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 €40.00 to €34.00, weekly sales change from 500 to 530. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €34.00Q1 = 500Q2 = 530
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1000 − 50P, with P in euros. At which price P is total revenue as large as possible?
Q = 1000 − 50P
P = €
3.Economics conceptsMedium
A Nash equilibrium is a situation where:
- AThe players agree to cooperate through a binding contract that maximises their combined total payoff
- BAll players achieve the highest possible total payoff
- COne player has won and the others have lost
- DNo player can improve their payoff by changing strategy alone, given the others' strategies
4.Economics conceptsHard
Price discrimination by a firm requires that:
- AAll consumers have identical elasticity of demand and buy the same amount
- BIt has market power, can separate markets and prevent resale
- CIt operates in perfect competition
- DIts costs differ for each customer
3Solutions
1.Price elasticity of demand
Answer: E = −0.3592
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
(530 − 500)/((500 + 530)/2) = 30/515 = 0.05825
Relative change in price
(34 − 40)/((40 + 34)/2) = −6/37 = −0.1622
Elasticity
E = 0.05825/−0.1622 = −0.3592
Answer
E = −0.3592
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·(1000 − 50P) = 1000P − 50P²
Set the derivative to zero
dR/dP = 1000 − 100P = 0
P = 1000/100 = €10.00
Answer
P = €10.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · No player can improve their payoff by changing strategy alone, given the others' strategies
Why this is the answer
In a Nash equilibrium each strategy is a best response to the others; the outcome need not be efficient, as the Prisoner's Dilemma shows.
Answer
D · No player can improve their payoff by changing strategy alone, given the others' strategies
4.Economics concepts
Answer: B · It has market power, can separate markets and prevent resale
Why this is the answer
To charge different prices for the same good, the firm needs market power, the ability to identify groups with different elasticities and to prevent arbitrage.
Answer
B · It has market power, can separate markets and prevent resale
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