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 €12.00 to €16.00, weekly sales change from 400 to 190. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €12.00P2 = €16.00Q1 = 400Q2 = 190
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1000 − 20P, with P in euros. At which price P is total revenue as large as possible?
Q = 1000 − 20P
P = €
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- ATreated as the opportunity cost of stopping
- BIgnored, because it is a sunk cost
- CAdded to the expected future costs
- DRecovered by raising prices
4.Economics conceptsHard
In the "Battle of the Sexes" coordination game, how many pure-strategy Nash equilibria are there?
- ANone
- BTwo
- COne
- DFour
3Solutions
1.Price elasticity of demand
Answer: E = −2.492
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
(190 − 400)/((400 + 190)/2) = −210/295 = −0.7119
Relative change in price
(16 − 12)/((12 + 16)/2) = 4/14 = 0.2857
Elasticity
E = −0.7119/0.2857 = −2.492
Answer
E = −2.492
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·(1000 − 20P) = 1000P − 20P²
Set the derivative to zero
dR/dP = 1000 − 40P = 0
P = 1000/40 = €25.00
Answer
P = €25.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: B · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
B · Ignored, because it is a sunk cost
4.Economics concepts
Answer: B · Two
Why this is the answer
Both outcomes where the players choose the same activity are Nash equilibria, so the problem is coordinating on one of them rather than avoiding defection.
Answer
B · Two
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