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 €4.00 to €5.00, weekly sales change from 500 to 300. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €5.00Q1 = 500Q2 = 300
E =
2.Price elasticity of demandHard
The demand for a product is Q = 250 − 5P, with P in euros. Find the price elasticity of demand E at a price of €30.
Q = 250 − 5PP = €30
E =
3.Economics conceptsMedium
Rising consumer confidence would most likely:
- AHave no effect on the economy
- BShift aggregate demand to the left
- CShift aggregate supply to the left
- DShift aggregate demand to the right
4.Economics conceptsHard
According to the quantity theory of money (MV = PY), if velocity and real output are constant, a 5% rise in the money supply leads to:
- AAbout a 5% rise in real output
- BAbout a 5% rise in the price level
- CA 5% fall in velocity
- DNo change in prices
3Solutions
1.Price elasticity of demand
Answer: E = −2.25
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.
Relative change in quantity
(300 − 500)/((500 + 300)/2) = −200/400 = −0.5
Relative change in price
(5 − 4)/((4 + 5)/2) = 1/4.5 = 0.2222
Elasticity
E = −0.5/0.2222 = −2.25
Answer
E = −2.25
2.Price elasticity of demand
Answer: E = −1.5
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 = 250 − 5·30 = 100
Point elasticity
dQ/dP = −5
E = (dQ/dP)·P/Q = −5·30/100 = −1.5
Answer
E = −1.5
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · Shift aggregate demand to the right
Why this is the answer
Higher confidence raises consumption at every price level, shifting AD right and raising output and, possibly, prices in the short run.
Answer
D · Shift aggregate demand to the right
4.Economics concepts
Answer: B · About a 5% rise in the price level
Why this is the answer
With V and Y constant, M and P move proportionally, so prices rise about 5%. This is the classical view of money neutrality in the long run.
Answer
B · About a 5% rise in the price level
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