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 €10.00 to €6.00, weekly sales change from 100 to 120. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €6.00Q1 = 100Q2 = 120
E =
2.Price elasticity of demandHard
The demand for a product is Q = 150 − 5P, with P in euros. At which price P is total revenue as large as possible?
Q = 150 − 5P
P = €
3.Economics conceptsMedium
The law of diminishing marginal returns states that:
- AConsumers get less satisfaction as prices rise
- BLong-run average costs always fall as output rises
- CAdding more of a variable input to a fixed input eventually lowers the extra output per unit added
- DTotal output always falls as more workers are hired
4.Economics conceptsHard
The Phillips curve originally suggested:
- AThat unemployment has no link to inflation
- BThat higher taxes always reduce inflation
- CA trade-off between inflation and unemployment in the short run
- DThat inflation and unemployment always rise and fall together in the short run
3Solutions
1.Price elasticity of demand
Answer: E = −0.3636
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
(120 − 100)/((100 + 120)/2) = 20/110 = 0.1818
Relative change in price
(6 − 10)/((10 + 6)/2) = −4/8 = −0.5
Elasticity
E = 0.1818/−0.5 = −0.3636
Answer
E = −0.3636
2.Price elasticity of demand
Answer: P = 15 €
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·(150 − 5P) = 150P − 5P²
Set the derivative to zero
dR/dP = 150 − 10P = 0
P = 150/10 = €15.00
Answer
P = €15.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: C · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
Why this is the answer
In the short run, with at least one fixed factor, marginal product eventually falls, which makes marginal cost rise.
Answer
C · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
4.Economics concepts
Answer: C · A trade-off between inflation and unemployment in the short run
Why this is the answer
Phillips found an inverse relationship between wage inflation and unemployment; expectations-augmented versions show no long-run trade-off at the natural rate.
Answer
C · A trade-off between inflation and unemployment in the short run
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