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 2 500 units per month at €8. Its price elasticity of demand is −0.3. The firm changes the price by +20%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €8Q1 = 2 500E = −0.3%ΔP = +20%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 640 − 8P, with P in euros. Find the price elasticity of demand E at a price of €32.
Q = 640 − 8PP = €32
E =
3.Economics conceptsMedium
Unexpectedly high inflation tends to benefit:
- ALenders who receive fixed interest payments
- BSavers holding cash
- CBorrowers with fixed-rate loans
- DPensioners on fixed nominal incomes
4.Economics conceptsHard
A monopolist maximises profit where:
- APrice equals marginal cost
- BMarginal revenue equals marginal cost
- CAverage cost is at its minimum
- DTotal revenue is at its maximum
3Solutions
1.Price elasticity of demand
Answer: ΔR = 2560 €
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 = 8·1.2 = €9.60
Q2 = 2 500·0.94 = 2350
Change in revenue
ΔR = 9.6·2350 − 8·2 500 = 22 560.00 − 20 000 = €2 560.00
Answer
ΔR = €2 560.00
|E| < 1: demand is inelastic.
2.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.
Quantity at this price
Q = 640 − 8·32 = 384
Point elasticity
dQ/dP = −8
E = (dQ/dP)·P/Q = −8·32/384 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · 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
C · Borrowers with fixed-rate loans
4.Economics concepts
Answer: B · Marginal revenue equals marginal cost
Why this is the answer
Profit is maximised where MR = MC. For a monopolist, price is above MR, so P > MC, causing a deadweight loss.
Answer
B · Marginal revenue equals marginal cost
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