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 €10.00 to €16.00, weekly sales change from 400 to 260. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €10.00P2 = €16.00Q1 = 400Q2 = 260
E =
2.Price elasticity of demandHard
The demand for a product is Q = 500 − 10P, with P in euros. At which price P is the price elasticity of demand equal to −0.5?
Q = 500 − 10PE = −0.5
P = €
3.Economics conceptsMedium
Unexpectedly high inflation tends to benefit:
- ABorrowers with fixed-rate loans
- BPensioners on fixed nominal incomes
- CLenders who receive fixed interest payments
- DSavers holding cash
4.Economics conceptsHard
Using the "rule of 70", an economy growing at 7% per year will double its real GDP in about:
- A10 years
- B7 years
- C70 years
- D49 years
3Solutions
1.Price elasticity of demand
Answer: E = −0.9192
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
(260 − 400)/((400 + 260)/2) = −140/330 = −0.4242
Relative change in price
(16 − 10)/((10 + 16)/2) = 6/13 = 0.4615
Elasticity
E = −0.4242/0.4615 = −0.9192
Answer
E = −0.9192
2.Price elasticity of demand
Answer: P = 16.67 €
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.
Elasticity as a function of price
E = −10P/(500 − 10P)
Solve for P
−10P = −0.5·(500 − 10P)
P·(−10 − 5) = −250 → P = €16.67
Answer
P = €16.67
Check: Q = 333.3, E = −10·16.67/333.3 = −0.5.
3.Economics concepts
Answer: A · 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
A · Borrowers with fixed-rate loans
4.Economics concepts
Answer: A · 10 years
Why this is the answer
The doubling time is approximately 70 divided by the percentage growth rate, so 70 / 7 = 10 years, showing the power of compound growth.
Answer
A · 10 years
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