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 €4.00 to €4.50, weekly sales change from 100 to 90. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €4.50Q1 = 100Q2 = 90
E =
2.Price elasticity of demandHard
The demand for a product is Q = 2000 − 50P, with P in euros. Find the price elasticity of demand E at a price of €12.
Q = 2000 − 50PP = €12
E =
3.Economics conceptsMedium
The marginal propensity to consume is:
- AThe average share of total income that households save over a year
- BThe interest rate on consumer loans
- CThe share of an extra euro of income that is spent on consumption
- DThe total consumption in an economy
4.Economics conceptsHard
In Spence's job market signalling model, education can be valuable to employers even if it does not raise productivity because:
- AIt guarantees that every graduate is highly productive
- BIt reduces the wages employers must pay
- CEmployers are required by law to hire graduates
- DIt is less costly for high-ability workers to acquire, so it reveals their type
3Solutions
1.Price elasticity of demand
Answer: E = −0.8947
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
(90 − 100)/((100 + 90)/2) = −10/95 = −0.1053
Relative change in price
(4.5 − 4)/((4 + 4.5)/2) = 0.5/4.25 = 0.1176
Elasticity
E = −0.1053/0.1176 = −0.8947
Answer
E = −0.8947
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.
Quantity at this price
Q = 2000 − 50·12 = 1400
Point elasticity
dQ/dP = −50
E = (dQ/dP)·P/Q = −50·12/1400 = −0.4286
Answer
E = −0.4286
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · The share of an extra euro of income that is spent on consumption
Why this is the answer
The MPC measures how consumption changes with income; it determines the size of the Keynesian multiplier, 1/(1 − MPC).
Answer
C · The share of an extra euro of income that is spent on consumption
4.Economics concepts
Answer: D · It is less costly for high-ability workers to acquire, so it reveals their type
Why this is the answer
If acquiring education costs less for able workers, only they find it worth getting, so it separates types and solves the hidden information problem.
Answer
D · It is less costly for high-ability workers to acquire, so it reveals their type
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