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 €12.00 to €14.00, weekly sales change from 200 to 130. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €12.00P2 = €14.00Q1 = 200Q2 = 130
E =
2.Price elasticity of demandHard
The demand for a product is Q = 320 − 8P, with P in euros. Find the price elasticity of demand E at a price of €16.
Q = 320 − 8PP = €16
E =
3.Economics conceptsMedium
Both supply and demand for a good increase. What can we say for certain about the new equilibrium?
- APrice rises, but the change in quantity is uncertain
- BBoth price and quantity fall
- CBoth price and quantity rise
- DQuantity rises, but the change in price is uncertain
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:
- AHalfway between monopoly price and marginal cost
- BZero
- CThe monopoly price
- DEqual to marginal cost
3Solutions
1.Price elasticity of demand
Answer: E = −2.758
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
(130 − 200)/((200 + 130)/2) = −70/165 = −0.4242
Relative change in price
(14 − 12)/((12 + 14)/2) = 2/13 = 0.1538
Elasticity
E = −0.4242/0.1538 = −2.758
Answer
E = −2.758
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 = 320 − 8·16 = 192
Point elasticity
dQ/dP = −8
E = (dQ/dP)·P/Q = −8·16/192 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: D · Quantity rises, but the change in price is uncertain
Why this is the answer
Both shifts raise quantity, but the demand shift raises price while the supply shift lowers it, so the price effect depends on their relative size.
Answer
D · Quantity rises, but the change in price is uncertain
4.Economics concepts
Answer: D · 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
D · Equal to marginal cost
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