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 1 000 units per month at €10. Its price elasticity of demand is −2.5. The firm changes the price by +10%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €10Q1 = 1 000E = −2.5%ΔP = +10%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 60 − 2P, with P in euros. At which price P is total revenue as large as possible?
Q = 60 − 2P
P = €
3.Economics conceptsMedium
Unexpectedly high inflation tends to benefit:
- ALenders who receive fixed interest payments
- BBorrowers with fixed-rate loans
- CSavers holding cash
- DPensioners on fixed nominal incomes
4.Economics conceptsHard
The time-inconsistency problem in monetary policy (Kydland and Prescott) is a key argument for:
- AFixing the money supply at zero growth
- BIndependent central banks with a credible commitment to low inflation
- CGovernments setting interest rates directly, especially before elections
- DAbolishing central banks entirely
3Solutions
1.Price elasticity of demand
Answer: ΔR = −1750 €
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 = 10·1.1 = €11.00
Q2 = 1 000·0.75 = 750
Change in revenue
ΔR = 11·750 − 10·1 000 = 8 250.00 − 10 000 = −€1 750.00
Answer
ΔR = −€1 750.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: P = 15 €
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·(60 − 2P) = 60P − 2P²
Set the derivative to zero
dR/dP = 60 − 4P = 0
P = 60/4 = €15.00
Answer
P = €15.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: B · Borrowers with fixed-rate loans
Why this is the answer
Unexpected inflation reduces the real value of debts, transferring purchasing power from lenders and fixed-income earners to borrowers.
Answer
B · Borrowers with fixed-rate loans
4.Economics concepts
Answer: B · Independent central banks with a credible commitment to low inflation
Why this is the answer
If the public expects policymakers to inflate later, expectations and inflation rise; delegating policy to an independent, credible central bank reduces this bias.
Answer
B · Independent central banks with a credible commitment to low inflation
ExamProblems · examproblems.com/courses/microeconomics