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 €25.00 to €23.00, weekly sales change from 200 to 210. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €23.00Q1 = 200Q2 = 210
E =
2.Price elasticity of demandHard
Demand for a product has a constant price elasticity of −2, so Q = A·P^−2. At a price of €12, 5 000 units are sold. How many units Q are sold at a price of €18.00?
E = −2P1 = €12Q1 = 5 000P2 = €18.00
Q = units
3.Economics conceptsMedium
In perfect competition in the long run, firms earn:
- AZero economic profit
- BMonopoly profits
- CLosses forever
- DLarge economic profits
4.Economics conceptsHard
Under perfect (first-degree) price discrimination, the monopolist:
- ACaptures all consumer surplus and produces the efficient output
- BProduces less than a single-price monopolist, creating a larger deadweight loss
- CCreates the largest possible deadweight loss
- DCharges every consumer the same price
3Solutions
1.Price elasticity of demand
Answer: E = −0.5854
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
(210 − 200)/((200 + 210)/2) = 10/205 = 0.04878
Relative change in price
(23 − 25)/((25 + 23)/2) = −2/24 = −0.08333
Elasticity
E = 0.04878/−0.08333 = −0.5854
Answer
E = −0.5854
2.Price elasticity of demand
Answer: Q = 2222 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 = 18/12 = 1.5
New quantity
Q = 5 000·1.5−2 = 5 000·0.4444 = 2222
Answer
Q = 2222
3.Economics concepts
Answer: A · Zero economic profit
Why this is the answer
Profits attract entry and losses cause exit until price equals minimum average cost and economic profit is zero.
Answer
A · Zero economic profit
4.Economics concepts
Answer: A · Captures all consumer surplus and produces the efficient output
Why this is the answer
Charging each buyer their reservation price means it sells until price equals MC, so there is no deadweight loss, but all surplus goes to the producer.
Answer
A · Captures all consumer surplus and produces the efficient output
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