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 €12.00, weekly sales change from 1000 to 880. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €12.00Q1 = 1000Q2 = 880
E =
2.Price elasticity of demandHard
The demand for a product is Q = 400 − 20P, with P in euros. Find the price elasticity of demand E at a price of €15.
Q = 400 − 20PP = €15
E =
3.Economics conceptsMedium
The marginal cost curve cuts the average total cost curve:
- AWhere average total cost equals zero
- BNever, as the two curves are parallel
- CAt the maximum point of average total cost
- DAt the minimum point of average total cost
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
- CExternalities cannot be corrected without direct government regulation or a Pigouvian tax
- DPrivate bargaining can reach an efficient outcome regardless of who holds the rights
3Solutions
1.Price elasticity of demand
Answer: E = −0.7021
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
(880 − 1000)/((1000 + 880)/2) = −120/940 = −0.1277
Relative change in price
(12 − 10)/((10 + 12)/2) = 2/11 = 0.1818
Elasticity
E = −0.1277/0.1818 = −0.7021
Answer
E = −0.7021
2.Price elasticity of demand
Answer: E = −3
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 = 400 − 20·15 = 100
Point elasticity
dQ/dP = −20
E = (dQ/dP)·P/Q = −20·15/100 = −3
Answer
E = −3
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · At the minimum point of average total cost
Why this is the answer
When MC is below ATC it pulls the average down, and when it is above it pushes the average up, so MC crosses ATC at its minimum.
Answer
D · At the minimum point of average total cost
4.Economics concepts
Answer: D · 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
D · Private bargaining can reach an efficient outcome regardless of who holds the rights
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