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 €8.00 to €6.50, weekly sales change from 1000 to 1230. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €8.00P2 = €6.50Q1 = 1000Q2 = 1230
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −0.8, so Q = A·P^−0.8. At a price of €4, 5 000 units are sold. How many units Q are sold at a price of €5.60?
E = −0.8P1 = €4Q1 = 5 000P2 = €5.60
Q = units
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic steel prices rise and domestic production increases
- BDomestic consumers gain surplus
- CThe world price of steel rises sharply for all countries that trade it
- DDomestic steel prices fall and imports rise
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:
- AZero
- BThe monopoly price
- CEqual to marginal cost
- DHalfway between monopoly price and marginal cost
3Solutions
1.Price elasticity of demand
Answer: E = −0.997
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
(1230 − 1000)/((1000 + 1230)/2) = 230/1115 = 0.2063
Relative change in price
(6.5 − 8)/((8 + 6.5)/2) = −1.5/7.25 = −0.2069
Elasticity
E = 0.2063/−0.2069 = −0.997
Answer
E = −0.997
2.Price elasticity of demand
Answer: Q = 3820 units
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.
Ratio of the prices
P2/P1 = 5.6/4 = 1.4
New quantity
Q = 5 000·1.4−0.8 = 5 000·0.764 = 3820
Answer
Q = 3820
3.Economics concepts
Answer: A · Domestic steel prices rise and domestic production increases
Why this is the answer
The tariff raises the domestic price, increasing domestic output and government revenue but reducing consumer surplus and creating deadweight losses.
Answer
A · Domestic steel prices rise and domestic production increases
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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