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 €7.50, weekly sales change from 400 to 80. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €7.50Q1 = 400Q2 = 80
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −1.5, so Q = A·P^−1.5. At a price of €20, 10 000 units are sold. How many units Q are sold at a price of €18.00?
E = −1.5P1 = €20Q1 = 10 000P2 = €18.00
Q = units
3.Economics conceptsMedium
A Nash equilibrium is a situation where:
- ANo player can improve their payoff by changing strategy alone, given the others' strategies
- BAll players achieve the highest possible total payoff
- COne player has won and the others have lost
- DThe players agree to cooperate through a binding contract that maximises their combined total payoff
4.Economics conceptsHard
A Giffen good is one where:
- ADemand rises because the good is a status symbol
- BQuantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
- CThe price never changes
- DDemand rises with income, like most goods
3Solutions
1.Price elasticity of demand
Answer: E = −3.333
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
(80 − 400)/((400 + 80)/2) = −320/240 = −1.333
Relative change in price
(7.5 − 5)/((5 + 7.5)/2) = 2.5/6.25 = 0.4
Elasticity
E = −1.333/0.4 = −3.333
Answer
E = −3.333
2.Price elasticity of demand
Answer: Q = 11712 units
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.
Ratio of the prices
P2/P1 = 18/20 = 0.9
New quantity
Q = 10 000·0.9−1.5 = 10 000·1.171 = 11712
Answer
Q = 11712
3.Economics concepts
Answer: A · 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
A · No player can improve their payoff by changing strategy alone, given the others' strategies
4.Economics concepts
Answer: B · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
Why this is the answer
For a Giffen good the income effect of a price rise (feeling poorer, buying more of the cheap staple) dominates the substitution effect, so demand slopes upward.
Answer
B · Quantity demanded rises when its price rises, because a strong income effect outweighs the substitution effect
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