Chapter 9: Index Numbers – Questions & Answers

📌 Part A – 1 Mark Questions (Very Short Answer)

1. What are index numbers?
   Index numbers are special averages that measure changes in variables like price, quantity, or value over time.
2. Index numbers are also called ________.
   Economic barometers.
3. Name one use of index numbers.
   They help measure the purchasing power of money.
4. What is the base year?
   The base year is the reference year against which changes in the current year are compared.
5. What is the formula for Simple Aggregate Price Index?
   P₀₁ = (ΣP₁ / ΣP₀) × 100, where P₁ = current year prices, P₀ = base year prices.
6. What is the formula for Laspeyre's Price Index?
   P₀₁ = (ΣP₁Q₀ / ΣP₀Q₀) × 100, where Q₀ = base year quantities.
7. Which index uses base year quantities as weights?
   Laspeyre's Price Index.
8. What does a price index of 125 mean?
   It means prices have increased by 25% compared to the base year.
9. What is the purpose of Dearness Allowance (DA)?
   DA is given to employees to compensate for the rise in prices, and it is determined using index numbers.
10. Name the two methods of constructing index numbers covered in this chapter.
    Simple Aggregate Price Index and Laspeyre's Price Index.
11. Why is Laspeyre's index called a weighted index?
    Because it gives importance (weight) to items based on base year quantities.
12. If ΣP₁Q₀ = 200 and ΣP₀Q₀ = 160, find Laspeyre's index.
    P₀₁ = (200/160) × 100 = 125.
13. If ΣP₁ = 150 and ΣP₀ = 120, find the Simple Aggregate Price Index.
    P₀₁ = (150/120) × 100 = 125.
14. Index numbers help in measuring the ________ of money.
    Purchasing power.
15. Give an example of how the government uses index numbers.
    To formulate economic policies and decide on salary hikes for employees.
16. What is the main limitation of the Simple Aggregate Price Index?
    It ignores the quantities (importance) of different commodities.
17. What does ΣP₁Q₀ represent in Laspeyre's formula?
    The total cost of base year quantities at current year prices.
18. What does ΣP₀Q₀ represent in Laspeyre's formula?
    The total cost of base year quantities at base year prices.
19. If prices double from the base year, what will be the index number?
    200.
20. If prices remain the same as the base year, what will be the index number?
    100.

📌 Part B – 2/4 Marks Questions (Short Answer)

1. Define index numbers. State any four uses of index numbers.

   Index numbers are statistical measures designed to show changes in a variable or a group of related variables over time, compared to a base period. They are like economic thermometers.

   Uses of Index Numbers:

   • They help the government formulate economic policies.
   • They show trends and tendencies in business and economic activities.
   • They are used to determine Dearness Allowance (DA) for employees.
   • They help measure the purchasing power of money.
   • Businesses use them to track price movements and plan for the future.

   (Any four uses are sufficient)

2. Explain the Simple Aggregate Price Index method with its formula.

   The Simple Aggregate Price Index is the simplest method to construct an index number. It compares the total cost of a basket of commodities in the current year with the total cost of the same basket in the base year.

   Formula: P₀₁ = (ΣP₁ / ΣP₀) × 100

   Where:
   ΣP₁ = Sum of prices of all commodities in the current year.
   ΣP₀ = Sum of prices of all commodities in the base year.

   Limitation: This method does not consider the relative importance (quantities) of different commodities. All items are given equal weight, which may not be realistic.

3. Explain Laspeyre's Price Index method with its formula.

   Laspeyre's Price Index is a weighted index number. It uses the quantities of the base year as weights to give importance to different commodities. It answers the question: "What is the cost of buying the base year basket at current year prices?"

   Formula: P₀₁ = (ΣP₁Q₀ / ΣP₀Q₀) × 100

   Where:
   P₁ = Current year prices.
   P₀ = Base year prices.
   Q₀ = Base year quantities.

   This method is more accurate than the simple aggregate method because it accounts for the consumption patterns of the base year.

4. Distinguish between Simple Aggregate Index and Laspeyre's Index.

   • Simple Aggregate Index: Uses only prices. Ignores quantities. All commodities have equal importance. Formula: (ΣP₁/ΣP₀)×100. Less accurate.
   • Laspeyre's Index: Uses both prices and base year quantities. Gives weight to commodities based on their importance. Formula: (ΣP₁Q₀/ΣP₀Q₀)×100. More realistic and accurate.

5. Construct a price index for 2014 taking 1991 as base using the simple aggregate method.

   Commodity	Price 1991 (P₀)	Price 2014 (P₁)
   Wheat	200	250
   Rice	300	400
   Pulses	400	500
   Milk	2	3
   Clothing	3	5

   Solution:
   ΣP₀ = 200 + 300 + 400 + 2 + 3 = 905
   ΣP₁ = 250 + 400 + 500 + 3 + 5 = 1158
   P₀₁ = (ΣP₁ / ΣP₀) × 100 = (1158 / 905) × 100 = 127.96

   Interpretation: Prices increased by 27.96% from 1991 to 2014.

📌 Part C – 6/8 Marks Questions (Long Answer)

1. What are index numbers? Explain their uses in detail.

   Index numbers are specialized averages designed to measure the relative changes in the level of a phenomenon (like price, quantity, or value) over time or across different locations. They are expressed as percentages, with a base year value usually taken as 100.

   Uses of Index Numbers:

   • Policy Formulation: Governments use index numbers (like CPI, WPI) to frame economic policies related to inflation, taxation, and interest rates.
   • Measuring Inflation: Index numbers are the primary tools to measure the rate of inflation in an economy. The Wholesale Price Index (WPI) and Consumer Price Index (CPI) are key examples.
   • Dearness Allowance (DA): Index numbers, especially the Consumer Price Index, are used to calculate the Dearness Allowance for government employees and workers in the organized sector to protect them from the rising cost of living.
   • Purchasing Power of Money: Index numbers help in determining the real value of money. As the price index rises, the purchasing power of money falls. The relationship is: Purchasing Power = 1 / Price Index.
   • Business and Industry: Businesses use index numbers to study market trends, forecast demand, and make decisions about production, pricing, and inventory.
   • Comparison Over Time: They allow us to compare the economic conditions of different time periods. For example, we can compare the price level of 2020 with that of 2010.
   • Economic Forecasting: Index numbers reveal trends and tendencies, which are essential for economic planning and forecasting future activities.

2. Explain the Simple Aggregate Method and Laspeyre's Method of constructing index numbers. Construct Laspeyre's index from the given data.

   1. Simple Aggregate Price Index:
   This method is calculated by dividing the sum of current year prices by the sum of base year prices and multiplying by 100.
   Formula: P₀₁ = (ΣP₁ / ΣP₀) × 100
   Drawback: It treats all commodities equally, ignoring their relative importance in consumption.

   2. Laspeyre's Price Index:
   This is a weighted index that uses base year quantities (Q₀) as weights. It shows the change in the cost of purchasing the base year's basket of goods at current prices.
   Formula: P₀₁ = (ΣP₁Q₀ / ΣP₀Q₀) × 100
   Advantage: It gives importance to commodities based on their base year consumption, making it more realistic.

   Problem: Construct Laspeyre's Price Index from the following data:

   Commodity	P₀ (Base Year Price)	Q₀ (Base Year Qty)	P₁ (Current Year Price)
   A	10	5	15
   B	15	8	20
   C	20	12	25

   Step 1: Calculate P₀Q₀ and P₁Q₀.

   Commodity	P₀Q₀	P₁Q₀
   A	10 × 5 = 50	15 × 5 = 75
   B	15 × 8 = 120	20 × 8 = 160
   C	20 × 12 = 240	25 × 12 = 300
   Total	ΣP₀Q₀ = 410	ΣP₁Q₀ = 535

   Step 2: Apply Laspeyre's formula.
   P₀₁ = (ΣP₁Q₀ / ΣP₀Q₀) × 100
   P₀₁ = (535 / 410) × 100
   P₀₁ = 1.3049 × 100 = 130.49

   Interpretation: The prices have increased by 30.49% from the base year to the current year, based on the base year consumption pattern.

3. From the following data, construct (a) Simple Aggregate Price Index and (b) Laspeyre's Price Index. Comment on the results.

   Commodity	P₀ (Base Price)	Q₀ (Base Qty)	P₁ (Current Price)
   A	2	8	4
   B	5	10	6
   C	4	14	5
   D	2	19	2

   Solution (a) Simple Aggregate Index:

   • ΣP₀ = 2 + 5 + 4 + 2 = 13
   • ΣP₁ = 4 + 6 + 5 + 2 = 17
   • P₀₁ = (17 / 13) × 100 = 130.77

   Solution (b) Laspeyre's Index:

   • First, calculate ΣP₀Q₀ = (2×8) + (5×10) + (4×14) + (2×19) = 16 + 50 + 56 + 38 = 160
   • Calculate ΣP₁Q₀ = (4×8) + (6×10) + (5×14) + (2×19) = 32 + 60 + 70 + 38 = 200
   • P₀₁ = (200 / 160) × 100 = 125.00

   Comment on Results:

   • The Simple Aggregate Index shows a 30.77% increase in prices (130.77).
   • Laspeyre's Index shows a 25% increase (125.00).
   • The difference arises because the Simple Aggregate Index treats all commodities equally, while Laspeyre's Index gives weight according to base year quantities. Laspeyre's is generally more accurate as it reflects the consumption pattern of the base year. Here, commodity D, whose price did not change, has a high quantity (19 units), pulling the weighted index down compared to the simple one.