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 −2. The firm changes the price by +20%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €8Q1 = 2 500E = −2%ΔP = +20%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 1200 − 20P, with P in euros. Find the price elasticity of demand E at a price of €42.
Q = 1200 − 20PP = €42
E =
3.Economics conceptsMedium
A Nash equilibrium is a situation where:
- AOne player has won and the others have lost
- BThe players agree to cooperate through a binding contract that maximises their combined total payoff
- CNo player can improve their payoff by changing strategy alone, given the others' strategies
- DAll players achieve the highest possible total payoff
4.Economics conceptsHard
A monopolist faces demand P = 100 − Q and has constant marginal cost of 20. What are its profit-maximising output and price?
- AQ = 50, P = 50
- BQ = 40, P = 20
- CQ = 80, P = 20
- DQ = 40, P = 60
3Solutions
1.Price elasticity of demand
Answer: ΔR = −5600 €
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 = 2 500·0.6 = 1500
Change in revenue
ΔR = 9.6·1500 − 8·2 500 = 14 400.00 − 20 000 = −€5 600.00
Answer
ΔR = −€5 600.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: E = −2.333
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 = 1200 − 20·42 = 360
Point elasticity
dQ/dP = −20
E = (dQ/dP)·P/Q = −20·42/360 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: C · No player can improve their payoff by changing strategy alone, given the others' strategies
Why this is the answer
In a Nash equilibrium each strategy is a best response to the others; the outcome need not be efficient, as the Prisoner's Dilemma shows.
Answer
C · No player can improve their payoff by changing strategy alone, given the others' strategies
4.Economics concepts
Answer: D · Q = 40, P = 60
Why this is the answer
Setting MR = MC gives 100 − 2Q = 20, so Q = 40; the price from the demand curve is 100 − 40 = 60.
Answer
D · Q = 40, P = 60
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