Cost of Living Index Number is constructed to study the effect of changes in the price of goods and services of consumers for a current period as compared with base period.

**Construction
of Cost of Living Index Number**

Cost of Living Index
Number is constructed to study the effect of changes in the price of goods and
services of consumers for a current period as compared with base period. The
change in the cost of living index number between any two periods means the
change in income which will be necessary to maintain the same standard of
living in both the periods. Therefore the cost of living index number measures
the average increase in the cost to maintain the same standard of life.
Further, the consumption habits of people differ widely from class to class
(rich, poor, middle class) and even with the region. The changes in the price
level affect the different classes of people, consequently the general price
index numbers fail to reflect the effect of changes in their cost of living of
different classes of people. Therefore, cost of living index number measures
the general price movement of the commodities consumed by different classes of
people.

(i) It indicates whether
the real wages of workers are rising or falling for a given time.

(ii) It is used by the
administrators for regulating dearness allowance or grant of bonus to the
workers.

The cost of living index
number can be constructed by the following methods,

(i) Aggregate
Expenditure Method (or) Weighted Aggregative Method.

(ii) Family Budget
Method.

This is the most common
method used to calculate cost of living index number. In this method, weights
are assigned to various commodities consumed by a group in the base year. In
this method the quantity of the base year is used as weight.

The formula is given by,

**Note**

The formula for
Aggregate Expenditure Method to calculate Cost of Living Index Number is same
as formula of Laspeyre’s Method.

In this method, the
weights are calculated by multiplying prices and quantity of the base year.
(i.e.)*V* =
∑ *p*_{0} *q*_{0}
. The formula is given by,

**Note**

This method is same as
the weighted average of price relative method.

**When to Use ? **

When the Price and
Quantity are given, Aggregate Expenditure Method is used

When the Price and
Weight are given, Family Budget Method is used.

**Example
9.15**

Calculate the cost of
living index number for the following data.

*Solution:*

**Example
9.16**

Calculate the cost of
living index number for the year 2015 with respect to base year 2010 of the
following data.

*Solution:*

Here the base year
quantities are given, therefore we can apply Aggregate Expenditure Method.

Hence, the Cost of Living Index
Number for a particular class of people for the year 2015 is increased by 12.61
% as compared to the year 2010.

**Example
9.17**

Calculate the cost of
living index number by consumer price index number for the year 2016 with
respect to base year 2011 of the following data.

*Solution:*

Here the base year
quantities are given, therefore we can apply Aggregate Expenditure Method.

Hence, the Cost of Living Index
Number for a particular class of people for the year 2016 is increased by
59.0679 % as compared to the year 2011.

**Example
9.18**

Construct the cost of
living index number for 2011 on the basis of 2007 from the given data using
family budget method.

*Solution:*

Hence, the Cost of Living Index
Number for a particular class of people for the year 2011 is increased by 25.25
% as compared to the year 2007.

Tags : Uses, Methods, Solved Example Problems | Applied Statistics , 12th Business Maths and Statistics : Chapter 9 : Applied Statistics

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12th Business Maths and Statistics : Chapter 9 : Applied Statistics : Construction of Cost of Living Index Number | Uses, Methods, Solved Example Problems | Applied Statistics

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