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
A product sells 4 000 units per month at €5. Its price elasticity of demand is −0.4. The firm changes the price by −20%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €5Q1 = 4 000E = −0.4%ΔP = −20%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 500 − 10P, with P in euros. Find the price elasticity of demand E at a price of €30.
Q = 500 − 10PP = €30
E =
3.Economics conceptsMedium
In an oligopoly, firms are typically:
- ACompletely unregulated by competition law
- BFew and interdependent in their decisions
- CA single seller in the market
- DMany and too small to affect the price
4.Economics conceptsHard
Why does the deadweight loss of a tax grow when the good's demand and supply are more elastic?
- AThe government collects more tax revenue
- BElastic markets have no consumer surplus
- CPrices do not change, so consumers bear the whole burden of the tax instead
- DQuantity traded falls more, so more mutually beneficial trades are lost
3Solutions
1.Price elasticity of demand
Answer: ΔR = −2720 €
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.
New price and quantity
P2 = 5·0.8 = €4.00
Q2 = 4 000·1.08 = 4320
Change in revenue
ΔR = 4·4320 − 5·4 000 = 17 280.00 − 20 000 = −€2 720.00
Answer
ΔR = −€2 720.00
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: E = −1.5
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 = 500 − 10·30 = 200
Point elasticity
dQ/dP = −10
E = (dQ/dP)·P/Q = −10·30/200 = −1.5
Answer
E = −1.5
|E| > 1: demand is elastic.
3.Economics concepts
Answer: B · Few and interdependent in their decisions
Why this is the answer
Oligopolies have a few large firms whose pricing and output decisions affect each other, often analysed with game theory.
Answer
B · Few and interdependent in their decisions
4.Economics concepts
Answer: D · Quantity traded falls more, so more mutually beneficial trades are lost
Why this is the answer
The more responsive buyers and sellers are, the more the tax reduces quantity, and the bigger the triangle of lost surplus; DWL also rises roughly with the square of the tax.
Answer
D · Quantity traded falls more, so more mutually beneficial trades are lost
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