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 €10.00 to €4.00, weekly sales change from 500 to 860. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €4.00Q1 = 500Q2 = 860
E =
2.Price elasticity of demandHard
The demand for a product is Q = 2000 − 25P, with P in euros. At which price P is total revenue as large as possible?
Q = 2000 − 25P
P = €
3.Economics conceptsMedium
The price of a good rises by 10% and quantity demanded falls by 20%. The price elasticity of demand is:
- A-2, so demand is elastic
- B-0.5, so demand is elastic
- C-0.5, so demand is inelastic
- D-2, so demand is inelastic
4.Economics conceptsHard
In the Bertrand model, two firms sell identical products with the same constant marginal cost and compete on price. The equilibrium price is:
- AThe monopoly price
- BZero
- CEqual to marginal cost
- DHalfway between monopoly price and marginal cost
3Solutions
1.Price elasticity of demand
Answer: E = −0.6176
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
(860 − 500)/((500 + 860)/2) = 360/680 = 0.5294
Relative change in price
(4 − 10)/((10 + 4)/2) = −6/7 = −0.8571
Elasticity
E = 0.5294/−0.8571 = −0.6176
Answer
E = −0.6176
2.Price elasticity of demand
Answer: P = 40 €
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·(2000 − 25P) = 2000P − 25P²
Set the derivative to zero
dR/dP = 2000 − 50P = 0
P = 2000/50 = €40.00
Answer
P = €40.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: A · -2, so demand is elastic
Why this is the answer
PED = -20% / 10% = -2; since the absolute value is above 1, demand is elastic.
Answer
A · -2, so demand is elastic
4.Economics concepts
Answer: C · Equal to marginal cost
Why this is the answer
Undercutting continues until price equals marginal cost, so even two firms reach the competitive outcome; in Cournot quantity competition, price stays above MC.
Answer
C · Equal to marginal cost
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