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 €25.00 to €21.00, weekly sales change from 400 to 450. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €21.00Q1 = 400Q2 = 450
E =
2.Price elasticity of demandHard
The demand for a product is Q = 150 − 5P, with P in euros. At which price P is the price elasticity of demand equal to −3?
Q = 150 − 5PE = −3
P = €
3.Economics conceptsMedium
In the long run in monopolistic competition, firms typically:
- AEarn large economic profits protected by entry barriers
- BProduce at the minimum of average total cost
- CCharge a price equal to marginal cost
- DEarn zero economic profit and have excess capacity
4.Economics conceptsHard
The "convergence hypothesis" from the Solow model predicts that:
- ARich countries always grow faster than poor ones, because they have more capital
- BExchange rates converge to a fixed value
- CAll countries will eventually have the same population
- DPoorer countries with similar fundamentals tend to grow faster than richer ones
3Solutions
1.Price elasticity of demand
Answer: E = −0.6765
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
(450 − 400)/((400 + 450)/2) = 50/425 = 0.1176
Relative change in price
(21 − 25)/((25 + 21)/2) = −4/23 = −0.1739
Elasticity
E = 0.1176/−0.1739 = −0.6765
Answer
E = −0.6765
2.Price elasticity of demand
Answer: P = 22.5 €
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.
Elasticity as a function of price
E = −5P/(150 − 5P)
Solve for P
−5P = −3·(150 − 5P)
P·(−5 − 15) = −450 → P = €22.50
Answer
P = €22.50
Check: Q = 37.5, E = −5·22.5/37.5 = −3.
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 · Poorer countries with similar fundamentals tend to grow faster than richer ones
Why this is the answer
Capital-poor economies have higher returns to investment, so, given similar saving rates and technology, they should catch up (conditional convergence).
Answer
D · Poorer countries with similar fundamentals tend to grow faster than richer ones
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