# BCom 1st Year Index Number Long Notes

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Q. 1. Write a short note on index number and its construction.

Or Define index number. How index number is constructed?

Or What are index numbers? Explain the types.

Ans. Index Numbers: An index number is a ratio or an average of ratio expressed as a pery other words, it is a statistics which assigns a single number to several individual statistics in order to quantify trends. Two or more time periods are involved one of which is the base time period. The value the base time period serves as the standard point of comparison.

An index time series is a list of index numbers for two or more periods of time, where each

index number employs the same base year.

It is a numerical value characterising the change in complex economic phenomena ovel apena of time or space!

‘Index numbers are used to measure changes over time in magnitudes which are not capable of direct measurement.

‘An index number is a statistical measure which is designed to show changes in variable or a group of related variables with respect to time, geographical location or other characteristic.  ‘Index number is a device for measuring differences in the magnitude of a group of related variables.

There are two methods of index number-simple/unweighted and weighted method.

Simple/Unweighted

It can be further divided into two types:

1. Simple Aggregative Method: This is the simplest method of constructing index numbers. When this method is used to construct a price index, the total of current year prices for the various commodities in question is divided by the total of base year prices and the quotient is multiplied by 100.

where, Ep1 = Total of current year prices for various commodities.

Epo= Total of base year prices for various commodities.

2. Simple Average of Price Relative Method: One way to rectify the drawbacks of a simple aggregative index is to construct a simple averages to measure the mple average of relatives. In this method, the price relative of relative changes in the level each item is calculated separately and it is then averaged. A price relative is the price of the current year expressed as a percentage of the base year symbolically,

where, N=Number of items.

When the geometric mean, then the formula is en the geometric mean, then the formula is

Weighted

It can be further divided into two types:

1. Weighted Aggregative Index. Under this method. we weight the price of each commodity by a suitable factor often taken as the quantity of value weight sold during the base year ow an average of some years. The choice of one or the other will depend on the importance warme want to give to a period besides the quantity used. The various alternative formulae in use are:

(a) Laspeyre’s Method: The Laspeyre’s price index is a weighted aggregate price index, where the weights are determined by quantities in the base period. The formula for constructing the m ex is:

(b) Paasche’s Method: The Paasche price index is a weighted aggregate price index in which the weights are determined by quantities in the given year. The formula for constructing the index is:

(c) Dorbish and Bowley’s Method: Dorbish and Bowley’s have suggested simple arithmetic mean of the two indices (Laspeyres and Paasche) mentioned above so as to take into account the influence of both the periods, i.e. current as well as base periods. The formula for constructing the index is:

where, L = Laspeyres index, P= Paasche index.

(d) Fisher’s Ideal Index: Prof. Irving Fisher has given a number of formulae for constructing index number and of these he calls one as the “ideal’ index. The Fisher’s ideal index is given by the formula:

(e) Marshall-Edgeworth Method: In this method, the current year as well as base vear prices and quantities are considered. The formula for constructing the index is:

2. Weighted Average of Price Relatives Method: Weighted average of price relatives index is obtained by multiplying the relatives with the weights assigned to each commodity and then summing these products year by year and finally dividing the totals for each year by the sum of the weights. weights. For averaging weighted price relatives, we may use the arithmetic mean or the geometric mean; symbolically:

Types of Index Numbers

Following are the different types of index numbers:

1. Price Index Number: This is the most popular and most commonly used index number that measure the changes in price of some commodities or group of commodities consumed in the given period with reference to the base period. It can be wholesale price index number and retail price index number.

2. Quantity Index Numbers: It helps in measuring and comparing the changes in the physical volume of goods produced or sold or purchased in a given period.

3. Simple Index Numbers: These are constructed for individual commodities.

4. Value Index Numbers: They measure the changes in the value of some commodities or group of commodities consumed or purchased in the given period with reference to base period.

5. Aggregate Index Numbers: These are constructed for a group of commodities and hence are aggregate.

6. Cost of Living Index Numbers: They help in comparing the average change in consumption and expenditure of the commodity from one time period to another and shows the average change in consumer expenditure of a particular class of consumers.

Q.2. Discuss the uses of index numbers and give the characteristics of index numbers.

Ans. Uses of Index Numbers: The important uses of index numbers are described below.

1. They are Economic Barometers: Index numbers are mainly used in business and a Like barometers are used in physics to measure atmospheric pressures, index numbers measure level of business and economic activities and and are, therefore, termed as ‘economic barometers’ or barometers of economic activity. For instance, price index numbers are those that relate to chane le level of prices of a commodity or a group of commodities over a period of time. Price index numbers e useful in studying price movements and determining their effect on the economy. It is often uc compare changes in general price level with changes in related series, such as bank deposits, bank loans etc. for formulating economic policies. 2. They Measure Comparative Changes: The important purpose of index numbers is to measure the relative change in a variable or a group of related variables with respect to time or place. The changes in the phenomena like price level, cost of living etc.are not capable of being measueed directly and are therefore, measured with the help of index numbers. Indices of physical change eriod of time in production, sales, imports etc. are extremely helpful in analysing the movement ese characteristics over time.

3. They Help in Forecasting: Many governmental and private agencies are engaged in computation of index numbers for the purpose of forecasting business and economic conditions. For example, index numbers of industrial and agricultural production not only reflect the trend but can also help future production. Similarly, index numbers of unemployment in a country not only reflect the trends in the phenomenon but are useful in determining factors leading to unemployment. The analysis of such trends and factors in unemployment activity help in framing a suitable employment

4. They Measure the Purchasing Power of Money: Consumer price index numbers are useful in finding the intrinsic worth of money as they are used for adjusting the original data related to wages for price changes. In other words, index numbers are helpful for transitions nominal wages into real wages. Based on this aspect, the Government of India or of the states use consumer price index numbers for determining the amount of additional wages or dearness allowance itional wages or dearness allowances to be given to their employees in order to compensate for changes in the price level or cost of living. Thus, governments now have index linked salary structures and an additional dearness allowance is granted to employees for a point rise in consumer price index.

5. They Measure the Real Gross National Product (G.N.P.): Index numbers are also used for determining the real Gross National Product (G.N.P.) or income calculated at current prices. near D r. is determined by dividing the G.N.P. at current price by price index of the current year, i.e

Characteristics of Index Numbers

For a proper understanding of the index numbers, one should be clear about its characteristics. The following are the important characteristics of an index number:

1. These are Expressed in Percentages: Index numbers are expressed in terms of percentages so as to show the extent of relative change.

2. These are Relative Measures: Index numbers are specialised averages used to show the relative change in a group of related variables. The group of variables may relate to prices of certain commodity or volume of production of certain items. They compare changes taking place overtime or between places. If the wholesale price index for the year 1990 is 140 as compared to 100 in 1988, then we conclude that the general price level has increased by 40% in two years.

3. Index Numbers are Specialised Averages: Simple averages can be used to compare those series which are expressed in the same units. However, index numbers are special type of averages which are used in comparing changes in series expressed in different units. In view of this, they are also called specialised averages.

4. Index Numbers Measure Changes which are not Directly Measurable: The index numbers are used for measuring the magnitude of changes in such phenomena which are not capable of direct measurement. For example, price level, cost of living and ups and downs in business activities are phenomena in which changes cannot be measured directly. However, by studying the relative changes directly, measurable factor affecting price level, cost of living and business activities, index numbers help us to measure relative changes in corresponding phenomenon which is otherwise not in corresponding phenomenon which is otherwise not directly measurable.

Q. 3. What are the problems faced in construction of index numbers?

Ans. Problems Faced in the Construction of Index Numbers: Before constructed for serving specific purposes. Therefore, it is important to know what kind of changes we are trying to measure and for what purposes. Therefore, it is important to know what kind of changes we intend to use. Obviously, a clear definition of the purpose and objective is the first major  problem in the construction of index numbers. For example, if the price index is to measure the cost of living of middle class families in a region, care must be taken to include items which are consumed by these families.

2 Selection of Items: Having defined the purpose of index numbers, the next problem rela selection of items. In this regard, a decision about the number of items is made first. 1 ted that the larger the number of items included, the more representative shall be the index but at the

the number of items is made first. It should be same time cost and time involved in the construction of index number will increase. Therefor the number of items selected should neither be too small nor too large. Secondly, the items selected represent the tastes, habits

po small nor too large. Secondly, one should ensure that constructed. For instance, while computing cost of living index for middle class families, gold, car, etc. will not be the relevant items. Thus, only relevant standardised items, which are easy to del describe, should be included in the construction of index numbers so that they reflect the change that

ardised items, which are easy to define and we wish to measure.

3. Data for Index Numbers: The data used in index numbers are usually concerned with the prices and quantities consumed of the selected items for different points of time. As such, we always face the mblem of selecting a reliable source of data. Thus, the data should be collected from standanuman ournals, official publications, chamber of commerce and other government agencies. Data dhe are collected through field studies or sample surveys. Here, the samples selected should be representative of the class to which they belong and then only the resulting data is expected to be reliable, accurate and homogeneous. For uniformity, it is often desirable to group the items into homogeneous groups or subgroups. For instance, in measuring price changes, domestic items may be grouped into cereals, milk, edible oils, clothing, electricity and fuel, etc. Similarly, items with elastic demand may be grouped separately from items which have inelastic demand. Type of price quotation is another consideration while collecting data. A wholesale price index needs wholesale price quotation while retail price quotations will be desirable in the construction of a cost of living index number.

4. Choice of Base Period: The period with which the comparison of the relative changes in the level of a phenomenon are made is termed as a ‘base period’ or ‘reference period. The index for the base period is always taken as 100. For reliable and precise comparisons of the relative changes, a base year should be a sufficiently ‘normal year. It should be a period free from all abnormalities like economic boom or depression, labour strikes, wars, earthquakes, etc. In other words, the base period. should be more or less stable and free from unusual ups and downs. It is also desirable that the base period should not be too distant from the given period with which relative changes are measured. In case, the base period is too distant, it is desirable to shift it.

(a) Fixed Base Period: If the base period or reference period is kept fixed for all current periods of comparison, it is called the fixed base period. For example, the year 1951, being the first vear of planning process, may be taken as the base period for studying relative planning development in the current years.

(b) Chain Base Period: In chain base method, the change in the level of the phenomenon for any given period is compared with the level of the phenomenon in the preceding period and not in the base period.

5. Choice ofan Average: We observed that index numbers are special type of averages. As such the choice of a suitable average is also important in the construction of index numbers. Arithmetic mean median and geometric mean are the commonly used averages in index numbers. Out of three averages.arithmetic mean and median are comparatively easier to calculate. However, median completely ghores the extreme observations while the arithmetic mean is unduly affected by such observations.

6. Selection of Weights: Unweighted index numbers give equal importance to all commodities. wever all items or commodities included in the construction of an index number are not of eaual portance. For example, in the construction of cost of living index, sugar cannot be given the same commodity to have a reasonable influence on the index, kliportance othecamole In order to allow each commodity to have a reasonable influence on the index numbers which give appropriate weights to different commodities cording to their importance. The selection of appropriate weights is again a difficult task.

7. Selection of Suitable Formula: Selection of a suitable formula for construction of an index number also poses some problems. There are various formulas for calculating index numbers, such as the aggregate method or the average of relatives methods. The average relative method In simple aggregate method, the price of each commodity is given in usual units and this leads to the dominance of a particular quantity in the index.

Q.4. Write a detailed note on cost of living index numbers.

Ans. Cost of Living Index Numbers: Cost of living index numbers, also termed st of living index numbers. also termed as ‘Consumer price Index numbers’ or ‘Retail price index numbers’ are designed to measure the erecis mars prices of a basket of goods and services on the purchasing power of a particular section was on the society during any given (current) period with respect to some fixed (base) period. They reject the average increase in the cost of the commodities consumed by a class of people so that they can maintain the same standard of living in the current year as in the base year. To study the effect of rise or fall in the prices of various commodities consumed by a particular group or class of people on their cost of living, the Cost of living index numbers’ are constructed separately for different classes of people or groups or sections of the society, say, urban wage earners, agricultural laborers, industrial workers, government employees, etc. and also for different geographical areas like town, city, rural area, urban area, hilly area, and so on.

Construction of a Cost of Living Index

The main steps in the construction of a cost of living index are as follows:

1. The first step is to decide on a particular class of people for whom the index number is

intended, such as industrial workers, government employees, low income or middle income class people, etc. together with a well defined geographical region of their stay, such as a city or an industrial area, etc. It is necessary that the selected class should form a homogeneous

group of people with respect to income.

2. Next step is to conduct a sample ‘family budget inquiry’ using the technique of random

sampling. The inquiry covers a reasonably adequate number of families’ and should be conducted during the normal period. This would give us information about the amount that an average family spends on different items of consumption. This also enables determination of weights for computing the index. Only those items which are used by majority of the class

of people are included in the index.

3. The commodities are broadly classified into the following five major groups:

(a) Food,

(b) Clothing,

(c) Fuel and lighting,

(d) House rent, and

(e) Miscellaneous.

Each of these major groups is further subdivided into smaller groups termed as sub-groups. For instance, the group ‘Food’ may be subdivided into cereals (wheat, rice, etc.), pulses, meat, fish and poultry, milk and milk products, fats and oils, fruits and vegetables. spices, sugar, non-alcoholic beverages, pan, subpar and tobacco, etc. Similarly, ‘Clothing’ may cover clothing. bedding, footwear, etc. The last item ‘Miscellaneous’ includes items like medical care, education and reading, amusement and recreation, gifts and charities, transport and communication, household requisites, and so on. It however does not include non-consumption money transactions, such as payments towards provident funds, insurance premiums, purchase of saving certificates and bonds etc.

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