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 €5.00 to €3.50, weekly sales change from 1200 to 1490. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €3.50Q1 = 1200Q2 = 1490
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 €25, 2 000 units are sold. How many units Q are sold at a price of €31.25?
E = −2P1 = €25Q1 = 2 000P2 = €31.25
Q = units
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AAverage total cost
- BAverage fixed cost
- CAverage variable cost
- DMarginal revenue
4.Economics conceptsHard
In the Solow growth model, sustained long-run growth in output per worker comes from:
- AGovernment budget deficits
- BPopulation growth
- CA higher saving rate alone
- DTechnological progress
3Solutions
1.Price elasticity of demand
Answer: E = −0.6109
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
(1490 − 1200)/((1200 + 1490)/2) = 290/1345 = 0.2156
Relative change in price
(3.5 − 5)/((5 + 3.5)/2) = −1.5/4.25 = −0.3529
Elasticity
E = 0.2156/−0.3529 = −0.6109
Answer
E = −0.6109
2.Price elasticity of demand
Answer: Q = 1280 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 = 31.25/25 = 1.25
New quantity
Q = 2 000·1.25−2 = 2 000·0.64 = 1280
Answer
Q = 1280
3.Economics concepts
Answer: C · Average variable cost
Why this is the answer
If price covers average variable cost, producing reduces losses by contributing to fixed costs; below AVC, shutting down loses less.
Answer
C · Average variable cost
4.Economics concepts
Answer: D · Technological progress
Why this is the answer
A higher saving rate raises the steady-state level of output per worker but not its long-run growth rate; only technological progress produces continuous growth.
Answer
D · Technological progress
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