Index Numbers Abhishek Dixit Nirbhay Kumar Rajan Dasgupta Prerna Tiwary Rashmi Yadav Iti Shree Bindu Singh
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.
CHARACTERISTICSSpecialized averagesMeasure the change in the level of aphenomenonMeasure the effect of changes over aperiod of time
USESHelp in framing suitable policiesReveal trends and tendenciesVery useful in deflating
CLASSIFICATION SpecialPrice Quantity Value Purpose
METHODS OF CONSTRUCTING INDEX NUMBERS Simple Aggregative Un-weighted Simple Average of Index Price RelativesNumbers Weighted Aggregative Weighted Weighted Average of Price Relatives
SIMPLE AGGREGATIVE METHODIt consists in expressing the aggregate price of all commoditiesin the current year as a percentage of the aggregate price in thebase 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
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
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 4351Index Number for 2008- p1 4351 P01 100 100 134.45 p0 3236It means the prize in 2008 were 34.45% higher than the previous year.
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
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
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
Weighted index numbersThese 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.
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 q0Paasche’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
Formula For Calculating Index NumbersDorbish & 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 2Fisher’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
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 qq refers to the quantities of the year which is selected as the base. It may be anyyear, either base year or current year.
Weighted average of price relative index numbersIn weighted Average of relative, the price relatives for thecurrent year are calculated on the basis of the base yearprice. These price relatives are multiplied by therespective weight of items. These products are added upand 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
Quantity Index NumberWhat is Quantity Index Numbers?Measure and permit comparison of the physical volumeof 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
Volume Index NumberThe Value of Single Commodity is the product of price andQuantity. p1q1 V 100 p0 q0 OR V1 V 100 V0
CONSUMER PRICE INDEX NUMBERSMeaning The consumer price index numbers, also known as cost ofliving index numbers, are generally intended to represent theaverage change over time in the prices paid by the ultimateconsumer of a specified basket of goods and services.Need The need for constructing consumer price indices arisesbecause the general index numbers fail to give an exact idea ofthe effect of the change in the general price level on the costof different classes of people in different manners.At present, the three terms, viz. cost of livingindex, consumer price index and retail price index are used indifferent countries with practically no difference in theirconnotation.
UTILITY OF CONSUMER PRICE INDICESWage 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.