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 €5.00 to €6.00, weekly sales change from 800 to 480. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €6.00Q1 = 800Q2 = 480
E =
2.Price elasticity of demandHard
The demand for a product is Q = 800 − 8P, with P in euros. At which price P is total revenue as large as possible?
Q = 800 − 8P
P = €
3.Economics conceptsMedium
A public good is:
- AAny good bought by the government
- BProvided only by private firms
- CRival and excludable
- DNon-rival and non-excludable
4.Economics conceptsHard
The J-curve effect describes why, after a depreciation, the trade balance may:
- ARemain unchanged for many years
- BWorsen at first and then improve
- CImprove immediately and permanently
- DImprove at first and then worsen
3Solutions
1.Price elasticity of demand
Answer: E = −2.75
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
(480 − 800)/((800 + 480)/2) = −320/640 = −0.5
Relative change in price
(6 − 5)/((5 + 6)/2) = 1/5.5 = 0.1818
Elasticity
E = −0.5/0.1818 = −2.75
Answer
E = −2.75
2.Price elasticity of demand
Answer: P = 50 €
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·(800 − 8P) = 800P − 8P²
Set the derivative to zero
dR/dP = 800 − 16P = 0
P = 800/16 = €50.00
Answer
P = €50.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · Non-rival and non-excludable
Why this is the answer
Public goods can be used by many at once and people cannot easily be excluded, leading to free-riding and under-provision by markets.
Answer
D · Non-rival and non-excludable
4.Economics concepts
Answer: B · 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
B · Worsen at first and then improve
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