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 €15.00 to €11.00, weekly sales change from 100 to 110. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €15.00P2 = €11.00Q1 = 100Q2 = 110
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1200 − 20P, with P in euros. Find the price elasticity of demand E at a price of €24.
Q = 1200 − 20PP = €24
E =
3.Economics conceptsMedium
Rising consumer confidence would most likely:
- AShift aggregate demand to the left
- BHave no effect on the economy
- CShift aggregate demand to the right
- DShift aggregate supply to the left
4.Economics conceptsHard
A lump-sum tax (a fixed amount, independent of output) is imposed on a profit-maximising monopolist. In the short run, its output will:
- AFall to zero
- BStay the same, because MR and MC do not change
- CFall, because the tax raises the firm's average cost
- DRise to make up for the tax
3Solutions
1.Price elasticity of demand
Answer: E = −0.3095
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
(110 − 100)/((100 + 110)/2) = 10/105 = 0.09524
Relative change in price
(11 − 15)/((15 + 11)/2) = −4/13 = −0.3077
Elasticity
E = 0.09524/−0.3077 = −0.3095
Answer
E = −0.3095
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.
Quantity at this price
Q = 1200 − 20·24 = 720
Point elasticity
dQ/dP = −20
E = (dQ/dP)·P/Q = −20·24/720 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · 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
C · Shift aggregate demand to the right
4.Economics concepts
Answer: B · Stay the same, because MR and MC do not change
Why this is the answer
A lump-sum tax is like a fixed cost: it lowers profit but does not change MR or MC, so the optimal quantity and price stay the same (unless the firm exits).
Answer
B · Stay the same, because MR and MC do not change
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