Cost of Living Index Number – Meaning, Uses and Formulas

 Q. What is the cost of Living Index Number? Discuss its uses. Give formulas you will use in the construction of cost of living index number.

Ans. Meaning of Cost of Living Index Number: Cost of living index numbers show the direction and magnitude of change taking place in the cost of living of specific group of persons at given time and place. Its purpose is to know how much increase or decrease has taken place in the expenditure made by a consumer on his living, therefore these are also known as consumer price index. Effect of changes in the prices is not uniform on all the classes of a society because different classes of people consume different commodities and changes in the prices of the commodities are different. Therefore, separate cost of living indices are constructed for different classes of people and for different places. Consumer Price Index Numbers are those index numbers which measure the effects on living conditions of different classes of consumers for any change in the level of prices over a period of time. Such types of indices are constructed in order to find out how the economic progress of a country has affected the standard of living of a particular class of people. 

Uses of Consumer Price Index: The different uses of consumer price index are given below.

(i) To Examine the Effects of Changes in Retail Prices: It is used to examine the effect of change in the retail prices on the cost of living of a particular class of people. 

(ii) Helpful in Policy Formulation: The government may decide its price control, minimum wages, rationing policies in the light of the changes in the cost of living index.

(iii) Fixation of Dearness Allowance: The amount of dearness allowance and revision of wages of different categories of employees are decided on the basis of consumer price index. 

Construction of Consumer Price Index: The procedure of constructing a consumer price index is as follows:

(1) Decision about the Class of People: First of all, it should be ascertained that for which class consumer price index will be constructed, i.e., whether the index is related to industrial workers, teachers, office employees, etc. At the same time, the scope of the index should also be well defined. 

(2) Conducting Family Budget Enquiry: After deciding about the specific class, some families from that class should be selected by random sampling and their budgets should be studied to make findings about their items of income-expenditure, quantities of commodities and size of families etc. According to convenience, the items of consumption are divided into five main categories: (i) Food, (ii) Clothing, (iii) Fuel and Lighting, (iv) House Rent, (v) Miscellaneous. 

(3) Obtaining Price Quotations: After selecting the commodities, their retail prices are obtained. Retail prices of the selected comodities are collected from the reliable sources and from those places from where the people of that class buy goods.

(4) To Decide Weight: To express the relative importance of the items of consumption, selective weights are assigned to them. Weights can be given into two ways: (i) In the proportion of consumption quantity in the base year (q₀) (ii) In the proportion of expenditure made on each commodity in the base year (p₀q₀)

(5) Methods of Constructing Consumer Price Index: After this, consumer price indices are constructed by the following methods:

▶ (i) Aggregate Expenditure Method: In this method, wages are assigned to items on the base of base year quantities.

Consumer Price Index (P₀₁) =

∑ p₁q₀∑ p₀q₀

× 100

Aggregative expenditure method is equal to Laspeyre’s Method.

Steps for Calculation

• (i) Quantity in base year (q₀) and prices in current year (p₁) are multiplied and their sum (∑ p₁q₀) is taken. This is the aggregate expenditure in current year.

• (ii) Quantity in base year (q₀) and price in base year (p₀) are multiplied and their sum (∑ p₀q₀) is taken. This is the aggregate expenditure in base year.

• (iii) ∑ p₁q₀ is divided by ∑ p₀q₀ and the quotient is multiplied by 100.

▶ (2) Family Budget Method: Under this method, the weights are assigned to items on the basis of percentage expenditure on the items.

Consumer Price Index (P₀₁) = 

∑ PW∑ W

Where, P = Price Relatives = 

p₁p₀

× 100,

W = Total Expenses = p₀ q₀.

If the geometric mean is used, then,

 P₀₁ = AL[

∑ W log P∑ W

]

Family budget method is equal to Weighted Average of Price Relative Method.

Steps for Calculation

• (i) Price relative of current year for each commodity is computed by the following formula:

• P = 

  p₁p₀

  × 100
• (ii) Price relative of each commodity is multiplied by the expenditure on it or (Value Weight or W) to find out weighted price relatives.
• (iii) Weighted price relatives are summed up (∑PW)
• (iv) ∑W, i.e., summation of weights which is ∑ p₀q₀ is determined.
• (v) ∑PW is divided by ∑W and the quotient is multiplied by 100.

Note I. It should be noted that prices and quantities must be same in units while multiplying. If the units of price and quantity are different, then the unit of quantity must be changed into the unit of price before carrying out multiplication. For example, if the price is per quantal and the quantity purchase is kg, then kg must be to be converted into quindals before carrying out multiplication.

Note 2. The consumer price index numbers (or cost of living index) obtained by both the methods are the same.

Note 3. Aggreate expenditure method should always be preferred to in as much as it proves to be easier than the family budget method so far as calculations are concerned.