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 €40.00 to €44.00, weekly sales change from 400 to 340. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €44.00Q1 = 400Q2 = 340
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −0.5, so Q = A·P^−0.5. At a price of €5, 1 000 units are sold. How many units Q are sold at a price of €6.25?
E = −0.5P1 = €5Q1 = 1 000P2 = €6.25
Q = units
3.Economics conceptsMedium
The marginal cost curve cuts the average total cost curve:
- AWhere average total cost equals zero
- BAt the maximum point of average total cost
- CAt the minimum point of average total cost
- DNever, as the two curves are parallel
4.Economics conceptsHard
A monopolist faces demand P = 100 − Q and has constant marginal cost of 20. What are its profit-maximising output and price?
- AQ = 40, P = 60
- BQ = 40, P = 20
- CQ = 50, P = 50
- DQ = 80, P = 20
3Solutions
1.Price elasticity of demand
Answer: E = −1.703
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
(340 − 400)/((400 + 340)/2) = −60/370 = −0.1622
Relative change in price
(44 − 40)/((40 + 44)/2) = 4/42 = 0.09524
Elasticity
E = −0.1622/0.09524 = −1.703
Answer
E = −1.703
2.Price elasticity of demand
Answer: Q = 894.4 units
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.
Ratio of the prices
P2/P1 = 6.25/5 = 1.25
New quantity
Q = 1 000·1.25−0.5 = 1 000·0.8944 = 894.4
Answer
Q = 894.4
3.Economics concepts
Answer: C · 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
C · At the minimum point of average total cost
4.Economics concepts
Answer: A · Q = 40, P = 60
Why this is the answer
Setting MR = MC gives 100 − 2Q = 20, so Q = 40; the price from the demand curve is 100 − 40 = 60.
Answer
A · Q = 40, P = 60
ExamProblems · examproblems.com/courses/microeconomics