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 €8.00 to €7.00, weekly sales change from 1000 to 1200. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €8.00P2 = €7.00Q1 = 1000Q2 = 1200
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −1.5, so Q = A·P^−1.5. At a price of €12, 2 000 units are sold. How many units Q are sold at a price of €6.00?
E = −1.5P1 = €12Q1 = 2 000P2 = €6.00
Q = units
3.Economics conceptsMedium
In an oligopoly, firms are typically:
- AA single seller in the market
- BCompletely unregulated by competition law
- CFew and interdependent in their decisions
- DMany and too small to affect the price
4.Economics conceptsHard
Why does the deadweight loss of a tax grow when the good's demand and supply are more elastic?
- AThe government collects more tax revenue
- BElastic markets have no consumer surplus
- CQuantity traded falls more, so more mutually beneficial trades are lost
- DPrices do not change, so consumers bear the whole burden of the tax instead
3Solutions
1.Price elasticity of demand
Answer: E = −1.364
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
(1200 − 1000)/((1000 + 1200)/2) = 200/1100 = 0.1818
Relative change in price
(7 − 8)/((8 + 7)/2) = −1/7.5 = −0.1333
Elasticity
E = 0.1818/−0.1333 = −1.364
Answer
E = −1.364
2.Price elasticity of demand
Answer: Q = 5657 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 = 6/12 = 0.5
New quantity
Q = 2 000·0.5−1.5 = 2 000·2.828 = 5657
Answer
Q = 5657
3.Economics concepts
Answer: C · Few and interdependent in their decisions
Why this is the answer
Oligopolies have a few large firms whose pricing and output decisions affect each other, often analysed with game theory.
Answer
C · Few and interdependent in their decisions
4.Economics concepts
Answer: C · 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
C · Quantity traded falls more, so more mutually beneficial trades are lost
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