as large as possible?
Q = 400 − 10P
P = €
3.Economics conceptsMedium
A per-unit tax is placed on a good with very inelastic demand and elastic supply. Who bears most of the tax burden?
- AIt is always split equally
- BThe government
- CConsumers
- DProducers
4.Economics conceptsHard
A Giffen good is one where:
- ADemand rises with income, like most goods
- BQuantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
- CThe price never changes
- DDemand rises because the good is a status symbol
3Solutions
1.Price elasticity of demand
Answer: E = −0.4768
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
(1390 − 1200)/((1200 + 1390)/2) = 190/1295 = 0.1467
Relative change in price
(11 − 15)/((15 + 11)/2) = −4/13 = −0.3077
Elasticity
E = 0.1467/−0.3077 = −0.4768
Answer
E = −0.4768
2.Price elasticity of demand
Answer: P = 20 €
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·(400 − 10P) = 400P − 10P²
Set the derivative to zero
dR/dP = 400 − 20P = 0
P = 400/20 = €20.00
Answer
P = €20.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: C · Consumers
Why this is the answer
The tax burden falls mainly on the side of the market that is less elastic; here buyers cannot cut back, so the price they pay rises by most of the tax.
Answer
C · Consumers
4.Economics concepts
Answer: B · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
Why this is the answer
For a Giffen good the income effect of a price rise (feeling poorer, buying more of the cheap staple) dominates the substitution effect, so demand slopes upward.
Answer
B · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
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