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 €15.00 to €13.00, weekly sales change from 500 to 550. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €15.00P2 = €13.00Q1 = 500Q2 = 550
E =
2.Price elasticity of demandHard
The demand for a product is Q = 400 − 20P, with P in euros. At which price P is total revenue as large as possible?
Q = 400 − 20P
P = €
3.Economics conceptsMedium
In the long run in monopolistic competition, firms typically:
- AEarn zero economic profit and have excess capacity
- BEarn large economic profits protected by entry barriers
- CProduce at the minimum of average total cost
- DCharge a price equal to marginal cost
4.Economics conceptsHard
Using the "rule of 70", an economy growing at 7% per year will double its real GDP in about:
- A10 years
- B49 years
- C7 years
- D70 years
3Solutions
1.Price elasticity of demand
Answer: E = −0.6667
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
(550 − 500)/((500 + 550)/2) = 50/525 = 0.09524
Relative change in price
(13 − 15)/((15 + 13)/2) = −2/14 = −0.1429
Elasticity
E = 0.09524/−0.1429 = −0.6667
Answer
E = −0.6667
2.Price elasticity of demand
Answer: P = 10 €
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.
Revenue as a function of price
R = P·(400 − 20P) = 400P − 20P²
Set the derivative to zero
dR/dP = 400 − 40P = 0
P = 400/40 = €10.00
Answer
P = €10.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: A · 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
A · Earn zero economic profit and have excess capacity
4.Economics concepts
Answer: A · 10 years
Why this is the answer
The doubling time is approximately 70 divided by the percentage growth rate, so 70 / 7 = 10 years, showing the power of compound growth.
Answer
A · 10 years
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