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 €10.00 to €8.00, weekly sales change from 800 to 860. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €8.00Q1 = 800Q2 = 860
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 120 − 0.2Q, with P in euros. Find the price elasticity of demand E when 360 units are sold.
P = 120 − 0.2QQ = 360
E =
3.Economics conceptsMedium
Unemployment benefits and progressive income taxes are called automatic stabilisers because they:
- AReduce fluctuations in demand without new government decisions
- BKeep the government budget balanced in every year of the business cycle
- CPrevent all recessions from happening
- DFix the exchange rate automatically
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACreates the largest possible deadweight loss
- BCaptures all consumer surplus and produces the efficient output
- CProduces less than a single-price monopolist, creating a larger deadweight loss
- DCharges every consumer the same price
3Solutions
1.Price elasticity of demand
Answer: E = −0.3253
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
(860 − 800)/((800 + 860)/2) = 60/830 = 0.07229
Relative change in price
(8 − 10)/((10 + 8)/2) = −2/9 = −0.2222
Elasticity
E = 0.07229/−0.2222 = −0.3253
Answer
E = −0.3253
2.Price elasticity of demand
Answer: E = −0.6667
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.
Price at this quantity
P = 120 − 0.2·360 = €48.00
Point elasticity
dQ/dP = −1/0.2 = −5
E = −5·48/360 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: A · Reduce fluctuations in demand without new government decisions
Why this is the answer
In a downturn tax revenue falls and benefit payments rise automatically, supporting incomes and spending; the reverse happens in a boom.
Answer
A · Reduce fluctuations in demand without new government decisions
4.Economics concepts
Answer: B · Captures all consumer surplus and produces the efficient output
Why this is the answer
Charging each buyer their reservation price means it sells until price equals MC, so there is no deadweight loss, but all surplus goes to the producer.
Answer
B · Captures all consumer surplus and produces the efficient output
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