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 €21.00, weekly sales change from 100 to 80. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €15.00P2 = €21.00Q1 = 100Q2 = 80
E =
2.Price elasticity of demandHard
The demand for a product is Q = 480 − 8P, with P in euros. At which price P is total revenue as large as possible?
Q = 480 − 8P
P = €
3.Economics conceptsMedium
A price ceiling set below the equilibrium price typically causes:
- ANo change in the market
- BAn increase in supply
- CA surplus
- DA shortage
4.Economics conceptsHard
The Marshall–Lerner condition states that a currency depreciation improves the trade balance if:
- AInterest rates rise at the same time
- BExports and imports have zero price elasticity
- CThe country has a budget surplus
- DThe sum of the price elasticities of demand for exports and imports exceeds 1
3Solutions
1.Price elasticity of demand
Answer: E = −0.6667
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
(80 − 100)/((100 + 80)/2) = −20/90 = −0.2222
Relative change in price
(21 − 15)/((15 + 21)/2) = 6/18 = 0.3333
Elasticity
E = −0.2222/0.3333 = −0.6667
Answer
E = −0.6667
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·(480 − 8P) = 480P − 8P²
Set the derivative to zero
dR/dP = 480 − 16P = 0
P = 480/16 = €30.00
Answer
P = €30.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · A shortage
Why this is the answer
A binding maximum price raises quantity demanded and lowers quantity supplied, creating excess demand, as with rent control.
Answer
D · A shortage
4.Economics concepts
Answer: D · The sum of the price elasticities of demand for exports and imports exceeds 1
Why this is the answer
If export and import demand are elastic enough (absolute values summing to more than 1), volume effects outweigh the higher import prices and the balance improves.
Answer
D · The sum of the price elasticities of demand for exports and imports exceeds 1
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