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 €2.00 to €3.50, weekly sales change from 800 to 560. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €2.00P2 = €3.50Q1 = 800Q2 = 560
E =
2.Price elasticity of demandHard
The demand for a product is Q = 160 − 4P, with P in euros. At which price P is total revenue as large as possible?
Q = 160 − 4P
P = €
3.Economics conceptsMedium
In country A, 1 car costs 2 tonnes of wheat to produce; in country B, 1 car costs 4 tonnes of wheat. Which statement is correct?
- ANeither country gains from trade
- BB has a comparative advantage in cars and A in wheat
- CA has a comparative advantage in cars and B in wheat
- DA has a comparative advantage in both goods
4.Economics conceptsHard
Why is the real-world government spending multiplier usually smaller than the simple 1/(1 − MPC)?
- AConsumers never spend extra income
- BGovernments cannot borrow money
- CTaxes, imports and crowding out leak part of each round of spending
- DThe MPC is always above 1
3Solutions
1.Price elasticity of demand
Answer: E = −0.6471
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
(560 − 800)/((800 + 560)/2) = −240/680 = −0.3529
Relative change in price
(3.5 − 2)/((2 + 3.5)/2) = 1.5/2.75 = 0.5455
Elasticity
E = −0.3529/0.5455 = −0.6471
Answer
E = −0.6471
2.Price elasticity of demand
Answer: P = 20 €
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·(160 − 4P) = 160P − 4P²
Set the derivative to zero
dR/dP = 160 − 8P = 0
P = 160/8 = €20.00
Answer
P = €20.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: C · A has a comparative advantage in cars and B in wheat
Why this is the answer
A gives up less wheat per car, so it should specialise in cars; B's opportunity cost of wheat (1/4 car) is lower than A's (1/2 car), so B specialises in wheat.
Answer
C · A has a comparative advantage in cars and B in wheat
4.Economics concepts
Answer: C · 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
C · Taxes, imports and crowding out leak part of each round of spending
ExamProblems · examproblems.com/courses/microeconomics