2. INDEX NUMBERS

3. An index number measures the relative change in price, quantity, value, or some other items of interest from one time period to another. A simple index number measures the relative change in one or more than one variable.

4. Index Numbers are a specialized type of averages. - M. Blair Index Numbers are devices for measuring differences in the magnitude of a group of related values. - Croxten and Cowden An index number is a statistical measure designed to show changes in a variable or group of related variables with respect to time, geographical location or other characteristics.-Spigel

6. Index numbers give the knowledge as to what changes have occurred in the past. HELPFUL IN PREDICTIONS By Index numbers relative changes occurring in the variables are determined, which simplifies the comparison of Data. HELPFUL IN COMPARISONS Index numbers measures the changes taking place in the Business World and are useful in making a comparative study of the changes. USEFUL IN BUSINESS

7. Choice of the base period.Choice of an average.Purpose of index numbers.Selection of commodities.Data collection.

8. Index Numbers Un-weighted Simple Aggregative Simple Average of Price Relatives Weighted Aggregative Weighted Average of Price Relatives

9. In this method, sum of current year’s prices is divided by sum of base year’s prices and the quotient is multiplied by 100. Its formula is: Where, P 01 = Index number of the current year. = Total of the current year’s price of all commodities. = Total of the base year’s price of all commodities.

10. COMMODITIESUNITS PRICE (Rs) 2007 PRICE (Rs) 2008 SugarQuintal22003200 MilkQuintal1820 Oil Litre 6871 WheatQuintal9001000 ClothingMeter5060

11. COMMODITIESUNITS PRICE (Rs) 2007 PRICE (Rs) 2008 SugarQuintal22003200 MilkQuintal1820 OilLitre6871 WheatQuintal9001000 ClothingMeter5060 Index Number for 2008: It means the prize in 2008 were 34.45% higher than the previous year.

12. In it, initially the price relatives of all the commodities are found out. To calculate price relatives, price of current year (p 1 ) is divided by price of base year (p 0 ) and then, the quotient is multiplied with 100. 1. When ARITHMETIC MEAN is used: 2. When GEOMETRIC MEAN is used: Where N is Numbers Of items.

13. 3. When MEDIAN is used:

14. From the data given below construct the index number for the year 2008 taking 2007 as base year by using arithmetic mean. Commodities Price (2007)Price (2008) P610 Q22 R46 S 12 T8

15. Index number using arithmetic mean Commodities Price (2007)Price (2008) Price Relative P610166.7 Q12216.67 R46150.0 S1012120.0 T812150.0 = 603.37

16. When index numbers is constructed taking into consideration the importance of different commodities, then they are called weighted index numbers. There are two methods of contructing weighted index numbers. 1. Weighted Aggregative Index Numbers. 2. Weighted Average of Price Relative Methods.

17. In it, commodities are assigned weights on the basis of the quantities purchased. Different statisticians have used different methods of assigning weights, which are as follows:  Laspeyre’s method.  Paasche’s method.  Fisher’s ideal method.  Dorbish and Bowley method.  Marshall-Edgeworth’s method.  Kelly’s method.

18. This method was devised by Laspeyres in 1871. In this method the weights are determined by quantities in the base. Paasche’s 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 Paasche’s Index number.

19. This method is a combination of Laspeyre’s and Paasche’s methods. If we find out the arithmetic average of Laspeyre’s and Paasche’s index we get the index suggested by Dorbish & Bowley. Fisher’s Ideal Method: Fisher’s ideal index number is the geometric mean of the Laspeyre’s and Paasche’s index numbers.

20. 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. Kelly’s Method: Kelly thinks that a ratio of aggregates with selected weights (not necessarily of base year or current year) gives the base index number. Where 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.

21. Given below are the price quantity data,with price quoted in Rs. per kg and production in qtls. Find: (1) Laspeyre’s Index (2) Paasche’s Index (3)Fisher Ideal Index. ITEMSPRICE PRODUCTION PRICEPRODUCTION BEEF 1550020600 MUTTON 1859023640 CHICKEN 2245024500 20022007

22. ITEMSPRICE PRODUCT ION PRICEPRODUC TION BEEF 1550020600100007500120009000 MUTTON 185902364013570106201472011520 CHICKEN 22450245001080099001200011000 TOTAL 34370280203872031520

23. 2. Paasche’s Index: 3. Fisher Ideal Index: 1.Laspeyre’s index:

24. In weighted Average of Price relative, the price relatives for the current year are calculated on the basis 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 is given by: Where: P=Price relative V=Value weights =

25. Quantity index numbers are designed to measure the change in physical quantity of goods over a given period. These index numbers represents increase or decrease in physical quantities of goods produce or sold. The method of construction of quantity index is same as that of price index. (1) Simple quantity index numbers (a)Simple Aggregative Method:

26. (b) Simple Average of Relative Method: (i) Using A.M. (ii) Using G.M.

27. (2) Weighted quantity index numbers I. Weighted Aggregate Method (a) Laspeyre’s quantity index no.: (b) Paasche’s quantity index no.:

28. (c) Fisher’s quantity index numbers: (d) Bowley’s quantity index: (e) Marshall’s quantity index:

29. II. Weighted Average of Relative Method: Where, and

30. 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.

31. Various formulae can be used for the construction of index numbers but it is necessary to select an appropriate/suitable formula out of them. Prof. Fisher has given the following tests to select an appropriate formula:  TIME REVERSAL TEST (TRT)  FACTOR REVERSAL TEST (FRT)

32. According to this test, if considering any year as a base year, some other year’s price index is computed and for another price index, time subscripts are reversed, then the both price indicies must be reciprocal to each other. TRT is satisfied when: Where, P 01 is price index for the year 1 with 0 as base and P 10 is the price index for the year 0 with 1 as base.

33. Time reversal test permits interchange of price and quantities without giving inconsistent results, i.e. the two results multiplied together should give the true value ratio: FRT is satisfied when: Price Index x Quantity Index = Value Index OR