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 €5.00 to €4.50, weekly sales change from 400 to 480. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €4.50Q1 = 400Q2 = 480
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 120 − 1Q, with P in euros. Find the price elasticity of demand E when 72 units are sold.
P = 120 − 1QQ = 72
E =
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- ATreated as the opportunity cost of stopping
- BRecovered by raising prices
- CIgnored, because it is a sunk cost
- DAdded to the expected future costs
4.Economics conceptsHard
Ricardian equivalence suggests that a debt-financed tax cut will:
- AAlways cause inflation
- BStrongly increase consumption, because households spend most of the tax cut through the multiplier
- CHave little effect on spending, because households save to pay expected future taxes
- DReduce interest rates sharply
3Solutions
1.Price elasticity of demand
Answer: E = −1.727
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
(480 − 400)/((400 + 480)/2) = 80/440 = 0.1818
Relative change in price
(4.5 − 5)/((5 + 4.5)/2) = −0.5/4.75 = −0.1053
Elasticity
E = 0.1818/−0.1053 = −1.727
Answer
E = −1.727
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 − 1·72 = €48.00
Point elasticity
dQ/dP = −1/1 = −1
E = −1·48/72 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
C · Ignored, because it is a sunk cost
4.Economics concepts
Answer: C · Have little effect on spending, because households save to pay expected future taxes
Why this is the answer
If consumers are forward-looking and see that government borrowing means higher taxes later, they save the tax cut, so aggregate demand barely changes.
Answer
C · Have little effect on spending, because households save to pay expected future taxes
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