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 €14.00, weekly sales change from 1200 to 820. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €14.00Q1 = 1200Q2 = 820
E =
2.Price elasticity of demandHard
The demand for a product is Q = 400 − 5P, with P in euros. At which price P is total revenue as large as possible?
Q = 400 − 5P
P = €
3.Economics conceptsMedium
Unemployment benefits and progressive income taxes are called automatic stabilisers because they:
- AFix the exchange rate automatically
- BKeep the government budget balanced in every year of the business cycle
- CReduce fluctuations in demand without new government decisions
- DPrevent all recessions from happening
4.Economics conceptsHard
The Laffer curve illustrates that:
- ALower tax rates always reduce tax revenue, whatever the starting rate
- BBeyond some point, raising tax rates can reduce total tax revenue
- CTax revenue is unrelated to tax rates
- DHigher tax rates always increase tax revenue
3Solutions
1.Price elasticity of demand
Answer: E = −1.129
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
(820 − 1200)/((1200 + 820)/2) = −380/1010 = −0.3762
Relative change in price
(14 − 10)/((10 + 14)/2) = 4/12 = 0.3333
Elasticity
E = −0.3762/0.3333 = −1.129
Answer
E = −1.129
2.Price elasticity of demand
Answer: P = 40 €
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·(400 − 5P) = 400P − 5P²
Set the derivative to zero
dR/dP = 400 − 10P = 0
P = 400/10 = €40.00
Answer
P = €40.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: C · 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
C · Reduce fluctuations in demand without new government decisions
4.Economics concepts
Answer: B · Beyond some point, raising tax rates can reduce total tax revenue
Why this is the answer
Very high rates discourage taxed activity or encourage avoidance, so revenue peaks at some rate between 0 and 100%; where that peak lies is debated.
Answer
B · Beyond some point, raising tax rates can reduce total tax revenue
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