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 €8.00 to €6.50, weekly sales change from 1000 to 1150. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €8.00P2 = €6.50Q1 = 1000Q2 = 1150
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1000 − 25P, with P in euros. Find the price elasticity of demand E at a price of €16.
Q = 1000 − 25PP = €16
E =
3.Economics conceptsMedium
When a central bank buys government bonds from banks in open market operations, it usually:
- AHas no effect on the money supply
- BReduces bank reserves and so shrinks the money supply
- CRaises tax revenue for the government
- DIncreases bank reserves and the money supply
4.Economics conceptsHard
In the Prisoner's Dilemma, the Nash equilibrium is:
- ABoth players defect, even though both cooperating would be better
- BOne player cooperates and the other defects, so only one of them gains
- CThere is no equilibrium
- DBoth players cooperate
3Solutions
1.Price elasticity of demand
Answer: E = −0.6744
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
(1150 − 1000)/((1000 + 1150)/2) = 150/1075 = 0.1395
Relative change in price
(6.5 − 8)/((8 + 6.5)/2) = −1.5/7.25 = −0.2069
Elasticity
E = 0.1395/−0.2069 = −0.6744
Answer
E = −0.6744
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 = 1000 − 25·16 = 600
Point elasticity
dQ/dP = −25
E = (dQ/dP)·P/Q = −25·16/600 = −0.6667
Answer
E = −0.6667
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: D · 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
D · Increases bank reserves and the money supply
4.Economics concepts
Answer: A · Both players defect, even though both cooperating would be better
Why this is the answer
Each player's best response is to defect whatever the other does, so mutual defection is the equilibrium, although mutual cooperation would give both a higher payoff.
Answer
A · Both players defect, even though both cooperating would be better
ExamProblems · examproblems.com/courses/microeconomics