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 €3.00, weekly sales change from 1200 to 1440. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €3.00Q1 = 1200Q2 = 1440
E =
2.Price elasticity of demandHard
The demand for a product is Q = 100 − 5P, with P in euros. At which price P is the price elasticity of demand equal to −1.5?
Q = 100 − 5PE = −1.5
P = €
3.Economics conceptsMedium
A negative externality occurs when:
- AConsumers pay more for a product than it costs the firm to produce
- BA firm makes a loss
- CA third party bears a cost not paid by the producer or consumer
- DThe government taxes a product
4.Economics conceptsHard
Ricardian equivalence suggests that a debt-financed tax cut will:
- AHave little effect on spending, because households save to pay expected future taxes
- BAlways cause inflation
- CReduce interest rates sharply
- DStrongly increase consumption, because households spend most of the tax cut through the multiplier
3Solutions
1.Price elasticity of demand
Answer: E = −0.6364
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
(1440 − 1200)/((1200 + 1440)/2) = 240/1320 = 0.1818
Relative change in price
(3 − 4)/((4 + 3)/2) = −1/3.5 = −0.2857
Elasticity
E = 0.1818/−0.2857 = −0.6364
Answer
E = −0.6364
2.Price elasticity of demand
Answer: P = 12 €
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.
Elasticity as a function of price
E = −5P/(100 − 5P)
Solve for P
−5P = −1.5·(100 − 5P)
P·(−5 − 7.5) = −150 → P = €12.00
Answer
P = €12.00
Check: Q = 40, E = −5·12/40 = −1.5.
3.Economics concepts
Answer: C · A third party bears a cost not paid by the producer or consumer
Why this is the answer
Negative externalities lead to overproduction relative to the social optimum; Pigouvian taxes or tradeable permits can correct them.
Answer
C · A third party bears a cost not paid by the producer or consumer
4.Economics concepts
Answer: A · 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
A · Have little effect on spending, because households save to pay expected future taxes
ExamProblems · examproblems.com/courses/microeconomics