Index numbers

index number 11th standard

1. Index Numbers By Poona jangid 11 th ‘B’

2. Learning objectives :

3. Content: Index numbers- meaning Features of index numbers Advantages of index numbers Problems in construction of index numbers Limitation of index number Methods of construction of index numbers Some important index numbers Uses of different types of index numbers Inflation and index numbers Conclusion (List of formula’s used in construction of index numbers)

4. Index numbers: meaning An index number is a statistical device for measuring relative changes in magnitude of a group of related variables over time Index numbers are expressed in terms of percentage Of the two periods, the period with which the comparison is to be made is known as the base period. Index number for base period is always taken as 100. Therefore the study of index numbers helps us to know percentage change in the values of different variables over a period of time with reference to the base year

5. Features or characteristics of index numbers

6. Advantages of index numbers

7. Problems in construction of index numbers

8. Problems in construction of index numbers

9. Problems in construction of index numbers

10. Limitations of index numbers Limited coverage- index numbers are based on sample items. Qualitative changes are ignored Ignores changes in the consumption pattern Limited applicability Misleading results- index numbers may not be perfect it wrong base year has been taken, wrong formulae or wrong weight age is taken etc Based on averages

11. Methods of constructing index numbers

12. Unweighted (simple) index numbers In this method all items of the series are given equal importance. Index numbers are constructed in two methods Simple aggregative method Simple average of price relative method

13. Simple aggregative method This method is also known as actual price method. It is simple to construct. In this method aggregate price of commodities in current year ( ) are divided by the aggregate price of these commodities in the base year( ) and expressed in percentage symbolically P 1 - price index of current year -sum of prices of commodities of current year - sum of prices of commodities of base year

14. Example: Construct index numbers for 2008 taking 2000 as the base year Solution - Commodities A B C D E Prices in 2000 16 40 35 9 2 Prices in 2008 20 60 70 18 1.50 Commodities Prices in 2000 (P0) Prices in 2008(P1) A 16 20 B 40 60 C 35 70 D 9 18 E 2 1.50 total 102 169.5 169.5 102 = 100 X = 166.18

15. Simple average of price relative method In this method first price relative of current year is calculated. A Price relative is the price for current year expressed as percentage of the period of base year. Symbolically or P1- prices of current year P0- prices of base year N- number of commodities R or - price relative

16. Example: Construct index numbers for following data using average of relative price method Commodities P Q R S T Prices in 1998 40 28 12.5 10 30 Prices in 2004 50 35 15 20 90 Solution: commodities Prices in 1998 Prices in 2004 Price relative (PR) P 40 5 125 Q 28 35 125 R 12.5 15 120 S 10 20 200 T 30 90 300 Total 120.5 210 870 210 120.5 5 = X 100 = 174 Or 870 5 = = 174

17. In the construction all the items of the series are assigned rational weights in an explicit manner. Weights are assigned to various items to reflect their relatives importance in the series. Weights in index numbers are constructed by the following methods Weighted index numbers

18. Weighted aggregative method In this method weights are assigned to various items. Weighted aggregate of the prices are calculated instead of simple aggregates Various techniques are used for assigning weights to items- On the basis of quantities of the base year or On the basis of quantities of current year or On the basis of quantities of current and base year

19. Laspeyre’s method This method was introduced by Mr. Laspeyre in 1871 . in this method weights are represented by the quantities of the commodities in the base year. Formulae is - prices of current year - prices of base year -Quantities of base year - sum total of the product of prices of current year ( ) and quantities of the base year( ) - sum total of the product of prices of base year ( ) and quantities of base year ( )

20. Example: Construct index numbers for following using Laspeyre’ method Commodities 1997 2008 prices quantity prices quantity A 20 4 40 6 B 50 3 60 5 C 40 5 50 10 D 20 10 40 20

21. commodities 1997 2008 prices quantity prices Quantity A 20 4 40 6 160 80 B 50 3 60 5 180 150 C 40 5 50 10 250 200 D 20 10 40 20 400 200 Total 990 630 Solution = 990 630 X 100 = 157.26

22. Paasche’s method This method was introduced by Mr.Paasche in . 1874 in this method weights are represented by the quantities of the commodities in their current year. Formulae Prices of current year prices of base year Quantities of the current year sum of total of the product of price of the current year ( ) and quantities of the current year ( ) sum of total of the product of price of base year ( ) and quantities of the current year ( )

23. Fisher’s method- This method was introduced by Prof.Irving fisher. This method combines the techniques of both Laspeyre’s method and paasche’s method. In other words in fisher’s method weights are represented by quantities of both base and current year. Formulae Prices of current year prices of base year Quantities of the current year Quantities of base year L- Laspeyre’s method and P- paasche’s method

24. Example: Construct index numbers for following Commodities Base year 1998 Current year 2009 prices quantities prices quantities A 2 100 3 100 B 8 200 10 50 C 10 300 15 100 D 6 400 10 50

25. Solution Commodities 1998 2009 prices quantity prices quantity A 2 100 3 100 300 200 300 200 B 8 200 10 50 2000 1600 500 400 C 10 300 15 100 4500 3000 1500 1000 D 6 400 10 50 4000 2400 500 300 Total 10800 7200 2800 1900

26. Weighted average of price relative method In this method, the price relatives of current year are calculated on the basis of base year prices. Since it is weighted method, we need to calculate weights and find the products of weights and price relatives and then average is calculated. We need to calculate weights (if not given) W= R or PR =

27. Example: Construct index number for given data Commodity A B C D E Quantity (units) in 1998 2 3 5 2 1 Price in 1998 50 40 40 100 160 Price in 2005 70 60 50 140 160

28. Solution: commodity Quantity in 1998 Price in 1998 Price in 2005 Weights W= R= RW A 2 50 70 100 140 14000 B 3 40 60 120 150 18000 C 5 40 50 200 125 25000 D 2 100 140 200 140 28000 E 1 160 160 160 100 16000 780 101000 101000 780 = = 129.49

29. Some important index numbers The following index numbers have been regularly published by the govt and used for determining various policy measures

30. Consumer price index Consumer price index (CPI) also known as the cost of living index, measures the average change in the retail prices. The CPI for industrial workers is increasingly considered the appropriate indicator of general inflation, which shows the most accurate impact of price rise on the cost of living of common people. The main groups of consumers for whom the consumer price index numbers have been calculated in India are: The industrial workers The urban non-manual workers and The agricultural labourers

31. Need to prepare CPI ? We need to prepare CPI because General index numbers fail to highlight the effect of increase or decrease in prices of various goods on cost of living of people Different classes of consumers, consume different commodities that too in different proportions CPI reflects the effect of increase or decrease of prices in the cost of living of different classes of people in a society.

32. Construction of CPI The following steps are observed to construct consumer price index Selection of class of consumer- consumers should be classified into various classes e.g., industrial labour, teachers etc Enquiry about the family budget- we select a sample of adequate number representative families from the selected group and following information is collected (I)Commodities consumed (II)quantity of these commodities (III)prices of these commodities (IV)total expenditure incurred by consumers Information about prices- the retail prices of selected goods and services should be gathered from the area to which these consumers belong. Assigning weightage- weightage to different items must be given according to their relative importance

33. Methods of construction Their are two methods to construct CPI

34. Example: Construct CPI using both aggregative expenditure and family budget method Commodity Base year Current year Prices Quantity Prices Quantity A 2 10 4 5 B 5 12 6 10 C 4 20 5 15 D 2 15 3 10

35. Solution: Aggregative expenditure method Commodity Base year Current year Prices quantity Prices Quantity A 2 10 4 5 40 20 B 5 12 6 10 72 60 C 4 20 5 15 100 80 D 2 15 3 10 45 30 total 257 190 257 190 = = X 100 135.26

36. Solution: commodity Base year Current year Weights W= R= RW prices quantity prices Quantity A 2 10 4 5 20 200 4000 B 5 12 6 10 60 120 7200 C 4 20 5 15 80 125 10000 D 2 15 3 10 30 150 4500 190 25700 25700 190 = = 135.26

37. Importance of CPI The CPI is used to determine the purchasing power of money and real wages It helps to formulate govt.policy If the prices of certain essential commodities increase due to shortage the govt may decided to provide them through faire price shops or rationing Consumer price index also used to analyse the market of specific commodities

38. Difficulties in construction of CPI As different sections of society have different standards of living becomes difficult to have one CPI for different classes of people Every family household has different budget set because proportion of expenditure incurred on given basket of goods varies from one family to other. The reasons is that the habits, tastes and preference of consumers keep changing Retail prices being used to construct CPI also fails to truly express the results because retail prices of commodities are not fixed they keep on changing whenever their is change in supply and demand Sample of consumers selected to construct index numbers may fail to truly represent the class if sample is not done carefully

39. Whole sale price index The whole sale price index numbers indicates the change in general price level . Unlike CPI, it does not have any reference consumer category. It does include items pertaining to services like barber charges, repairing etc. the commodity weights in WPI are determined by the estimates of the commodity value of domestic production and value of imports inclusive of import duty during the base year. It is available on weekly basis. Commodity are broadly classified into three categories- (I) primary articles, (II)fuel, power, light & lubricants (III) manufactured products

40. Uses of wholesale price index The index number is helpful in forecasting the demand and supply conditions of the commodities in the economy. If there is increase in wholesale price index, it means the demand of commodities is more than their supply. It helps us to understand monetary and real value of macro aggregates. Monetary value is based on prices of the current year and real value is based on prices of the base year. The WPI is used to calculate the rate of inflation in the country. The weekly inflation rate is given by = whole sale price index for t th week = whole sale price index for(t -1)th week

41. Example: If wholesale price index for week 1 = 800 and for week 2= 880 calculate weekly rate of inflation Solution: Rate of inflation= here t=880 and t-1=800 880-800 800 X 100 = 80 800 X 100 = 10%

42. Industrial production index The index number of industrial production measures changes in the level of industrial changes in the level of industrial production comprisng many industries. It include production of public and private sector. It is weighted average of quantity relatives Formula, - quantity production in current year - quantity production in base year W- weights

43. Purpose of construction This is designed to measure the increase or decrease min output of some industries It is a quantity index which measure changes in the quantity index which measures changes in the quantity of production Data of industrial production are collected under the following categories: (I) mining and quarrying industries – coal, aluminium, petroleum etc. (II)mechanical industries- ships, aeroplanes etc (III)textile industries- woollen cotton silk etc. (IV)metallurgical industries- iron and steel, rolling mills etc. (V)miscellaneous- glass, washing powder, chemical etc. The data for above are collected monthly, quarterly or yearly We use quantity relative method for construction

44. Example: Construct index number of industrial production for the following Industries Mining Textiles Cement Iron and steel Output (base year) 125 80 40 60 Output (current year) 250 120 50 180 Weights 30 40 20 10

45. Solution: Industries Base year quantity Current year quantity Weights W quantity relative w Mining 125 250 30 200 6000 Textile 80 120 40 150 6000 Cement 40 50 20 125 2500 Iron and steel 60 180 10 300 3000 100 17500 17500 100 = = 175

46. Agriculture production index Index numbers of agricultural production is a weighted average of quantity relatives Its base period is triennium ending 1981-82 In 2003-04 the index number of agricultural production was 179.5 it means that agricultural production has increased by 79.5% over the average of three years 1979-80, 1980-81 and 1981-82 Food grains have a weight of 62.92% in this index

47. Sensex Sensex is an index numbers representing the movement in share price of major companies listed in the B ombay stock exchange. It is one number that represents whole share markets. The movement of S ensex tells us about prices of shares of listed companies with B ombay stock exchange if the Sensex goes up it means that prices of the stock of most of the companies under BSE Sensex have gone up If Sensex goes down it means that prices of the stock of companies under BSE have gone down .

48. Other useful index numbers Human development index- this index measures literacy, life expectancy, attainment of education and per capita GDP for different countries. This index number measures human development which helps to compare human development in different countries to determine whether the country is developed or underdeveloped.

49. Producer price index Producer price index numbers measures price changes from the producer’s perspective. It uses only basic price including taxes, trade margins, and transport costs. A working group on revision of whole sale price index (1933-34 = 100) is inter alia examining the feasibility of switching over from WPI to a PPI in India as in many countries.

50. Inflation and index numbers Inflation refers to general rise in price level. Inflation is the persistent rise in prices. If the inflation is not controlled money will not able to perform its function as a unit of value or medium of exchange. Inflation lowers the value of money that is purchasing power of money goes down. The WPI is widely used to measure the rate of inflation. This index has capability to measure the price fluctuations of all commodities in a comprehensive way. Real income of wages = present wages present price index X 100

51. Example: Calculate real wages if present wages are Rs.340 and current price index is Rs.250 Solution : Real income of wages = 340 250 680 5 present wages present price index X 100 100 = = = 136 X

52. Important formula’s Unweighted (simple) index numbers Simple aggregative method 2 . Simple average of price relative method Weighted index numbers Weighted aggregative method Laspeyre’s method Paasche’s method

53. 3. Fisher’s method Weighted average of price relative method Construction of CPI Aggregative expenditure method Family budget method Wholesale price index Industrial production index Real income of wages = Important formula’s present wages present price index X 100

54. Thank you