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 €14.00, weekly sales change from 100 to 110. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €20.00P2 = €14.00Q1 = 100Q2 = 110
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1500 − 25P, with P in euros. Find the price elasticity of demand E at a price of €12.
Q = 1500 − 25PP = €12
E =
3.Economics conceptsMedium
If the ECB raises its main interest rate, the most likely short-term effect is:
- AHigher borrowing and spending, which adds to inflationary pressure
- BAn immediate rise in GDP
- CA fall in the value of the euro
- DLower borrowing and spending, reducing inflationary pressure
4.Economics conceptsHard
For a normal good, when its price falls, the substitution effect and income effect:
- ABoth decrease the quantity demanded
- BBoth increase the quantity demanded
- CCancel out exactly
- DWork in opposite directions
3Solutions
1.Price elasticity of demand
Answer: E = −0.2698
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
(110 − 100)/((100 + 110)/2) = 10/105 = 0.09524
Relative change in price
(14 − 20)/((20 + 14)/2) = −6/17 = −0.3529
Elasticity
E = 0.09524/−0.3529 = −0.2698
Answer
E = −0.2698
2.Price elasticity of demand
Answer: E = −0.25
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 = 1500 − 25·12 = 1200
Point elasticity
dQ/dP = −25
E = (dQ/dP)·P/Q = −25·12/1200 = −0.25
Answer
E = −0.25
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: D · Lower borrowing and spending, reducing inflationary pressure
Why this is the answer
Higher rates make credit more expensive and saving more attractive, reducing demand and inflation; they also tend to strengthen the currency.
Answer
D · Lower borrowing and spending, reducing inflationary pressure
4.Economics concepts
Answer: B · Both increase the quantity demanded
Why this is the answer
The substitution effect always favours the cheaper good, and for a normal good the higher real income also raises demand, so both effects reinforce each other.
Answer
B · Both increase the quantity demanded
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