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 €4.00 to €3.50, weekly sales change from 1000 to 1100. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €3.50Q1 = 1000Q2 = 1100
E =
2.Price elasticity of demandHard
The demand for a product is Q = 2500 − 25P, with P in euros. Find the price elasticity of demand E at a price of €80.
Q = 2500 − 25PP = €80
E =
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- ARecovered by raising prices
- BIgnored, because it is a sunk cost
- CAdded to the expected future costs
- DTreated as the opportunity cost of stopping
4.Economics conceptsHard
Under a fixed exchange rate with free capital movement, a country:
- ACannot trade with other countries
- BCan set any interest rate it likes
- CMust have a budget surplus
- DLoses control of independent monetary policy
3Solutions
1.Price elasticity of demand
Answer: E = −0.7143
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
(1100 − 1000)/((1000 + 1100)/2) = 100/1050 = 0.09524
Relative change in price
(3.5 − 4)/((4 + 3.5)/2) = −0.5/3.75 = −0.1333
Elasticity
E = 0.09524/−0.1333 = −0.7143
Answer
E = −0.7143
2.Price elasticity of demand
Answer: E = −4
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 = 2500 − 25·80 = 500
Point elasticity
dQ/dP = −25
E = (dQ/dP)·P/Q = −25·80/500 = −4
Answer
E = −4
|E| > 1: demand is elastic.
3.Economics concepts
Answer: B · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
B · Ignored, because it is a sunk cost
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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