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 €20.00 to €22.00, weekly sales change from 1000 to 920. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €20.00P2 = €22.00Q1 = 1000Q2 = 920
E =
2.Price elasticity of demandHard
The demand for a product is Q = 100 − 5P, with P in euros. At which price P is total revenue as large as possible?
Q = 100 − 5P
P = €
3.Economics conceptsMedium
Crowding out refers to:
- AToo many firms entering a market
- BHigher government borrowing raising interest rates and reducing private investment
- COvercrowded public services
- DImports replacing domestic production
4.Economics conceptsHard
The Laffer curve illustrates that:
- AHigher tax rates always increase tax revenue
- BTax revenue is unrelated to tax rates
- CBeyond some point, raising tax rates can reduce total tax revenue
- DLower tax rates always reduce tax revenue, whatever the starting rate
3Solutions
1.Price elasticity of demand
Answer: E = −0.875
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
(920 − 1000)/((1000 + 920)/2) = −80/960 = −0.08333
Relative change in price
(22 − 20)/((20 + 22)/2) = 2/21 = 0.09524
Elasticity
E = −0.08333/0.09524 = −0.875
Answer
E = −0.875
2.Price elasticity of demand
Answer: P = 10 €
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·(100 − 5P) = 100P − 5P²
Set the derivative to zero
dR/dP = 100 − 10P = 0
P = 100/10 = €10.00
Answer
P = €10.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: B · Higher government borrowing raising interest rates and reducing private investment
Why this is the answer
When government borrowing raises interest rates, some private investment is no longer profitable, reducing the net effect of fiscal expansion.
Answer
B · Higher government borrowing raising interest rates and reducing private investment
4.Economics concepts
Answer: C · 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
C · Beyond some point, raising tax rates can reduce total tax revenue
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