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 €34.00, weekly sales change from 400 to 420. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €34.00Q1 = 400Q2 = 420
E =
2.Price elasticity of demandHard
The demand for a product is Q = 750 − 25P, with P in euros. Find the price elasticity of demand E at a price of €9.
Q = 750 − 25PP = €9
E =
3.Economics conceptsMedium
Education generates benefits for society beyond the individual student. Without intervention, the market will likely:
- AProvide exactly the efficient amount of education, as prices reflect all benefits
- BUnder-provide education compared with the social optimum
- COver-provide education compared with the social optimum
- DStop providing education altogether
4.Economics conceptsHard
The Fisher effect predicts that, in the long run, a permanent 2 percentage point rise in expected inflation will:
- ALower nominal interest rates by about 2 points
- BRaise real interest rates by about 2 points
- CRaise nominal interest rates by about 2 points, leaving real rates unchanged
- DHave no effect on nominal interest rates, so real interest rates fall by about 2 points
3Solutions
1.Price elasticity of demand
Answer: E = −0.3008
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
(420 − 400)/((400 + 420)/2) = 20/410 = 0.04878
Relative change in price
(34 − 40)/((40 + 34)/2) = −6/37 = −0.1622
Elasticity
E = 0.04878/−0.1622 = −0.3008
Answer
E = −0.3008
2.Price elasticity of demand
Answer: E = −0.4286
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 = 750 − 25·9 = 525
Point elasticity
dQ/dP = −25
E = (dQ/dP)·P/Q = −25·9/525 = −0.4286
Answer
E = −0.4286
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: B · Under-provide education compared with the social optimum
Why this is the answer
Private decisions ignore external benefits, so output is below the socially optimal level; subsidies or public provision can raise it.
Answer
B · Under-provide education compared with the social optimum
4.Economics concepts
Answer: C · Raise nominal interest rates by about 2 points, leaving real rates unchanged
Why this is the answer
Lenders demand compensation for expected inflation, so nominal rates move one-for-one with it in the long run while the real rate is set by real factors.
Answer
C · Raise nominal interest rates by about 2 points, leaving real rates unchanged
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