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 €5.00 to €5.50, weekly sales change from 400 to 320. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €5.50Q1 = 400Q2 = 320
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −0.8, so Q = A·P^−0.8. At a price of €4, 5 000 units are sold. How many units Q are sold at a price of €4.40?
E = −0.8P1 = €4Q1 = 5 000P2 = €4.40
Q = units
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 Marshall–Lerner condition states that a currency depreciation improves the trade balance if:
- AThe country has a budget surplus
- BThe sum of the price elasticities of demand for exports and imports exceeds 1
- CExports and imports have zero price elasticity
- DInterest rates rise at the same time
3Solutions
1.Price elasticity of demand
Answer: E = −2.333
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
(320 − 400)/((400 + 320)/2) = −80/360 = −0.2222
Relative change in price
(5.5 − 5)/((5 + 5.5)/2) = 0.5/5.25 = 0.09524
Elasticity
E = −0.2222/0.09524 = −2.333
Answer
E = −2.333
2.Price elasticity of demand
Answer: Q = 4633 units
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.
Ratio of the prices
P2/P1 = 4.4/4 = 1.1
New quantity
Q = 5 000·1.1−0.8 = 5 000·0.9266 = 4633
Answer
Q = 4633
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: 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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