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 €25. Its price elasticity of demand is −0.5. The firm changes the price by +10%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €25Q1 = 4 000E = −0.5%ΔP = +10%
ΔR = €
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 80 − 0.01Q, with P in euros. Find the price elasticity of demand E when 3 200 units are sold.
P = 80 − 0.01QQ = 3 200
E =
3.Economics conceptsMedium
Both supply and demand for a good increase. What can we say for certain about the new equilibrium?
- ABoth price and quantity fall
- BBoth price and quantity rise
- CPrice rises, but the change in quantity is uncertain
- DQuantity rises, but the change in price is uncertain
4.Economics conceptsHard
The Marshall–Lerner condition states that a currency depreciation improves the trade balance if:
- AThe sum of the price elasticities of demand for exports and imports exceeds 1
- BThe country has a budget surplus
- CInterest rates rise at the same time
- DExports and imports have zero price elasticity
3Solutions
1.Price elasticity of demand
Answer: ΔR = 4500 €
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 = 25·1.1 = €27.50
Q2 = 4 000·0.95 = 3800
Change in revenue
ΔR = 27.5·3800 − 25·4 000 = 104 500.00 − 100 000 = €4 500.00
Answer
ΔR = €4 500.00
|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.
Price at this quantity
P = 80 − 0.01·3 200 = €48.00
Point elasticity
dQ/dP = −1/0.01 = −100
E = −100·48/3 200 = −1.5
Answer
E = −1.5
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · Quantity rises, but the change in price is uncertain
Why this is the answer
Both shifts raise quantity, but the demand shift raises price while the supply shift lowers it, so the price effect depends on their relative size.
Answer
D · Quantity rises, but the change in price is uncertain
4.Economics concepts
Answer: A · 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
A · The sum of the price elasticities of demand for exports and imports exceeds 1
ExamProblems · examproblems.com/courses/microeconomics