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 €12.00 to €2.00, weekly sales change from 100 to 150. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €12.00P2 = €2.00Q1 = 100Q2 = 150
E =
2.Price elasticity of demandHard
The demand for a product is Q = 150 − 5P, with P in euros. Find the price elasticity of demand E at a price of €21.
Q = 150 − 5PP = €21
E =
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- AThe world price of steel rises sharply for all countries that trade it
- BDomestic steel prices fall and imports rise
- CDomestic consumers gain surplus
- DDomestic steel prices rise and domestic production increases
4.Economics conceptsHard
Which is a key difference between the CPI and the GDP deflator?
- AThe GDP deflator includes imported goods; the CPI does not
- BThey always give exactly the same inflation rate
- CThe CPI covers investment goods; the GDP deflator does not
- DThe CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
3Solutions
1.Price elasticity of demand
Answer: E = −0.28
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
(150 − 100)/((100 + 150)/2) = 50/125 = 0.4
Relative change in price
(2 − 12)/((12 + 2)/2) = −10/7 = −1.429
Elasticity
E = 0.4/−1.429 = −0.28
Answer
E = −0.28
2.Price elasticity of demand
Answer: E = −2.333
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 = 150 − 5·21 = 45
Point elasticity
dQ/dP = −5
E = (dQ/dP)·P/Q = −5·21/45 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · 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
D · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: D · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
Why this is the answer
The CPI uses a fixed basket of consumer goods, including imports, while the deflator covers all domestically produced output with changing weights.
Answer
D · The CPI includes prices of imported consumer goods; the GDP deflator covers only domestically produced goods
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