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 €10.00 to €14.00, weekly sales change from 800 to 160. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €14.00Q1 = 800Q2 = 160
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 €10, 1 000 units are sold. How many units Q are sold at a price of €7.50?
E = −1.5P1 = €10Q1 = 1 000P2 = €7.50
Q = units
3.Economics conceptsMedium
In the long run in monopolistic competition, firms typically:
- ACharge a price equal to marginal cost
- BEarn large economic profits protected by entry barriers
- CProduce at the minimum of average total cost
- DEarn zero economic profit and have excess capacity
4.Economics conceptsHard
The "paradox of thrift" suggests that if all households try to save more during a recession:
- AInterest rates will rise sharply
- BInflation will increase
- CInvestment and growth will rise immediately
- DTotal income may fall, so total saving does not rise
3Solutions
1.Price elasticity of demand
Answer: E = −4
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
(160 − 800)/((800 + 160)/2) = −640/480 = −1.333
Relative change in price
(14 − 10)/((10 + 14)/2) = 4/12 = 0.3333
Elasticity
E = −1.333/0.3333 = −4
Answer
E = −4
2.Price elasticity of demand
Answer: Q = 1540 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 = 7.5/10 = 0.75
New quantity
Q = 1 000·0.75−1.5 = 1 000·1.54 = 1540
Answer
Q = 1540
3.Economics concepts
Answer: D · Earn zero economic profit and have excess capacity
Why this is the answer
Entry removes profits, but because each firm faces a downward-sloping demand curve, the tangency is to the left of minimum ATC, leaving excess capacity.
Answer
D · Earn zero economic profit and have excess capacity
4.Economics concepts
Answer: D · Total income may fall, so total saving does not rise
Why this is the answer
Higher saving reduces consumption and aggregate demand, lowering income; with lower income, aggregate saving may end up no higher, as Keynes argued.
Answer
D · Total income may fall, so total saving does not rise
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