Construction of an Index Number:

(a) Concept of price relative

Simplest example of an index number is a price relative. It define as a ratio of price of a single commodity in a given period is called current period Equation to its price in some past period is called base or reference period Equation .

Price Relative (PR) Equation

Example: In 1990 a loaf of bread was being sold at Rs. 2. But in 1998 the consumers had to pay Rs. 10 for the same bread. By how much the bread had become costlier in 1998?

Solution:

Base year price Equation

Current year price Equation

Price relative Equation

Equation

(b) Concept of weights

There are two types of index number such as simple and weighted. Weight represent importance of different items in relation to each other.

  • Simple index number are index numbers with equal weights.

  • Weighted index numbers are with unequal weights.

Construction of simple index number

There are two methods of constructing simple index numbers:

(a) Simple aggregate method

(b) Simple average of price relative method

Example: The price of three commodities A, B and C increased from Rs. 50, 7 and 3 in 1997 to Rs. 52, 8 and 5 respectively in 1998. Find how much on an average price have increased?

(a) Simple aggregate method

Equal weight are given.

Steps:

1. Find the sum of current year prices of all items included in list Equation

2. Find the sum of base year prices of the same items Equation

3. Use the formula: Equation

Solution:

Example of Simple aggregate method

Commodity

Price in 1997 Equation

Price in 1998 Equation

A

50

52

B

7

8

C

3

5

Equation

Equation

Equation

Price increase in one year Equation

(b) Simple average of price relative method

Steps:

1. Find % price relative for each commodity Equation

2. Find sum of these % price relative Equation

3. Divide Equation by number of commodities included in the list.

Formula: Equation

Solution:

Example of Simple average of price relative method

Sr. No.

Commodities

Price (in Rs.)

Price relative (PR) Equation

1997 Equation

1998 Equation

1

A

50

52

Equation

2

B

7

8

Equation

3

C

3

5

Equation

N Equation

Equation

Equation

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