Index number
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An index number measures relative changes in price, quantity, or value over time. It can help frame policies, reveal trends, and deflate values. Index numbers are classified by what they measure (price, quantity, value) and their construction method (simple, weighted aggregate, weighted average of price relatives). Common uses include analyzing purchasing power, incomes, and markets. Weighted indexes assign weights to items, with methods including Laspeyres, Paasche, Fisher, and Kelly. Consumer price indexes measure price changes in consumer baskets.
Index number
- 1. Index Numbers Abhishek Dixit Nirbhay Kumar Rajan Dasgupta Prerna Tiwary Rashmi Yadav Iti Shree Bindu Singh
- 2. INTRODUCTION • An INDEX NUMBER measures the relative change in price, quantity, value, or some other item of interest from one time period to another. • A simple index number measures the relative change in just one variable.
- 3. CHARACTERISTICS Specialized averages Measure the change in the level of a phenomenon Measure the effect of changes over a period of time
- 4. USES Help in framing suitable policies Reveal trends and tendencies Very useful in deflating
- 5. CLASSIFICATION Special Price Quantity Value Purpose
- 6. METHODS OF CONSTRUCTING INDEX NUMBERS Simple Aggregative Un-weighted Simple Average of Index Price Relatives Numbers Weighted Aggregative Weighted Weighted Average of Price Relatives
- 7. SIMPLE AGGREGATIVE METHOD It consists in expressing the aggregate price of all commodities in the current year as a percentage of the aggregate price in the base year. p1 P01 100 p0 P01= Index number of the current year. p1 = Total of the current year’s price of all commodities. p0 = Total of the base year’s price of all commodities
- 8. EXAMPLE:- From the data given below construct the index number for the year 2007 on the base year 2008 in Rajasthan state. PRICE (Rs) PRICE (Rs) COMMODITIES UNITS 2007 2008 Sugar Quintal 2200 3200 Milk Quintal 18 20 Oil Litre 68 71 Wheat Quintal 900 1000 Clothing Meter 50 60
- 9. Solution:- PRICE (Rs) PRICE (Rs) COMMODITIES UNITS 2007 2008 Sugar Quintal 2200 3200 Milk Quintal 18 20 Oil Litre 68 71 Wheat Quintal 900 1000 Clothing Meter 50 60 p0 3236 p1 4351 Index Number for 2008- p1 4351 P01 100 100 134.45 p0 3236 It means the prize in 2008 were 34.45% higher than the previous year.
- 10. SIMPLE AVERAGE OF RELATIVES METHOD. The current year price is expressed as a price relative of the base year price. These price relatives are then averaged to get the index number. The average used could be arithmetic mean, geometric mean or even median . p1 100 p0 P01 N Where N is Numbers Of items. When geometric mean is used- p1 log 100 p0 log P01 N
- 11. Example:- From the data given below construct the index number for the year 2008 taking 2007 as by using arithmetic mean. Commodities Price (2007) Price (2008) P 6 10 Q 2 2 R 4 6 S 10 12 T 8 12
- 12. Solution:- Index number using arithmetic mean- Commodities Price (2007) Price (2008) Price Relative p0 p1 p1 p0 100 P 6 10 166.7 Q 12 2 16.67 R 4 6 150.0 S 10 12 120.0 T 8 12 150.0 p1 100 =603.37 p0 p1 100 p0 603.37 P01 120.63 N 5
- 13. Weighted index numbers These are those index numbers in which rational weights are assigned to various chains in an explicit fashion. (A) Weighted aggregative index numbers- These index numbers are the simple aggregative type with the fundamental difference that weights are assigned to the various items included in the index. Laspeyres method. Paasche method. Dorbish and bowley’s method. Fisher’s ideal method. Marshall-Edgeworth method. Kelly’s method.
- 14. Laspeyres Method. This method was devised by Laspeyres in 1871. In this method the weights are determined by quantities in the base. p1q0 p01 100 p0 q0 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. p1q1 p01 100 p0 q1
- 15. Formula For Calculating Index Numbers Dorbish & Bowleys Method: 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. p1q0 p1q1 p0 q0 p0 q1 P01 100 2 Fisher’s Ideal Index: Fisher’s deal index number is the geometric mean of the Laspeyre’s and Paasche’s index numbers. p1q0 p1q1 P01 100 p0 q0 p0 q1
- 16. Marshall-Edgeworth Method. 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. p1q0 p1q1 p01 100 p0 q0 p0 q1 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. p1q p01 100 p0 q 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.
- 17. Weighted average of price relative index numbers In weighted Average of 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- PV P01 V P1 Where- P 100 P0 P=Price relative V=Value weights= p 0 q0
- 18. Quantity Index Number What is Quantity Index Numbers? Measure and permit comparison of the physical volume of goods produced or distributed or consumed. Q = L P q1 p0 q1 p1 Q01 100 q0 p0 q0 p1 Where Q=Quantity q1 p0 q1 p1 L 100 V 100 Index Number q0 p0 q0 p0
- 19. Volume Index Number The Value of Single Commodity is the product of price and Quantity. p1q1 V 100 p0 q0 OR V1 V 100 V0
- 20. CONSUMER PRICE INDEX NUMBERS Meaning The consumer price index numbers, also known as cost of living index numbers, are generally intended to represent the average change over time in the prices paid by the ultimate consumer of a specified basket of goods and services. Need The need for constructing consumer price indices arises because the general index numbers fail to give an exact idea of the effect of the change in the general price level on the cost of different classes of people in different manners. At present, the three terms, viz. cost of living index, consumer price index and retail price index are used in different countries with practically no difference in their connotation.
- 21. UTILITY OF CONSUMER PRICE INDICES Wage negotiations & wage contracts. At Govt. level, mainly used for wage policy, price policy, rent control, taxation & general economic policies. To measure changing purchasing power of the currency, real income etc. Analyzing markets for particular goods and services.