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 €27.00, weekly sales change from 100 to 90. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €27.00Q1 = 100Q2 = 90
E =
2.Price elasticity of demandHard
The demand for a product is Q = 5000 − 50P, with P in euros. At which price P is total revenue as large as possible?
Q = 5000 − 50P
P = €
3.Economics conceptsMedium
Education generates benefits for society beyond the individual student. Without intervention, the market will likely:
- AOver-provide education compared with the social optimum
- BStop providing education altogether
- CUnder-provide education compared with the social optimum
- DProvide exactly the efficient amount of education, as prices reflect all benefits
4.Economics conceptsHard
Under a fixed exchange rate with free capital movement, a country:
- ACannot trade with other countries
- BMust have a budget surplus
- CCan set any interest rate it likes
- DLoses control of independent monetary policy
3Solutions
1.Price elasticity of demand
Answer: E = −1.368
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
(90 − 100)/((100 + 90)/2) = −10/95 = −0.1053
Relative change in price
(27 − 25)/((25 + 27)/2) = 2/26 = 0.07692
Elasticity
E = −0.1053/0.07692 = −1.368
Answer
E = −1.368
2.Price elasticity of demand
Answer: P = 50 €
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·(5000 − 50P) = 5000P − 50P²
Set the derivative to zero
dR/dP = 5000 − 100P = 0
P = 5000/100 = €50.00
Answer
P = €50.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: C · 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
C · Under-provide education compared with the social optimum
4.Economics concepts
Answer: D · Loses control of independent monetary policy
Why this is the answer
A country cannot simultaneously have a fixed exchange rate, free capital flows and an independent monetary policy; it must give up one of the three.
Answer
D · Loses control of independent monetary policy
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