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 €8.00 to €9.00, weekly sales change from 200 to 190. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €8.00P2 = €9.00Q1 = 200Q2 = 190
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1500 − 25P, with P in euros. At which price P is total revenue as large as possible?
Q = 1500 − 25P
P = €
3.Economics conceptsMedium
The price of petrol rises sharply. What happens to the demand curve for large cars?
- AIt becomes vertical
- BIt shifts to the right
- CThere is a movement along it
- DIt shifts to the left
4.Economics conceptsHard
Why is the real-world government spending multiplier usually smaller than the simple 1/(1 − MPC)?
- ATaxes, imports and crowding out leak part of each round of spending
- BGovernments cannot borrow money
- CConsumers never spend extra income
- DThe MPC is always above 1
3Solutions
1.Price elasticity of demand
Answer: E = −0.4359
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 − 200)/((200 + 190)/2) = −10/195 = −0.05128
Relative change in price
(9 − 8)/((8 + 9)/2) = 1/8.5 = 0.1176
Elasticity
E = −0.05128/0.1176 = −0.4359
Answer
E = −0.4359
2.Price elasticity of demand
Answer: P = 30 €
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·(1500 − 25P) = 1500P − 25P²
Set the derivative to zero
dR/dP = 1500 − 50P = 0
P = 1500/50 = €30.00
Answer
P = €30.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · It shifts to the left
Why this is the answer
Petrol and cars are complements, so a higher petrol price lowers demand for cars at every car price, shifting the demand curve left.
Answer
D · It shifts to the left
4.Economics concepts
Answer: A · Taxes, imports and crowding out leak part of each round of spending
Why this is the answer
Income taxes, spending on imports, higher interest rates (crowding out) and saving reduce the extra spending in each round, so the multiplier shrinks.
Answer
A · Taxes, imports and crowding out leak part of each round of spending
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