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 €15.00, weekly sales change from 400 to 590. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €15.00Q1 = 400Q2 = 590
E =
2.Price elasticity of demandHard
The demand for a product is Q = 100 − 2P, with P in euros. Find the price elasticity of demand E at a price of €10.
Q = 100 − 2PP = €10
E =
3.Economics conceptsMedium
When a central bank buys government bonds from banks in open market operations, it usually:
- AReduces bank reserves and so shrinks the money supply
- BHas no effect on the money supply
- CIncreases bank reserves and the money supply
- DRaises tax revenue for the government
4.Economics conceptsHard
The Marshall–Lerner condition states that a currency depreciation improves the trade balance if:
- AExports and imports have zero price elasticity
- BThe sum of the price elasticities of demand for exports and imports exceeds 1
- CThe country has a budget surplus
- DInterest rates rise at the same time
3Solutions
1.Price elasticity of demand
Answer: E = −0.7677
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
(590 − 400)/((400 + 590)/2) = 190/495 = 0.3838
Relative change in price
(15 − 25)/((25 + 15)/2) = −10/20 = −0.5
Elasticity
E = 0.3838/−0.5 = −0.7677
Answer
E = −0.7677
2.Price elasticity of demand
Answer: E = −0.25
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 = 100 − 2·10 = 80
Point elasticity
dQ/dP = −2
E = (dQ/dP)·P/Q = −2·10/80 = −0.25
Answer
E = −0.25
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · Increases bank reserves and the money supply
Why this is the answer
Buying bonds injects reserves into the banking system, which tends to increase the money supply and lower interest rates.
Answer
C · Increases bank reserves and the money supply
4.Economics concepts
Answer: B · The sum of the price elasticities of demand for exports and imports exceeds 1
Why this is the answer
If export and import demand are elastic enough (absolute values summing to more than 1), volume effects outweigh the higher import prices and the balance improves.
Answer
B · The sum of the price elasticities of demand for exports and imports exceeds 1
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