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 €5.00 to €3.50, weekly sales change from 400 to 540. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €3.50Q1 = 400Q2 = 540
E =
2.Price elasticity of demandHard
The demand for a product is Q = 3000 − 50P, with P in euros. At which price P is total revenue as large as possible?
Q = 3000 − 50P
P = €
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic steel prices rise and domestic production increases
- BDomestic consumers gain surplus
- CDomestic steel prices fall and imports rise
- DThe world price of steel rises sharply for all countries that trade it
4.Economics conceptsHard
Moral hazard arises when:
- AOne party changes behaviour after a contract because they do not bear the full consequences
- BPrices are too high for poor consumers
- CA buyer cannot observe product quality before buying, so low-quality sellers dominate the market
- DTwo firms collude on price
3Solutions
1.Price elasticity of demand
Answer: E = −0.844
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
(540 − 400)/((400 + 540)/2) = 140/470 = 0.2979
Relative change in price
(3.5 − 5)/((5 + 3.5)/2) = −1.5/4.25 = −0.3529
Elasticity
E = 0.2979/−0.3529 = −0.844
Answer
E = −0.844
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·(3000 − 50P) = 3000P − 50P²
Set the derivative to zero
dR/dP = 3000 − 100P = 0
P = 3000/100 = €30.00
Answer
P = €30.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: A · Domestic steel prices rise and domestic production increases
Why this is the answer
The tariff raises the domestic price, increasing domestic output and government revenue but reducing consumer surplus and creating deadweight losses.
Answer
A · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: A · One party changes behaviour after a contract because they do not bear the full consequences
Why this is the answer
Moral hazard is hidden action after the contract, such as an insured driver taking more risks. Adverse selection is hidden information before the contract.
Answer
A · One party changes behaviour after a contract because they do not bear the full consequences
ExamProblems · examproblems.com/courses/microeconomics