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What methods of Index Number calculation is used to calculate Cost ofLiving Index (CLI)

A cost-of-living index is an ideal price index that measures di erences in theprice of goods and services over a period of time or region and allows forsubstitution to other items as prices vary. In simple terms, exact cost-of-living

index is the cost of achieving a certain standard of living in one year relative tothe cost of achieving the same level next year. Since we cannot directly measurethe standard of living, therefore true cost-of-living index is only a theoreticalconcept not a practical price index formula.

The consumer price Index is most of the times called a cost-of-living indexbut it is di erent in many important ways from a complete cost-of- livingmeasure. oth !"I and !#I would re$ect changes in the price of goods andservices that are directly purchased in the mar%et place but a complete !#Iwould also ta%e into account changes in governmental and environmental factorsthat a ect consumer&s well-being.

!ost -of-living index number can be constructed by the following two '()*formulae+

. Aggregate expenditure method or weighted aggregative method.

). amily budget method or method of weighted relatives.

Aggregate expenditure method or weighted aggregative method

In this method, approximate cost-of-living index is given by the formula

,(./p

/p

((

(,

0ere,,p

1efers to the prices of commodities in the current year

(/ 1efers to the /uantities of the base year

(p 1efers to the prices of the commodities in the base year

The prices of commodities for various groups for the current year are multipliedby the /uantities of the base year and their aggregate expenditure of currentyear is obtained. Then the prices of commodities for base year are multiplied by

the /uantities of the base year and their aggregate expenditure of base year isobtained. inally, the aggregate expenditure of the current year is divided by theaggregate expenditure of the base year and the /uotient is multiplied by ((.

Famil budget method or method of weighted relatives

In this method, the family budgets of a large number of people are collected andthe aggregate expenditure of the average family on di erent items is used asweights. Then current year&s price are converted into price relatives on the basisof base year&s prices and these prices relatives are multiplied by the respectivevalues of the commodities, in the base year. The summation of these products isdivided by the sum of the weights and the resulting 2gure is the re/uired indexnumbers.

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In this method, approximate cost-of-living index is given by the formula

v

pv

0ere,

00 q pv =, values for the base year

,(.pp

3po

,

, for each item#et us consider an example shown in the table below '4alues indicated are notactual*.Commodities

!uantit

consumed in"g in#$$$(

(/*

%rices#$$$

( (p

*

#$&'

' ,p

*

A 5 &$$ #$$6 #$$ '$$

C 7 $ &$$

8(, /p

3 ' )((9 6((97((* 3 : ((

8(( /p

3 '5((9 (((9)((*3 ;((So, C%I * &+#,##

!onsumer "rice Indexes or cost-of-living indexes are used in compensatingthe employees in form of increasing the allowances. nit believes that the weighting pattern mentioned in this report 2tsthe re/uirement, it is clear that special circumstances may arise whereby acompany would feel that a modi2cation in the weights might be needed. In suchcases, the =I> has the authority to o er companies a ?tailor-made? index basedon any national or individual weighting pattern that may be necessary .