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 €40.00 to €42.00, weekly sales change from 200 to 190. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €42.00Q1 = 200Q2 = 190
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 100 − 0.01Q, with P in euros. Find the price elasticity of demand E when 2 000 units are sold.
P = 100 − 0.01QQ = 2 000
E =
3.Economics conceptsMedium
In an oligopoly, firms are typically:
- AMany and too small to affect the price
- BA single seller in the market
- CFew and interdependent in their decisions
- DCompletely unregulated by competition law
4.Economics conceptsHard
A monopolist maximises profit where:
- AAverage cost is at its minimum
- BTotal revenue is at its maximum
- CPrice equals marginal cost
- DMarginal revenue equals marginal cost
3Solutions
1.Price elasticity of demand
Answer: E = −1.051
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
(190 − 200)/((200 + 190)/2) = −10/195 = −0.05128
Relative change in price
(42 − 40)/((40 + 42)/2) = 2/41 = 0.04878
Elasticity
E = −0.05128/0.04878 = −1.051
Answer
E = −1.051
2.Price elasticity of demand
Answer: E = −4
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 = 100 − 0.01·2 000 = €80.00
Point elasticity
dQ/dP = −1/0.01 = −100
E = −100·80/2 000 = −4
Answer
E = −4
|E| > 1: demand is elastic.
3.Economics concepts
Answer: C · Few and interdependent in their decisions
Why this is the answer
Oligopolies have a few large firms whose pricing and output decisions affect each other, often analysed with game theory.
Answer
C · Few and interdependent in their decisions
4.Economics concepts
Answer: D · 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
D · Marginal revenue equals marginal cost
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