Methods of construction Index Numbers A Aggregative Method

Methods of construction Index Numbers A. Aggregative Method 1. Simple aggregative method or Unweighted index Nos. B. Simple average of price relative method 2. Weighted aggregative method Lasperyer’s Index Number(method) *Fisher’s Index Number Paache’s Index Numbers (method)

A. Aggregative Method 1. Simple OR Unweighted index Numbers: This is the simplest of all the methods of constructing index numbers. In this method, Index Numbers is calculated by using the following formula : P o 1 = ΣP 1 ______ X 100 ΣP 0 Po 1 = Price Index no. of current year P 1 = Current year price Po = Base year price ΣPo = Total of base year price of all commodities. ΣP 1 = Total of current year price of all commodities.

A. Aggregative Method Example : With the help of following data. Calculate index number for 2010 taking 2006 as base year. commodity Price in 2006(Rs. ) A 100 Price in 2010(Rs. ) 145 B 90 130 C 145 200 D 180 275 E 85 150

Solution: commodity Price in 2006(Rs. )(Po) Price in 2010(Rs. )(P 1) A 100 145 B 90 130 C 145 200 D 180 275 E 85 150 ∑Po =600 ∑P 1 = 900

Solution: ∑P 1 ____ X ∑Po Po 1 = 100 900 ____ X 100 600 900 ____ = 6 =150 It means that there is a net increase of 50% in the price of commodities in 2010 A compared to the price of 2006

2. Weighted Aggregative Method There are various methods and formulae of calculating index numbers by using weighted aggregative method. Some of them are given below 1. Laspeyers Index Number : ΣP 1 qo ______ Po 1 = ΣP 0 qo X 100 P 1 = one time 2. Paasche’s Index Number P o 1 = ΣP 1 q 1 ______ X 100 ΣP 0 q 1 P 0 = one time 3. Fisher’s Ideal Index Number: ΣP 1 qo ΣP 1 q 1 ______ X X 100 ΣP 0 qo ΣP 0 q 1 Example -

2. Weighted Aggregative Method Example : Construct index Numbers of Prices from the data given below by applying : (1) Laspeyer’s formula (2) Paasche’s formula (3) Fisher’s formula Commodities Base year Current year Price (po) Quantity (qo) Price (P 1) Quantity (q 1) A 2 40 3 20 B 1. 5 30 2. 5 40 C 1 50 1. 5 30 D 2. 5 20 2 80

Solution Commodities Base year Current year p 1 q 0 p 0 q 0 P 1 q 1 p 0 q 1 Price (po) Quantity (qo) Price (P 1) Quantity (q 1) A 2 40 3 20 120 80 60 40 B 1. 5 30 2. 5 40 75 45 100 60 C 1 50 1. 5 30 75 50 45 30 D 2. 5 20 2 80 40 50 160 200 ∑p 1 q 0 =310 ∑p 0 q 0= 225 ∑p 1 q 1= 365 ∑p 0 q 1= 330 Total = 1. Laspeyers Index Number : ΣP 1 qo ______ Po 1 = ΣP 0 qo X 100 Laspeyers Index Number : P o 1 = 310 ______ X 100 225 = 137. 8

2. Paasche’s Index Number P o 1 = ΣP 1 q 1 ______ X 100 ΣP 0 q 1 Paasche’s Index Number P o 1 = 365 ______ X 100 330 = 110. 6 3. Fisher’s Ideal Index Number: ΣP 1 qo ΣP 1 q 1 ______ X X 100 ΣP 0 qo ΣP 0 q 1 Fisher’s Ideal Index Number: 310 365 ______ X X 100 225 330 1. 378 x 1. 106 x 100 =1. 23 x 100 = 123 Ans.

B. Simple Average of Price relatives Method Steps : 1. Price relatives of the current year will be calculated by applying the formula = __1 X 100 P Po 2. Total of the price relatives shall be obtained. 3. Aggregate of the price relatives will be divided by the price of commodities. 4. Finally we shall apply the following formula : Po 1 P 1 x 100 Σ __ Po = ______ N Po 1 = Price Index of the current year. __1 X 100 = Price Relatives of the current year P Po N= Number of commodities.

Example. 1: Construct index number by simple average of price relatives method for 2007 taking the price of 2006 as base from the data given below- Commodities Price (in Rs. ) 2006 2007 A 30 45 B 40 50 C 60 72 D 80 88 E 10 13

Solution : Commodities Price (in Rs. ) Price relatives __ X 100 P 1 Po 2006 (po) 2007 (P 1) A 30 45 45/30 x 100 =150 B 40 50 50/40 x 100 =125 C 60 72 72/60 x 100 =120 D 80 88 88/80 x 100 =110 E 10 13 13/10 x 100 = 130 Σ( p 1/po x 100) = 635 N= 5 Po 1 P 1 x 100 Σ __ Po = ______ N = ____ 635 5 =127 Ans.

Example 2. Calculate Price index Numbers from the following data taking ; (i) 2003 as base year (ii) 2006 as base year (ii) 2003 to 2005 as base year Year Price 2003 60 2004 70 2005 80 2006 90 2007 100

Solution (i) Calculation of price relatives taking 2003 as base year Year Price (Rs. ) Price ralatives 2003 60 =100 2004 70 70/60 x 100 =116. 67 2005 80 80/60 x 100 =133. 33 2006 90 90/60 x 100 =150. 00 2007 100/60 x 100 =166. 67 (ii) Calculation of price relatives taking 2006 as base year Year Price (Rs. ) Price ralatives 2003 60 60/90 x 100 =66. 67 2004 70 70/90 x 100 =77. 78 2005 80 80/90 x 100 =88. 89 2006 90 2007 100 =100 100/90 x 100 =111. 11

(iii) Calculation of price relatives taking 2003 to 2005 as base year Average price of 2003 , 2004, 2005 = 60+70+80 _____ 3 210 = ____ = 70 3 Therefore 2004 will be assumed as Rs. 100 Calculation of Price relatives with average Price =70 Year Price (Rs. ) Price ralatives 2003 60 60/70 x 100 =85. 71 2004 70 = 100 2005 80 80/70 x 100 =114. 29 2006 90 90/70 x 100=128. 57 2007 100/70 x 100 =142. 86

Limitations of the Simple Aggregative Method : (1) Weight age not given (2) Greater influence of items with largest unit price :

Types of Index Number: There are 03 in numbers as follows : - 1. Consumer price Index number or cost of living or retail price index number 2. Wholesale Price index number – 3. Industrial number of industrial production 1. Consumer price Index number Consumer price index numbers are intended to represent the average change over a time in the prices paid by the ultimate consumers. This index is also called cost of living index number. To study the effects of rise and fall in the prices of different commodities on different Classes of consumers. The commodities are broadly classified into following groups : (1)Food (2) Clothing (3) Fuel and lighting (4) House rent and (5) Miscellaneous

Features of Consumer Price Index Number (1) CPIN measures only changes in prices (2) CPIN only tell us how much, the consumer of a particular class have to pay to get a basket of goods and services at a particular point of time. (3) CPIN are constructed separately for different classes of people or groups or sections of society, such as Govt. employees, Industrial workers, Agricultural workers etc. (4) CPIN can be constructed on the basis of the following; (i) Aggregative expenditure Method or Aggregative method (ii) Family Budget or Weighted relative method

Importance of CPIN (1) Helpful in wage negotiations : (2) Measures for changing purchasing power (3) Helpful in analyzing markets : (4) Helpful in determining govt. policy :

Methods of Construction of CPIN (1) Aggregative Expenditure method or weighted aggregative method (2) Family Budget method or Weighted average of price relatives method 1. Aggregative Expenditure method or weighted aggregative method –also known as Laspeyer’s method ΣP 1 qo ______ P o 1 = ΣP 0 qo X 100 2. Family Budget method or Weighted average of price relatives method P o 1 ΣPV ____ = ΣV __1 X 100 P Po V = Value weights = Po qo (weight i. e. quantity) P= Price relatives = = Σ PV total of product of price relatives and weight ΣV = Total of weights

Construct the consumer price Index Number for 2005 on the basis of 2004 From the following data using 1. Aggregative expenditure method 2. Family Budget method Articles Quantity consumed in 2004 Unit Price in 2008(Rs. ) Price in 2010(Rs. ) Whet 2 Per Quintals 150 165 Gram 1 Per Quintals 80 100 Rice 1 Per Quintals 120 150 Bajra 1. 5 Per Quintals 60 90 Arhar 1. 5 Per Quintals 100 140 Oil 10 Kg. Per kg 10 12 Sugar 40 kg Per Kg 2 3

Solution 1. Aggregative expenditure method Articles Quantity consumed in 2004 (qo) Unit Price in 2008(Rs. ) (po) Price in 2010(Rs. ) (P 1) Poqo P 1 q 0 Whet 2 Per Quintals 150 165 300 330 Gram 1 Per Quintals 80 100 Rice 1 Per Quintals 120 150 Bajra 1. 5 Per Quintals 60 90 90 135 Arhar 1. 5 Per Quintals 100 140 150 210 Oil 10 Kg. Per kg 10 12 100 120 Sugar 40 kg Per Kg 2 3 80 120 ΣPoq 0= 920 ΣP 1 qo= 1165 ΣP 1 qo ______ CPIN = ΣP 0 qo X 100 1165 ______ CPIN = 920 X 100 = 126. 63 ANS

Solution Articles 2. Index Number By Family Budget Method Quantity consumed in 2004 (qo) Unit Price in 2008(Rs. ) (PO) Price in 2010(Rs. ) (P 1) Wheat 2 Qtl Per Quintals 150 165 Gram 1 Qtl Per Quintals 80 Rice 1 Qtl Per Quintals Bajra 1. 5 Qtl Arhar Poqo (V) PV 110 300 33000 125 80 10000 120 150 125 120 15000 Per Quintals 60 90 150 90 13500 1. 5 Qtl Per Quintals 100 140 150 21000 Oil 10 Kg. Per kg 10 12 120 100 12000 Sugar 40 kg Per Kg 2 3 150 80 12000 ΣV= 920 ΣPV= 116500 ΣPV ______ CPIN = ΣV P 1 __ Po (p) X 100 116500 ______ CPIN = 920 = 126. 63 ANS

2. Wholesale price Index Number Wholesale price index number is that index which represents general change In the prices of the commodities. In India the wholesale price index numbers are constructed on weekly basis. The wholesale price index series with base year 1993 -94 became effective in India from April 1, 2000 shifting from the earlier base year of 1981 -82. In India for the construction of wholesale price index, goods are mainly classified into the following three main groups : (1) Primary groups : It includes 98 commodities like –rice, fruits, vegetables and non- food articles like cotton, jute, metals. These are given weight as 22. 02. (2) Energy groups : In this category 19 items like coal, petroleum products, electricity, fuel light & lubricants etc. are included and are given weight as 14. 23. (3) Manufacturing groups : Under this category 318 articles like textiles, sugar, paper, machinery, chemicals , fertilizers, leather etc. are inluded and are given as 63. 75 Weight = 22. 02 + 14. 23 + 63. 75 = 100%

Utility or Uses of Wholesale Price Index 1. Forecasting Demand & Supply 2. Determination of real changes in Aggregates : Real change in National Income – Example – Suppose the NI of a country in 2004 on the basis of current prices amounts 900 crores has increased to 1050 in 2005. further suppose the whole sale price index during the same time period Rises from 130 to 140. The real change can be computed as follows Wholesale price of base year NI at current prices X ____________ Wholesale price of current year 1050 X ___ 130 140 = 975 crores Thus the real increase in NI is of rupee 75 crore (975 -900) against the monetary increase of Rs. 150 crore(1050 -900)

3. Indicator of Rate of inflation : Current year WPI (-) Previous year WPI ________________ X 100 Rate of inflation = Previous year WPI OR = X 2 (-) X 1 _____ X 100 X 1 500 - 400 _____ X 100 400 = 25% inflation

Index Number of Industrial Production The index number of industrial production is designed to measure the change in the level of industrial production in a given period compared to some base period. It measures changes in the quantity of output instead of change in its money value. Index of industrial production = q 1 Σ __ W qo = ______ ΣW OR Q 1=quantity produced in the current year Qo= quantity produced in the base year W= Relative importance of different output ΣRW _____ ΣW R =Relative value i. e. q 1/qo x 100

Example : Construct Index number of industrial production from the following data : Industry OUTPUT Weights Units Base year Current year 1. Manufacturing Production 244 600 85 M. Tones 2. Electrical Products 406 800 5 Th. Tones 3. Mining 130 174 10 M. Tones

Solution 600/244 x 100=245. 90 800/406 x 100=197 Industry OUTPUT Relative Weights RW Value (R) (W) q 1/qo x 100 Base Current year(qo) year (q 1) 1. Manufacturing Production 244 600 245. 90 85 20901. 5 2. Electrical Products 406 800 197 5 985 3. Mining 130 174 134 10 1340. 00 ΣW= 100 ΣRW=23226. 50 Index No. of Industrial. Production = ΣRW _____ ΣW 23226. 50 ____ 100 = 232. 27 (approx. )

Limitations of Index Numbers 1. Estimated : 2. International Comparison 3. Limited use:

Thank You Good Luck