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
A product sells 5 000 units per month at €8. Its price elasticity of demand is −0.4. The firm changes the price by +15%. Assuming %ΔQ = E·%ΔP, by how much ΔR does monthly revenue change?
P1 = €8Q1 = 5 000E = −0.4%ΔP = +15%
ΔR = €
2.Price elasticity of demandHard
The demand for a product is Q = 600 − 20P, with P in euros. Find the price elasticity of demand E at a price of €23.
Q = 600 − 20PP = €23
E =
3.Economics conceptsMedium
When a central bank buys government bonds from banks in open market operations, it usually:
- AReduces bank reserves and so shrinks the money supply
- BRaises tax revenue for the government
- CIncreases bank reserves and the money supply
- DHas no effect on the money supply
4.Economics conceptsHard
The "paradox of thrift" suggests that if all households try to save more during a recession:
- ATotal income may fall, so total saving does not rise
- BInvestment and growth will rise immediately
- CInflation will increase
- DInterest rates will rise sharply
3Solutions
1.Price elasticity of demand
Answer: ΔR = 3240 €
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.
New price and quantity
P2 = 8·1.15 = €9.20
Q2 = 5 000·0.94 = 4700
Change in revenue
ΔR = 9.2·4700 − 8·5 000 = 43 240.00 − 40 000 = €3 240.00
Answer
ΔR = €3 240.00
|E| < 1: demand is inelastic.
2.Price elasticity of demand
Answer: E = −3.286
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 = 600 − 20·23 = 140
Point elasticity
dQ/dP = −20
E = (dQ/dP)·P/Q = −20·23/140 = −3.286
Answer
E = −3.286
|E| > 1: demand is elastic.
3.Economics concepts
Answer: C · Increases bank reserves and the money supply
Why this is the answer
Buying bonds injects reserves into the banking system, which tends to increase the money supply and lower interest rates.
Answer
C · Increases bank reserves and the money supply
4.Economics concepts
Answer: A · Total income may fall, so total saving does not rise
Why this is the answer
Higher saving reduces consumption and aggregate demand, lowering income; with lower income, aggregate saving may end up no higher, as Keynes argued.
Answer
A · Total income may fall, so total saving does not rise
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