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 €1.50, weekly sales change from 1200 to 2700. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €4.00P2 = €1.50Q1 = 1200Q2 = 2700
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1000 − 50P, with P in euros. At which price P is total revenue as large as possible?
Q = 1000 − 50P
P = €
3.Economics conceptsMedium
Unexpectedly high inflation tends to benefit:
- ASavers holding cash
- BLenders who receive fixed interest payments
- CPensioners on fixed nominal incomes
- DBorrowers with fixed-rate loans
4.Economics conceptsHard
Okun's law describes:
- AThe link between money supply and prices
- BA negative relationship between output growth and changes in unemployment
- CA positive relationship between inflation and nominal interest rates over time
- DThe relationship between tax rates and revenue
3Solutions
1.Price elasticity of demand
Answer: E = −0.8462
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
(2700 − 1200)/((1200 + 2700)/2) = 1500/1950 = 0.7692
Relative change in price
(1.5 − 4)/((4 + 1.5)/2) = −2.5/2.75 = −0.9091
Elasticity
E = 0.7692/−0.9091 = −0.8462
Answer
E = −0.8462
2.Price elasticity of demand
Answer: P = 10 €
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.
Revenue as a function of price
R = P·(1000 − 50P) = 1000P − 50P²
Set the derivative to zero
dR/dP = 1000 − 100P = 0
P = 1000/100 = €10.00
Answer
P = €10.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · Borrowers with fixed-rate loans
Why this is the answer
Unexpected inflation reduces the real value of debts, transferring purchasing power from lenders and fixed-income earners to borrowers.
Answer
D · Borrowers with fixed-rate loans
4.Economics concepts
Answer: B · A negative relationship between output growth and changes in unemployment
Why this is the answer
Okun observed that unemployment falls when real GDP grows faster than its trend rate and rises when growth is below trend.
Answer
B · A negative relationship between output growth and changes in unemployment
ExamProblems · examproblems.com/courses/microeconomics