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 €20.00 to €16.00, weekly sales change from 1200 to 1680. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €20.00P2 = €16.00Q1 = 1200Q2 = 1680
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 100 − 0.02Q, with P in euros. Find the price elasticity of demand E when 3 500 units are sold.
P = 100 − 0.02QQ = 3 500
E =
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AAverage variable cost
- BAverage fixed cost
- CMarginal revenue
- DAverage total cost
4.Economics conceptsHard
The Coase theorem states that, if property rights are clearly defined and transaction costs are low:
- AExternalities cannot be corrected without direct government regulation or a Pigouvian tax
- BPrivate bargaining can reach an efficient outcome regardless of who holds the rights
- CGovernments must always tax externalities
- DThe polluter must always compensate the victim
3Solutions
1.Price elasticity of demand
Answer: E = −1.5
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
(1680 − 1200)/((1200 + 1680)/2) = 480/1440 = 0.3333
Relative change in price
(16 − 20)/((20 + 16)/2) = −4/18 = −0.2222
Elasticity
E = 0.3333/−0.2222 = −1.5
Answer
E = −1.5
2.Price elasticity of demand
Answer: E = −0.4286
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.
Price at this quantity
P = 100 − 0.02·3 500 = €30.00
Point elasticity
dQ/dP = −1/0.02 = −50
E = −50·30/3 500 = −0.4286
Answer
E = −0.4286
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: A · 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
A · Average variable cost
4.Economics concepts
Answer: B · Private bargaining can reach an efficient outcome regardless of who holds the rights
Why this is the answer
With costless bargaining, parties will negotiate to the efficient level of the externality; who holds the rights only decides who pays whom.
Answer
B · Private bargaining can reach an efficient outcome regardless of who holds the rights
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