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 €38.00, weekly sales change from 100 to 110. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €38.00Q1 = 100Q2 = 110
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −2, so Q = A·P^−2. At a price of €5, 8 000 units are sold. How many units Q are sold at a price of €6.50?
E = −2P1 = €5Q1 = 8 000P2 = €6.50
Q = units
3.Economics conceptsMedium
The marginal cost curve cuts the average total cost curve:
- ANever, as the two curves are parallel
- BWhere average total cost equals zero
- CAt the minimum point of average total cost
- DAt the maximum point of average total cost
4.Economics conceptsHard
Why does the deadweight loss of a tax grow when the good's demand and supply are more elastic?
- AQuantity traded falls more, so more mutually beneficial trades are lost
- BElastic markets have no consumer surplus
- CThe government collects more tax revenue
- DPrices do not change, so consumers bear the whole burden of the tax instead
3Solutions
1.Price elasticity of demand
Answer: E = −1.857
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
(38 − 40)/((40 + 38)/2) = −2/39 = −0.05128
Elasticity
E = 0.09524/−0.05128 = −1.857
Answer
E = −1.857
2.Price elasticity of demand
Answer: Q = 4734 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 = 6.5/5 = 1.3
New quantity
Q = 8 000·1.3−2 = 8 000·0.5917 = 4734
Answer
Q = 4734
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 · Quantity traded falls more, so more mutually beneficial trades are lost
Why this is the answer
The more responsive buyers and sellers are, the more the tax reduces quantity, and the bigger the triangle of lost surplus; DWL also rises roughly with the square of the tax.
Answer
A · Quantity traded falls more, so more mutually beneficial trades are lost
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