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 €2.00 to €2.50, weekly sales change from 200 to 140. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €2.00P2 = €2.50Q1 = 200Q2 = 140
E =
2.Price elasticity of demandHard
The demand for a product is Q = 500 − 10P, with P in euros. At which price P is total revenue as large as possible?
Q = 500 − 10P
P = €
3.Economics conceptsMedium
The marginal cost curve cuts the average total cost curve:
- AAt the maximum point of average total cost
- BWhere average total cost equals zero
- CNever, as the two curves are parallel
- DAt the minimum point of average total cost
4.Economics conceptsHard
The principal–agent problem arises when:
- ATwo firms agree to fix prices
- BA buyer and seller have identical information
- CThe government owns a firm
- DAn agent acting for a principal has different goals and the principal cannot fully monitor them
3Solutions
1.Price elasticity of demand
Answer: E = −1.588
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
(140 − 200)/((200 + 140)/2) = −60/170 = −0.3529
Relative change in price
(2.5 − 2)/((2 + 2.5)/2) = 0.5/2.25 = 0.2222
Elasticity
E = −0.3529/0.2222 = −1.588
Answer
E = −1.588
2.Price elasticity of demand
Answer: P = 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.
Revenue as a function of price
R = P·(500 − 10P) = 500P − 10P²
Set the derivative to zero
dR/dP = 500 − 20P = 0
P = 500/20 = €25.00
Answer
P = €25.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · At the minimum point of average total cost
Why this is the answer
When MC is below ATC it pulls the average down, and when it is above it pushes the average up, so MC crosses ATC at its minimum.
Answer
D · At the minimum point of average total cost
4.Economics concepts
Answer: D · An agent acting for a principal has different goals and the principal cannot fully monitor them
Why this is the answer
Hidden action and conflicting interests let the agent pursue their own aims; incentive contracts such as performance pay try to align interests.
Answer
D · An agent acting for a principal has different goals and the principal cannot fully monitor them
ExamProblems · examproblems.com/courses/microeconomics