1. INDEX NUMBERS

2. Index Number 2  An index number is a statistical measure designed to show changes in variables or a group of related variables with respect to time, geographic area, or related characteristics.  For example, Cost of Living Index, Price, Quantity and Value Relatives Index. Rahul Chandra

3. Methods of Index Numbers Construction 3  Unweighted Methods:  Single price Index: Rahul Chandra

4. Weighted Methods 4  Laspeyeres Method  Paasche Method  Fisher Method Rahul Chandra

5. Some Index Numbers 5  Wholesale Price Index  Consumer Price Index  Index of Industrial Production  SENSEX (Stock Exchange Mumbai) Rahul Chandra

6. Cost of Living Index 6  Cost of Living Index represents change in prices paid or expenditure incurred for a basket of specified goods and services. Rahul Chandra

7. Price, Quantity and Value Relatives 7  The impact on the cost of living could also be worked out by taking the weighted average of price relatives i.e. the ratio of prices of various items in the current and the base year.  Price relative of an item is defined as the ratio of price in the current year to the price in the base year Rahul Chandra

8. Weighted Index Methods 8  There are three basic index numbers used for assessing increase in price, quantity and value. They are :  Laspeyre’s Index  Paasche’s Index  Fisher’ Ideal Index  These are subsequently used in forming other index numbers used for specific situations Rahul Chandra

9. Laspeyre ’ s Index 9  In general, it is defined as where, ◦ p 1 are the prices of items in the current year ◦ p 0 are the prices of items in the base year ◦ q 0 are quantities of items consumed in the base year. ◦ Laspeyre’s Index (also called Base year method) is weighted aggregate price index with base year quantity weights Rahul Chandra

10. Paasche ’ s Index 10  Is defined as where,  p 1 are the prices of items in the current year  p 0 are the prices of items in the base year  q 1 are the quantities of items consumed in the current year. Rahul Chandra

11. Fisher ’ s Ideal Index 11  Is Defines as  Being the geometric mean of Laspeyre’s and Paasche’s Index numbers, it can be mathematically proved that the Fisher’s index lies between these two index numbers.  Since Laspeyre’s Index tends to overestimate and Paasche’s Index tends to underestimate, it implies that Fisher’s index lying between the two, provides a better estimate than either Laspeyre’s or Paasche’s Index. Rahul Chandra

12. Issues to be taken into Consideration for Construction of Index Numbers 12  Selection of appropriate base year which is normally taken as a rather stable year and not some exceptional year when the prices might be abnormally low or high.  Consumption pattern of different items may change. This could result in the change of weights to be applied to the prices of commodities  Some items of consumption may change i.e. some items may be added or / and some items of consumption may be deleted. For example people may shift to more consumption of vegetables and fruits.  Prices may undergo changes not so much due to increase in prices but due to improvement in quality of items or from unbranded to branded items. Rahul Chandra

13. Uses of Index Numbers 13  Provide economic indicators like prices of commodities, financial instruments  Like shares, output like industrial and agricultural production, exports, imports, etc.  Studying trends of economic activities and their comparisons among states and nations.  Policy formulation at state, national and international levels  Measuring and comparing purchasing power of money Rahul Chandra

14. Uses of Index Numbers 14  In India, as also in several other countries, consumer price index number is used to decide the amount of dearness allowance to the employees of public and organised sectors.  The whole sale price indicator is used as a bench mark for deciding the interest rate on Government securities, bank rate for the Reserve Bank’s lending to commercial banks, the rates for deposits and loans of commercial bank’s, etc.  The index numbers are also used for deflating time series data on wages, cost of living, national income, etc. Rahul Chandra

15. SENSEX 15  The Stock Exchange, Mumbai (BSE), in 1986, came out SENSEX that subsequently became the barometer of the Indian stock market. SENSEX is not only scientifically designed but also based on globally accepted construction and review methodology.  First compiled in 1986, SENSEX is a basket of 30 constituent stocks representing a sample of large, liquid and representative companies. The base year of SENSEX is 1978-79 and the base value is 100. Due to is wide acceptance amongst the Indian investors; SENSEX is regarded to be the pulse of the Indian stock market. Rahul Chandra

16. Criteria for Adequacy of Index Numbers 16  Unit Test  Time Reversal Test  Factor Reversal Test  Circular or Cyclical Test Rahul Chandra

17. Unit Test 17  This test requires that the index number should not have any dimension or measurement like, Rs., Kilograms, Meters, etc.  This is so because the index number is a ratio of two quantities and indicates only the relative change.  As can be seen that all the three index numbers mentioned above do satisfy this criterion Rahul Chandra

18. Time Reversal Test 18  This criterion stipulates that if the base and current years are interchanged then the index number so formed is the reciprocal of the index formed with the original base and current year.  This test stipulates that if the time subscripts of a price index formula are interchanged to form another index number then the product of the new formula (without multiplication by 100) with the original formula (without multiplication by 100) should be equal to 1. Rahul Chandra

19. Time Reversal Test 19  Laspeyre’s index number does not satisfy the adequacy criterion of Time Reversal test.  Paasche’s index number does not satisfy the adequacy criterion of Time Reversal test.  Fisher’s ideal index number satisfies the adequacy criterion of Time Reversal Test. Rahul Chandra

20. Factor Reversal Test 20  If the two factors viz. p and q of an index number are interchanged to form a new index number, then the product of these two index numbers should be equal to the ratio of the value ( product × quantity) in the current year to the value ( product × quality) in the base year. Rahul Chandra

21. Factor Reversal Test 21  Factor reversal criterion is not satisfied by the Laspeyre’s Index number.  Factor reversal criterion is not satisfied by the Laspeyre’s Index number  Fisher’s ideal index number satisfies the criterion of Factor Reversal test. Rahul Chandra

22. Fisher ’ s Index Number 22  Fisher’s Index Number satisfies both the time reversal and factor reversal tests. That is how the word “ Ideal” is attached to this index number.  Fisher’s index tends to strike a balance between the Laspeyer’s and Paasche’s index numbers. This is also one of the reasons that Fisher’s index number is labeled as ‘ideal index number’ Rahul Chandra

23. Question 1 23  The retail price of a commodity over a period of four years are:  Year: 2000 2001 2002 2003  Price: 24.6 25.35 26 26.5  Calculate price Index based on 2000 prices. Rahul Chandra

24. Question 2 24  Calculate aggregate price index for the following data. Take 2001 as base year. 2001 2002 Milk 18 20 Butter 20 150 Banana 5 18 Bread 9 11 Rahul Chandra

25. Question 3 25 Commodity Consumption Price Price in base year Base Current Wheat 200 1 1.2 Rice 50 3 3.5 Pulses 50 4 5 Ghee 20 20 30 Sugar 40 2.5 5 Oil 50 10 15 Fuel 60 2 2.5 Clothing 40 15 18 Rahul Chandra

26. Question 4 26 Commodity 2000 2001 Price Quantity Price Quantity Wheat 20 8 40 6 Rice 50 10 60 5 Pulses 40 15 50 15 Ghee 20 20 20 25 Calculate all three INDEX and check which of them satisfy Time & Factor reversal test. Rahul Chandra

27. Question 5 27 Commodity 2000 2001 QPQP A 12101512 B 157205 C 24 5209 D 516514 Calculate Fisher INDEX and check if it satisfy Time & Factor reversal test Rahul Chandra

28. Question 6 28 Commodity 2000 2001 PQPQ A 8200651950 B 201400301650 C 58020900 D 1036015300 E27216010600 Calculate Fisher INDEX and check if it satisfy Time & Factor reversal test Rahul Chandra