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 €50.00, weekly sales change from 1200 to 1020. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €50.00Q1 = 1200Q2 = 1020
E =
2.Price elasticity of demandHard
The demand for a product is Q = 300 − 5P, with P in euros. At which price P is total revenue as large as possible?
Q = 300 − 5P
P = €
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic consumers gain surplus
- BDomestic steel prices fall and imports rise
- CDomestic steel prices rise and domestic production increases
- DThe world price of steel rises sharply for all countries that trade it
4.Economics conceptsHard
The J-curve effect describes why, after a depreciation, the trade balance may:
- AImprove immediately and permanently
- BWorsen at first and then improve
- CImprove at first and then worsen
- DRemain unchanged for many years
3Solutions
1.Price elasticity of demand
Answer: E = −0.7297
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
(1020 − 1200)/((1200 + 1020)/2) = −180/1110 = −0.1622
Relative change in price
(50 − 40)/((40 + 50)/2) = 10/45 = 0.2222
Elasticity
E = −0.1622/0.2222 = −0.7297
Answer
E = −0.7297
2.Price elasticity of demand
Answer: P = 30 €
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·(300 − 5P) = 300P − 5P²
Set the derivative to zero
dR/dP = 300 − 10P = 0
P = 300/10 = €30.00
Answer
P = €30.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: C · 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
C · Domestic steel prices rise and domestic production increases
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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