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 €22.00, weekly sales change from 500 to 470. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €20.00P2 = €22.00Q1 = 500Q2 = 470
E =
2.Price elasticity of demandHard
The demand for a product is Q = 800 − 8P, with P in euros. Find the price elasticity of demand E at a price of €40.
Q = 800 − 8PP = €40
E =
3.Economics conceptsMedium
In a simple closed economy without taxes, the MPC is 0.8. The Keynesian spending multiplier is:
- A0.8
- B5
- C8
- D1.25
4.Economics conceptsHard
In the Bertrand model, two firms sell identical products with the same constant marginal cost and compete on price. The equilibrium price is:
- AThe monopoly price
- BHalfway between monopoly price and marginal cost
- CEqual to marginal cost
- DZero
3Solutions
1.Price elasticity of demand
Answer: E = −0.6495
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
(470 − 500)/((500 + 470)/2) = −30/485 = −0.06186
Relative change in price
(22 − 20)/((20 + 22)/2) = 2/21 = 0.09524
Elasticity
E = −0.06186/0.09524 = −0.6495
Answer
E = −0.6495
2.Price elasticity of demand
Answer: E = −0.6667
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.
Quantity at this price
Q = 800 − 8·40 = 480
Point elasticity
dQ/dP = −8
E = (dQ/dP)·P/Q = −8·40/480 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: B · 5
Why this is the answer
1 / (1 − 0.8) = 1 / 0.2 = 5, so an extra €1 of spending can raise income by up to €5.
Answer
B · 5
4.Economics concepts
Answer: C · Equal to marginal cost
Why this is the answer
Undercutting continues until price equals marginal cost, so even two firms reach the competitive outcome; in Cournot quantity competition, price stays above MC.
Answer
C · Equal to marginal cost
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