Index Number

 INDEX NUMBER

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Introduction

·       It measures the relative change in price, quantity, value or some other items of interest from one time period to another.

·       It can be easily calculated by finding the ratio of the current value to a base value.

 

Characteristics

·       These are specialized averages

·       Measures the change in the level of a phenomenon

·       Measures the effect of changes over a period of time

 

Uses

·       In framing of suitable policies

·       To reveals the trends and tendencies

·       Very much useful in deflating

 

Methods of Constructing Index Number

·       Unweighted

o   Simple Aggregative

o   Simple Average of Price Relative

·       Weighted

o   Weighted Aggregated

o   Weighted Average of Price Relatives

 

1)   Simple Aggregative

 

In Simple Aggregative Method, the total price of commodities in a given (current) year is divided by the total price of commodities in a base year and expressed as a percentage.

Steps involved in Simple Aggregative Method:

1.     Add the prices of all the commodities in the current year. Denote the sum as ∑ P₁

2.     Add the prices of all the commodities in the base year. Denote the sum as ∑ P_o

3.     Use the following formula to find simple price index number of current year based on the base year.

 

Example – 01:

Prices of commodities for the year 2000 and 2004 are as given in the table. Find the simple aggregative price index from the data displayed in the table.

Commodity	Unit	Price in Rs. Per unit
		2000	2004
Wheat	1 kg	10	15
Rice	1 kg	40	30
Pulses	1 kg	10	12
Onions	1 kg	5	13
Oil	1 litre	40	50

Solution:

Commodity	Unit	Price in Rs. Per unit
		2000	2004
Wheat	1 kg	10	15
Rice	1 kg	40	30
Pulses	1 kg	10	12
Onions	1 kg	5	13
Oil	1 litre	40	50
Total		∑P1 = 105	∑Po = 120

The price index number for 2004 taking 2000 as base year is given by

P₀₁ = (∑P₁ / ∑P₀) × 100

P₀₁ = (120 / 105) × 100

P₀₁ = 114.3

It indicates that the prices in the year 2004 had increased by 14.3 % as compared to the year 2000.

 

2)   Simple Average of Relatives Method

In this method, average of price relative of commodity is calculated.

Steps involved

1.     Find price relative for each commodity for the current year using the formula R = (P1 / P0) × 100.

2.     Add all price relatives of all the commodities.

3.     Divide sum obtained in step 2 by the number of commodities (N).

4.     Overall formula for the method is.

Example – 01:

Prices of commodities for the year 2000 and 2004 are as given in the table. Find the price index by a simple average of relative method and using the arithmetic mean from the data given in the table.

Commodity	Unit	Price in Rs. Per unit
		2000	2004
Wheat	1 kg	10	15
Rice	1 kg	40	30
Pulses	1 kg	10	12
Onions	1 kg	5	13
Oil	1 litre	40	50

Solution:

Commodity	Unit	Price in Rs. Per unit		R = (P1 / P0) × 100
		2000	2004
Wheat	1 kg	10	15	(15/10) x 100 = 150.0
Rice	1 kg	40	30	(30/40) x 100 = 75.0
Pulses	1 kg	10	12	(12/10) x 100 = 120.0
Onions	1 kg	5	13	(13/5) x 100 = 260.0
Oil	1 litre	40	50	(50/40) x 100 = 125.0
Total				∑ R = 730

The price index number by simple average of relative method using arithmetic mean for 2004 taking 2000 as base year is given by

P₀₁ = (1/N)(∑ R)

P₀₁ = (1/5)(730)

P₀₁ = 146.0

 

3)    Weighted Aggregated Method

This method involves assigning weights to different items and obtaining weighted aggregate of the prices instead of finding a simple aggregate of prices. Some important methods of constructing Weighted Aggregative Index are as follows:

·        Laspeyre’s Method

·        Paasche’s Method

·        Fisher’s Ideal Method

·        Drobish and Bowley’s Method

·        Marshall Edgeworth Method

·        Walsch’s Method

·        Kelly’s Method

 

Note: According to your Syllabus, we will be only studying Laspeyre’s, Paasche’s, and Fisher’s Methods.

 

i) Laspeyre’s Method

The method of calculating Weighted Index Numbers under which the base year quantities are used as weights of different items is known as Laspeyre’s Method. The formula for Laspeyre’s Price Index is:

P01=∑P1Q0∑P0Q0×100

Here,

P₀₁ = Price Index of the current year

p₀ = Price of goods at base year

q₀ = Quantity of goods at base year

p₁ = Price of goods at the current year

 

ii) Pasche’s Method

The method of calculating Weighted Index Numbers under which the current year’s quantities are used as weights of different items is known as Pasche’s Method. The formula for Pasche’s Price Index is:

P01=∑P1Q1∑P0Q1×100

Here,

P₀₁ = Price Index of the current year

p₀ = Price of goods in the base year

q₁ = Quantity of goods in the base year

p₁ = Price of goods in the current year

 

iii) Fisher’s Method

The method of calculating Weighted Index Numbers under which the combined techniques of Pasche and Laspeyre are used is known as Fisher’s Method. In other words, both the base year and current year’s quantities are used as weights. The formula for Fisher’s Price Index is:

P01=√[(∑P1Q0∑P0Q0)∗(∑P1Q1∑P0Q1)]×100.

Here,

P₀₁ = Price Index of the current year

p₀ = Price of goods in the base year

q₁ = Quantity of goods in the base year

p₁ = Price of goods in the current year

Fisher’s Method is considered the Ideal Method for Constructing Index Numbers.

4)      Weighted Average of Price Relatives Method

Under this method, the base year prices of the commodities are taken as the basis to calculate the price relatives for the current year. The calculated price relatives are then multiplied by their respective weights of the items. After that, the products determined are added up and divided by the sum of weights.

The steps required to construct index number through this method are as follows:

1.     Firstly, calculate the price relatives of the current year (P1/P0)*100; i.e., divide the price of each commodity in the current year by the price in the base year, and denote the value calculated as R.

2.     Now, multiply the price of commodities in the base year (p₀) with their respective weights (q₀), and denote the value weights by W.

3.     After that, multiply the price relatives (R) with value weights (W) and obtain their total; i.e., ∑RW.

4.     Determine the total of value weights; i.e., ∑W.

5.     Use the following formula to determine Index Number:

P01=∑RW/∑W

Example:

Use Weighted Relatives Method and determine the index number from the following data for the year 2021 with 2010 as the base year.

Solution:

Weighted Average of Price Relatives

P01=∑RW/∑W

=102182/790

=129.34

The Index Number of 129.34 shows that there is an increase of 29.34% in the prices in the year 2021 as compared to the year 2010.

 

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