CIMA BA1 · Chapter 10
Index numbers MCQs with Answers
10 multiple-choice questions on Index numbers for CIMA BA1 Fundamentals of Business Economics. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
The price of a product was $2.40 in the base year and is $2.70 in the current year. What is the simple price index for the current year (base year = 100)?
- A) 88.9
- B) 12.5
- C) 130.0
- D) 112.5
Show answer & explanation
Answer: D) 112.5
Simple price index = current price / base price x 100 = 2.70 / 2.40 x 100 = 112.5. This shows a 12.5% increase in price since the base year.
Question 2
A Laspeyres price index is calculated using:
- A) Current period quantities as weights
- B) The average of base and current period quantities as weights
- C) Base period quantities as weights
- D) No weights, only the prices of the items
Show answer & explanation
Answer: C) Base period quantities as weights
A Laspeyres index measures the change in the cost of buying the base period basket of goods, so it weights prices by base period quantities. A Paasche index weights by current period quantities.
Question 3
Price and quantity data for two items are: Item X: base price $4, base quantity 10, current price $5, current quantity 8 Item Y: base price $10, base quantity 5, current price $11, current quantity 7 What is the Laspeyres price index for the current period (base = 100, to one decimal place)?
- A) 114.7
- B) 116.7
- C) 114.3
- D) 85.7
Show answer & explanation
Answer: B) 116.7
Laspeyres = sum(p1 x q0) / sum(p0 x q0) x 100. Numerator = 5 x 10 + 11 x 5 = 105. Denominator = 4 x 10 + 10 x 5 = 90. Index = 105 / 90 x 100 = 116.7.
Question 4
Using the same data: Item X: base price $4, base quantity 10, current price $5, current quantity 8 Item Y: base price $10, base quantity 5, current price $11, current quantity 7 What is the Paasche price index for the current period (base = 100, to one decimal place)?
- A) 114.7
- B) 116.7
- C) 87.2
- D) 130.0
Show answer & explanation
Answer: A) 114.7
Paasche = sum(p1 x q1) / sum(p0 x q1) x 100. Numerator = 5 x 8 + 11 x 7 = 40 + 77 = 117. Denominator = 4 x 8 + 10 x 7 = 32 + 70 = 102. Index = 117 / 102 x 100 = 114.7. Dividing 117 by the base value of 90 gives 130.0, which is a value index, not a price index.
Question 5
An index series has Year 1 = 100. The index stands at 125 in Year 4 and 150 in Year 7. If the series is rebased so that Year 4 = 100, what is the index for Year 7?
- A) 125
- B) 150
- C) 175
- D) 120
Show answer & explanation
Answer: D) 120
Rebased index = old index for the year / old index for the new base year x 100 = 150 / 125 x 100 = 120.
Question 6
An employee's weekly wage was $400 in Year 1 and $460 in Year 3. A retail price index was 100 in Year 1 and 112 in Year 3. What is the Year 3 wage expressed in Year 1 prices (to the nearest cent)?
- A) $515.20
- B) $460.00
- C) $410.71
- D) $448.00
Show answer & explanation
Answer: C) $410.71
Real wage = money wage x (base index / current index) = 460 x 100 / 112 = $410.71. In real terms the wage has risen by 2.68%, much less than the 15% money increase. $448.00 is the Year 1 wage restated in Year 3 prices.
Question 7
The main reason for using a weighted index rather than a simple aggregate index is to:
- A) Remove the need to choose a base year
- B) Reflect the relative importance of each item in the index
- C) Ensure the index always increases over time
- D) Avoid the need to collect price data
Show answer & explanation
Answer: B) Reflect the relative importance of each item in the index
In a simple aggregate index every item counts equally, regardless of how much is bought. Weighting (by quantities or expenditure shares) ensures that items forming a larger part of spending have a greater influence on the index.
Question 8
Why is a Laspeyres price index often said to overstate the rise in the cost of living?
- A) It assumes the base period basket is still bought, ignoring consumers switching towards goods whose prices have risen relatively less
- B) It uses current quantities, which are always higher than base quantities
- C) It excludes items whose prices have risen
- D) It uses a geometric rather than an arithmetic mean of price relatives
Show answer & explanation
Answer: A) It assumes the base period basket is still bought, ignoring consumers switching towards goods whose prices have risen relatively less
Laspeyres keeps base period quantities fixed. In practice, consumers substitute away from items that have become relatively more expensive. Because the index does not reflect this substitution, it tends to overstate the increase in the cost of maintaining living standards. Paasche tends to understate it.
Question 9
A chain-based price index shows prices rising by 8% in Year 2, rising by 6% in Year 3 and falling by 4% in Year 4. If Year 1 = 100, what is the fixed-base index for Year 4 (to one decimal place)?
- A) 110.0
- B) 91.0
- C) 96.0
- D) 109.9
Show answer & explanation
Answer: D) 109.9
The chain links must be multiplied, not added: 100 x 1.08 x 1.06 x 0.96 = 109.9. Adding the percentage changes (8 + 6 - 4 = 10) incorrectly gives 110.0.
Question 10
An index is calculated as the weighted average of price relatives. Item A has a price relative of 120 and a weight of 3. Item B has a price relative of 105 and a weight of 2. What is the index?
- A) 112.5
- B) 111
- C) 114
- D) 570
Show answer & explanation
Answer: C) 114
Weighted average = (120 x 3 + 105 x 2) / (3 + 2) = (360 + 210) / 5 = 114. A simple average of the relatives gives 112.5, and reversing the weights gives 111.