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
A product sells 2 000 units per month at €8. Its price elasticity of demand is −2.5. The firm changes the price by −15%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €8Q1 = 2 000E = −2.5%ΔP = −15%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 1000 − 10P, with P in euros. At which price P is the price elasticity of demand equal to −1.5?
Q = 1000 − 10PE = −1.5
P = €
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 rise and domestic production increases
- CDomestic steel prices fall and imports rise
- DDomestic consumers gain surplus
4.Economics conceptsHard
In the Prisoner's Dilemma, the Nash equilibrium is:
- AOne player cooperates and the other defects, so only one of them gains
- BThere is no equilibrium
- CBoth players cooperate
- DBoth players defect, even though both cooperating would be better
3Solutions
1.Price elasticity of demand
Answer: ΔR = 2700 €
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.
New price and quantity
P2 = 8·0.85 = €6.80
Q2 = 2 000·1.375 = 2750
Change in revenue
ΔR = 6.8·2750 − 8·2 000 = 18 700.00 − 16 000 = €2 700.00
Answer
ΔR = €2 700.00
|E| > 1: demand is elastic.
2.Price elasticity of demand
Answer: P = 60 €
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.
Elasticity as a function of price
E = −10P/(1000 − 10P)
Solve for P
−10P = −1.5·(1000 − 10P)
P·(−10 − 15) = −1500 → P = €60.00
Answer
P = €60.00
Check: Q = 400, E = −10·60/400 = −1.5.
3.Economics concepts
Answer: B · 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
B · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: D · Both players defect, even though both cooperating would be better
Why this is the answer
Each player's best response is to defect whatever the other does, so mutual defection is the equilibrium, although mutual cooperation would give both a higher payoff.
Answer
D · Both players defect, even though both cooperating would be better
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