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 €2.50, weekly sales change from 800 to 1120. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €2.50Q1 = 800Q2 = 1120
E =
2.Price elasticity of demandHard
The demand for a product is Q = 500 − 10P, with P in euros. At which price P is total revenue as large as possible?
Q = 500 − 10P
P = €
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 variable cost
- CAverage fixed cost
- DMarginal revenue
4.Economics conceptsHard
Under a fixed exchange rate with free capital movement, a country:
- ALoses control of independent monetary policy
- BCannot trade with other countries
- CCan set any interest rate it likes
- DMust have a budget surplus
3Solutions
1.Price elasticity of demand
Answer: E = −0.5
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.
Relative change in quantity
(1120 − 800)/((800 + 1120)/2) = 320/960 = 0.3333
Relative change in price
(2.5 − 5)/((5 + 2.5)/2) = −2.5/3.75 = −0.6667
Elasticity
E = 0.3333/−0.6667 = −0.5
Answer
E = −0.5
2.Price elasticity of demand
Answer: P = 25 €
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·(500 − 10P) = 500P − 10P²
Set the derivative to zero
dR/dP = 500 − 20P = 0
P = 500/20 = €25.00
Answer
P = €25.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: B · 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
B · Average variable cost
4.Economics concepts
Answer: A · Loses control of independent monetary policy
Why this is the answer
A country cannot simultaneously have a fixed exchange rate, free capital flows and an independent monetary policy; it must give up one of the three.
Answer
A · Loses control of independent monetary policy
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