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 €34.00, weekly sales change from 100 to 120. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €34.00Q1 = 100Q2 = 120
E =
2.Price elasticity of demandHard
The demand for a product is Q = 400 − 5P, with P in euros. At which price P is total revenue as large as possible?
Q = 400 − 5P
P = €
3.Economics conceptsMedium
A negative externality occurs when:
- AA firm makes a loss
- BA third party bears a cost not paid by the producer or consumer
- CThe government taxes a product
- DConsumers pay more for a product than it costs the firm to produce
4.Economics conceptsHard
The J-curve effect describes why, after a depreciation, the trade balance may:
- ARemain unchanged for many years
- BImprove at first and then worsen
- CWorsen at first and then improve
- DImprove immediately and permanently
3Solutions
1.Price elasticity of demand
Answer: E = −1.121
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
(120 − 100)/((100 + 120)/2) = 20/110 = 0.1818
Relative change in price
(34 − 40)/((40 + 34)/2) = −6/37 = −0.1622
Elasticity
E = 0.1818/−0.1622 = −1.121
Answer
E = −1.121
2.Price elasticity of demand
Answer: P = 40 €
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.
Revenue as a function of price
R = P·(400 − 5P) = 400P − 5P²
Set the derivative to zero
dR/dP = 400 − 10P = 0
P = 400/10 = €40.00
Answer
P = €40.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: B · 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
B · A third party bears a cost not paid by the producer or consumer
4.Economics concepts
Answer: C · Worsen at first and then improve
Why this is the answer
In the short run, volumes are slow to adjust while import prices rise immediately, so the balance worsens before the Marshall–Lerner condition takes hold.
Answer
C · Worsen at first and then improve
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