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 €30.00, weekly sales change from 200 to 230. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €30.00Q1 = 200Q2 = 230
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −1.2, so Q = A·P^−1.2. At a price of €20, 10 000 units are sold. How many units Q are sold at a price of €28.00?
E = −1.2P1 = €20Q1 = 10 000P2 = €28.00
Q = units
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic steel prices fall and imports rise
- BDomestic consumers gain surplus
- CDomestic steel prices rise and domestic production increases
- DThe world price of steel rises sharply for all countries that trade it
4.Economics conceptsHard
The Coase theorem states that, if property rights are clearly defined and transaction costs are low:
- AGovernments must always tax externalities
- BThe polluter must always compensate the victim
- CPrivate bargaining can reach an efficient outcome regardless of who holds the rights
- DExternalities cannot be corrected without direct government regulation or a Pigouvian tax
3Solutions
1.Price elasticity of demand
Answer: E = −0.4884
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
(230 − 200)/((200 + 230)/2) = 30/215 = 0.1395
Relative change in price
(30 − 40)/((40 + 30)/2) = −10/35 = −0.2857
Elasticity
E = 0.1395/−0.2857 = −0.4884
Answer
E = −0.4884
2.Price elasticity of demand
Answer: Q = 6678 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 = 28/20 = 1.4
New quantity
Q = 10 000·1.4−1.2 = 10 000·0.6678 = 6678
Answer
Q = 6678
3.Economics concepts
Answer: C · 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
C · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: C · Private bargaining can reach an efficient outcome regardless of who holds the rights
Why this is the answer
With costless bargaining, parties will negotiate to the efficient level of the externality; who holds the rights only decides who pays whom.
Answer
C · Private bargaining can reach an efficient outcome regardless of who holds the rights
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