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 €25.00 to €31.00, weekly sales change from 1200 to 740. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €31.00Q1 = 1200Q2 = 740
E =
2.Price elasticity of demandHard
The demand for a product is Q = 160 − 4P, with P in euros. At which price P is total revenue as large as possible?
Q = 160 − 4P
P = €
3.Economics conceptsMedium
The marginal cost curve cuts the average total cost curve:
- AAt the minimum point of average total cost
- BAt the maximum point of average total cost
- CNever, as the two curves are parallel
- DWhere average total cost equals zero
4.Economics conceptsHard
A regulator forces a natural monopoly to set price equal to marginal cost. The likely problem is that:
- AThe firm makes very large profits
- BConsumers face a shortage, because demand exceeds supply at that price
- COutput falls below the monopoly level
- DThe firm makes a loss because average cost is above marginal cost
3Solutions
1.Price elasticity of demand
Answer: E = −2.213
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
(740 − 1200)/((1200 + 740)/2) = −460/970 = −0.4742
Relative change in price
(31 − 25)/((25 + 31)/2) = 6/28 = 0.2143
Elasticity
E = −0.4742/0.2143 = −2.213
Answer
E = −2.213
2.Price elasticity of demand
Answer: P = 20 €
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·(160 − 4P) = 160P − 4P²
Set the derivative to zero
dR/dP = 160 − 8P = 0
P = 160/8 = €20.00
Answer
P = €20.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: A · At the minimum point of average total cost
Why this is the answer
When MC is below ATC it pulls the average down, and when it is above it pushes the average up, so MC crosses ATC at its minimum.
Answer
A · At the minimum point of average total cost
4.Economics concepts
Answer: D · The firm makes a loss because average cost is above marginal cost
Why this is the answer
With falling average cost, marginal cost is below average cost, so marginal cost pricing does not cover total costs; subsidies or average cost pricing are alternatives.
Answer
D · The firm makes a loss because average cost is above marginal cost
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