In this paper we are deals that various type of index numbers and measured value an index number is a statistical value that measures the change in a variable with respect to time. Index numbers are meant to study changes in the effects of factors which cannot be measured directl

P, ELAVARASI

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 TYPES OF INDEX NUMBERS AND METHOD OF INDEX NUMBERS (P.ELAVARASI,R.RAMYA,Dr.S.SANGEETHA,M.MAHALAKSHMI) (priyaperiyasammy13@gmail.com,sangeethasankar2016@gmailcom ) Department of Mathematics Dhanalakshmi Srinivasan College of  Arts and Science for Women (Autonomous) Perambalur Abstract:  In this paper  we are deals  that  various type of index numbers and measured value an index number is a statistical value that measures the change in a variable with respect to time. Index numbers are meant to study changes in the effects of factors which cannot be measured directly   Keywords:  Price Index ,  Quantity Index numbers , WPI, RPI, weight Introduction:    An index number is a statistical value that measures the change in a variable with respect to time. Index numbers are meant to study changes in the effects of factors which cannot be measured directly .  Two variables that are often considered in this analysis are price and quantity. With the aid of index numbers, the average price of several articles in one year may be compound with the average price of the same quantity of the same articles in a number of different years. These are several sources of ‘official’ statistics that contain index numbers for quantities such as food prices. Clothing prices housing, wages and so on BASIC DEFINITION  Definition : 1.1  An index number is a statistical measure designed to show changes in a variable or a group or related variable with respect to time, geographic location or other characteristics such as income. Profession etc.  Definition : 1.2  Measure changes in price over a specified period at time it is basically the ratio of the price of a certain number of commodities at the present years again base year.     Definition : 1.3   As the name suggest, these indices pertain to measuring changes in volumes of commodities like goods produced or good consumed etc.  Definition : 1.4   These pertain to compare change in the monetary value of imports, exports, production or consumption of commodities.  Definition : 1.5  In the fixed base, a particular year is chosen as base year and numbers are expressed as relative of that year.  Types of index number : 2.1  Types of index numbers    Price index     Quantity index    Value index  Wholesale price           Retail Price   Index (WPI)       index (RPI)      Price Index : 2.2   For measuring the value of money, the general price index is used. It is an index number which compares the prices for a group of commodities at a certain time rate place with prices of a base period.   a) Whole sale price Index (WPI)   The wholesale price index reveals the changes in the general price level of a country.  b) Retail price Index (RPI)  Retail price index reveals the changes in the retail prices of commodities, such as consumption goods, bank, deposits, bonds etc.   Quantity Index numbers : 2.3  Quantity index numbers study the changes in the volume of goods produced or consumed for instance, industrial production, agricultural production import, export, etc. They are useful and helpful to study the output in an economy.   Value Index Numbers 2.4  Value index numbers are easy to calculate. Here value in Product of Price and Quantity. The value index or V is the sum of the values of a given year divided by the sum of the values of the base year. The value index is a type not in wide use. The formula is   Value index or V =  x 100 or  ∑  0 0 V =  Where,  V1 = Total values of all commodities in the given period.  V0 = Total values of all commodities in the base period.      Methods of Index Numbers : 2.5  Methods of index numbers   Unweighted (simple)       Weighted   Simple aggregate   simple average of   Weighted              weighted      Price relative     Aggresate             Average of                      Price relative   Unweighted 2.6 1.Simple aggregate method :    This is the simplest methodof constructing the index numbers. The prices of the different commodities of the current year are added and the total is divided by the sum of the prices of the base year commodity and multiplied by 100 :  symbolically,    P  x 100  ∑  0 P01 = Price index number for the current year with reference to the base year.  ∑  1 =Aggregate of prices for the current year.   ∑  0 =Aggregate of prices for the base year.   Example : 1   Commodity  Price in 1990  Price in 1991  A  B  C  D  90  40  90  30  95  60  110  35     Construct an index number for 1991 taking 1990 as base.   Commodity Price in 1990 Price in 1991 Solution :  Construction of price index   P01 = ∑        ∑               x 100  = 120 2. Simple average of price relative method  In this method, the price relative of each item is calculated separately and then averaged. A price relative is the price of the current year expressed as a percentage of the price of the base year symbolically  P01=            ∑       N = Number of items. When the geometric mean is employed instead of the arithmetic mean then the formula is  P01 = antilog ∑                   = antilog ∑          A B C D 90 40 90 30 95 60 110 35  ∑        = 250 ∑            Where P =            Weighted index numbers : 1. Weighted aggregate index numbers : According to this method, prices them selves are weighted by Quantities, ie, p x q. Thus physical Quantities are used as weights. There are various methods of assigning weights and thus various formulas have been formed for the construction of index numbers. Some of the important formulae are given below : 1. Laspeyres method 2. Paasche’s method 3. Bowley’s method 4. Fisher’s ideal method 5. Marshall – Edgeworth method 6. Kelly’s method 7. Walsch’s method. A. Lasypeyre’s method : In this method the base year Quantities are taken as weights : symbolically P01 (La) = ∑         ∑       x 100  B. Paasche’s method In this method , the current year Quantities are taken as weights symbolically. P01 (Pa) = ∑        ∑          x 100 C. Bowley’s method This is an index number got by the arithmetic mean of Laspeyre’s and Passche’s method symbolically This method takes into account both the current and the base (Periods) symbolically. P01 (B) = ∑       ∑        ∑       ∑            x 100 =      L = Laspeyre’s method P = Paasche’s method D. Fisher’s Ideal method : Fisher’s price index number is given by the geometric mean of Laspeyre’s and Paasche’s formula symbolically P01 (B) =        = ∑        ∑            ∑        ∑           x 100 E. Marshall edge worth method : In marshall – Edge worth’s index number the arithmetic mean of base year – current year Quantities is taken as the weights.  P01 (Ma) = ∑             ∑                x 100 P01 = ∑         ∑        ∑         ∑           x 100 F. Kelly’s method Kelly’s index number uses Quantities of some period as weights. This weight is kept constant for all periods. If we denote it by q, then kelly’s index number is given by P01 (K) = ∑       ∑         x 100 G. Walsch’s method Walsch’s index number uses the geometric mean of the base year and current year Quantities as weight. P01 (wa) = ∑           ∑             x 100 2. Weighted average of price relative Price relative is not calculated by the weighted aggregate method. If we know the values consumed in the base year, then we can construct the weighted index number according to the weighted average of relative method. P01 =              ∑          x 100 = ∑       ∑      P = price relative              ,  V = Value weight (    ) Exmaple : Compute the five different weighted index numbers for 1990 from the following data. Commodity Price Quantity 1980 1990 1980 1990 A B C D E 2 5 4 2 4 6 5 2 8 10 14 19 6 5 10 13  Solution : Commodity 1980 1990 P0  q0 P1 q0 P0  q1 P1 q1 P0 q0 P1 q1 A B C D 2 5 4 2 8 10 14 19 4 6 5 2 6 5 10 13 16 50 46 38 32 60 70 38 12 25 40 26 24 30 50 26   160 200 103 130  1) Laspayre’s index = P01 =∑        ∑         x 100 =        x 100 = 125    2) Paasche’s index = P01 = ∑        ∑         x 100 =         x 100 = 126.21 3) Fisher’s ideal index P01 = ∑             ∑        ∑            ∑         x 100 =                    x 100 =                =           = 125.6 4) Dorbish and Bowley’s method P01 =      =            = 125.6 P01 = ∑        ∑       ∑         ∑         x 100 =                   x 100 =            x 100 = 125.6 1) Marshall – Edge worth index P01 = ∑             ∑              x 100 = ∑             ∑              x 100 =                x 100 =        x 100 = 1.2547 x 100 = 125.5 Example : Products P0 q0 P1 q1 A B C D 12 4 8 20 100 200 120 60 20 4 12 24 120 240 150 50    Fort the data given above, find the index number by Paasche’s method and Laspeyre’s method. Commodity P0 q0 P1 q1 P0  q0 P0 q1 P1  q0 P1 q1 A B C D 12 4 8 20 100 200 120 60 20 4 12 24 120 240 150 50 1200 800 960 1200 1440 960 1200 1000 2000 800 1440 1440 2400 960 1800 1200               4160             4600             5680             6360  1) Laspayre’s index = P01 =∑        ∑         x 100 =          x 100 = 136.54   2) Paasche’s index = P01 = ∑        ∑         x 100 =           x 100 = 136.54 Example : Compute Laspeyre’s, Paasche’s and Fisher ideal index x numbers for the following data Products P0 q0 P1 q1 A B C D 6 2 4 10 10 2 6 12 50 100 60 30 50 120 60 25  Commodity P0 q0 P1 q1 P0  q0 P0 q1 P1  q0 P1 q1 A B C 6 2 4 10 2 6 50 100 60 50 120 60 300 200 240 300 240 240 500 200 360 500 240 360 D 10 12 30 25 300 250 360 300               1040             1030             1420             1400  1) Laspayre’s index = P01 =∑        ∑         x 100 =          x 100                                                   = 136.54   2) Paasche’s index = P01 = ∑        ∑         x 100 =           x 100                                                  = 135.92 Conclusion:    The index numbers are used to measures all types of Quantitative changes in the agricultural, industrial and commercial fields, as also in such economic magnitudes as income, employment, exports, imports, prices, etc.  References:     1. Dr.V.S.Soundara pandian, “Business Statistics” Soundhar Publications, First Edition – 2002.  g 2. Bagavathi. V pillai R.S.N, “ Statistics” Rajendra Ravindra printers (pv). Ltd. Seventeenth edition – 1984.  3. Navitham.Pa M.sc., M.Phil, “Bussiness Statistics” Jai publishers, Trichy –  21.  4. Dr.D.Joseph Anbarasu “Bussiness Statistics” Learntech press, Trichy – 102.  5. S.P.Gupta “ Statistical Methods” Twenty – Eighth Edition – 1997 sultan chand & Sons New Delhi – 2.   

TYPES OF INDEX NUMBERS AND METHOD OF INDEX NUMBERS

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TYPES OF INDEX NUMBERS AND METHOD OF INDEX NUMBERS

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