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 €25.00 to €29.00, weekly sales change from 100 to 90. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €29.00Q1 = 100Q2 = 90
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 80 − 0.01Q, with P in euros. Find the price elasticity of demand E when 5 600 units are sold.
P = 80 − 0.01QQ = 5 600
E =
3.Economics conceptsMedium
A negative externality occurs when:
- AConsumers pay more for a product than it costs the firm to produce
- BA firm makes a loss
- CA third party bears a cost not paid by the producer or consumer
- DThe government taxes a product
4.Economics conceptsHard
Price discrimination by a firm requires that:
- AIt has market power, can separate markets and prevent resale
- BAll consumers have identical elasticity of demand and buy the same amount
- CIt operates in perfect competition
- DIts costs differ for each customer
3Solutions
1.Price elasticity of demand
Answer: E = −0.7105
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
(90 − 100)/((100 + 90)/2) = −10/95 = −0.1053
Relative change in price
(29 − 25)/((25 + 29)/2) = 4/27 = 0.1481
Elasticity
E = −0.1053/0.1481 = −0.7105
Answer
E = −0.7105
2.Price elasticity of demand
Answer: E = −0.4286
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.
Price at this quantity
P = 80 − 0.01·5 600 = €24.00
Point elasticity
dQ/dP = −1/0.01 = −100
E = −100·24/5 600 = −0.4286
Answer
E = −0.4286
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · A third party bears a cost not paid by the producer or consumer
Why this is the answer
Negative externalities lead to overproduction relative to the social optimum; Pigouvian taxes or tradeable permits can correct them.
Answer
C · A third party bears a cost not paid by the producer or consumer
4.Economics concepts
Answer: A · It has market power, can separate markets and prevent resale
Why this is the answer
To charge different prices for the same good, the firm needs market power, the ability to identify groups with different elasticities and to prevent arbitrage.
Answer
A · It has market power, can separate markets and prevent resale
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