INDEX NUMBERS

INDEX NUMBERSPresented by- neha mehta(4222)B.COM - I - smriti rana(4276)1CONTENTSIntroductionDefinitionUsesCharacteristicsClassificationProblemsMethods Value index numbersChain base indexFixed base indexBase conversion INTRODUCTIONA simple index number measures the relative change in one or more than one variable.

An index number measures the relative change in price, quantity, value, or some other item of interest from one time period to another.

. WHAT IS AN INDEX NUMBERAn index number measures how much a variable changes over time.

We calculate the index number by finding the ratio of the current value to a base value.

USES OF INDEX NUMBERS To simplify complexities.

Helpful in comparison.

Useful in Business.

Helpful in Predictions.

To measure purchasing power.

CHARACTERISTICS OF INDEX NUMBERSIndex numbers measure the change in the level of a phenomenon.

Index numbers are specialized averages.

Index numbers measure the effect of changes over a period of time.

6CLASSIFICATION OF INDEX NUMBERSPrice Index

Quantity Index

Value Index

PROBLEMS RELATED TO INDEX NUMBERSSelection of Items.Selection of Prices.Selection of Base Year.Selection of Weights.Selection of An Average.Selection of An Appropriate Formula.

METHODS OF CONSTRUCTING INDEX NUMBERS

SIMPLE AGGREGATIVE METHOD

It consists in expressing the aggregate price of all commodities in the current year as a percentage of the aggregate price in the base year. P01= Index number of the current year. P1 = Total of the current years price of all commodities. P0 = Total of the base years price of all commodities.EXAMPLE

From the data given below construct the index number for the year 2007 on the base year 2008 in Rajasthan state.COMMODITIESUNITSPRICE (Rs)2007PRICE (Rs)2008SugarQuintal22003200MilkQuintal1820OilLitre

6871WheatQuintal9001000ClothingMeter5060Solution :COMMODITIESUNITSPRICE (Rs)2007PRICE (Rs)2008SugarQuintal22003200MilkQuintal1820OilLitre

6871WheatQuintal9001000ClothingMeter5060

index Number for 2008-

It means the prize in 2008 were 34.45% higher than the previous year.SIMPLE AVERAGE OF RELATIVES METHOD.The current year price is expressed as a price relative of the base year price. These price relatives are then averaged to get the index number. The average used could be arithmetic mean, geometric mean or even median.

When geometric mean is used-

Example:From the data given below construct the index number for the year 2008 taking 2007 as by using arithmetic mean.Commodities Price (2007)Price (2008)P610Q22R46S1012T812Solution-

Commodities Price (2007)

Price (2008)

Price RelativeP610166.7Q12216.67R46150.0S1012120.0T812150.0

=603.37These are those index numbers in which rational weights are assigned to various chains in an explicit fashion.

Weighted aggregative index numbers- These index numbers are the simple aggregative type with the fundamental difference that weights are assigned to the various items included in the index. Dorbish and bowleys method. Fishers ideal method. Marshall-Edgeworth method. Laspeyres method.Paasche method. Kellys method.

Weighted Index NumbersLaspeyres Method-This method was devised by Laspeyres in 1871. In this method the weights are determined by quantities in the base.

Paasches Method.

This method was devised by a German statistician Paasche in 1874. The weights of current year are used as base year in constructing the Paasches Index number.

Dorbish & Bowleys Method:This method is a combination of Laspeyres and Paasches methods. If we find out the arithmetic average of Laspeyres and Paasches index we get the index suggested by Dorbish & Bowley.

Fishers Ideal Index:

Fishers deal index number is the geometric mean of the Laspeyres and Paasches index numbers.

Marshall-Edgeworth Method:In this index the numerator consists of an aggregate of the current years price multiplied by the weights of both the base year as well as the current year.

Kellys Method:

Kelly thinks that a ratio of aggregates with selected weights (not necessarily of base year or current year) gives the base index number.

q refers to the quantities of the year which is selected as the base. It may be any year, either base year or current year. Example: Given below are the price quantity data, with price quoted in Rs. per kg and production in qtls. Find- (1) Laspeyers Index (2) Paasches Index (3)Fisher Ideal Index.ITEMSPRICEPRODUCTIONPRICEPRODUCTIONBEEF1550020600MUTTON1859023640CHICKEN2245024500Solution:ITEMSPRICE

PRODUCTION

PRICEPRODUCTIONBEEF1550020600100007500120009000MUTTON185902364013570106201472011520CHICKEN22450245001080099001200011000TOTAL34370280203872031520

Solution:1.)Laspeyres index:

2.) Paasches Index :

3.) Fisher Ideal Index:

Weighted Average Of Price Relative: In weighted Average of relative, the price relatives of the base year price. These price relatives are multiplied by the respective weight of items. These products are added up and divided by the sum of weights. Weighted arithmetic mean of price relative-

P=Price relativeV=Value weights =

Value Index Numbers

Value is the product of price and quantity. A simple ratio is equal to the value of the current year divided by the value of base year. If the ratio is multiplied by 100 we get the value index number. CHAIN BASE INDEX NUMBERSChain base index is that index number in which the year immediately preceeding the one is taken as base year. Steps in construction of Chain base index 1)Computation of link relatives :Link Relatives = Current Years Price 100 Previous Years Price 2) Conversion of link relatives into chain base index : Chain Base Index= LR of current year Chain Index of Previous Year 100 Example: Construct Chain Base IndexYear198519861987198819891990Price

94981029598100YearsPricesLink RelativesChain Base Index1985941001001986 98 98 100 = 104.394

104.3 100 = 104.3 100

1987102102 100 = 104.198104.1 104.3= 108.6 100

19889595 100 = 93.110293.1 108.6 = 101.1 100

19899898 100 = 103.295103.2 101.1= 104.3 100

1990100100 100 = 10298102 104.3= 106.4 100

FIXED BASE INDEX NUMBERS In Fixed base index, the base year remains fixed. For example: We take 1990 as base year for 1991 and1992.

Steps in construction of Fixed Base Index : 1) Computation of Price Relatives Price Relatives = Current Years Price 100 Base Years Price Example: Calculate Chain Base Index and Fixed Index.

Year1992199319941995199619971998Price3122282430272532Solution :

YearPriceLink relativesCBIFBI19923110010010019932270.9670.9670.96199428127.2790.3090.319952485.7177.4077.4199630125.0096.7596.7719972790.0087.0787.0919982592.5980.6180.64BASE CONVERSION

1) Conversion of CBI into FBI Current Years FBI =Current years CBIPrevious Years FBI 100

2) Conversion of FBI into CBI Current Years CBI = Current Years FBI 100 Previous Years FBI

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