Maharashtra Board Class 12 Maths Commerce Part II Chapter 5 Index Numbers PDF Download

5 Index Numbers

Let's Study

Definition of Index Numbers

Types of Index Numbers

Terminology and Notation

Construction of Index Numbers

Simple Aggregate Method

Weighted Aggregate Method

Cost of Living Index Number

Aggregative Expenditure Method

Family Budget Method

Uses of Cost of Living Index Number

Introduction

The value of money does not remain the same for all the time. It cannot be observed directly but can be understood by observing the general level of prices. A rise in the price level indicates a fall in the value of money and a fall in the price level indicates a rise in the value of money. Changes in the value of money are reflected in changes in general level of prices over a period of time. Changes in the value of money are found to be inversely related to changes in price levels. So changes in the value of money can be understood by observing changes in the general level of prices over a specified time period. Changes in the general level of prices are measured using a statistical tool known as index numbers. Index numbers provide one of the most popular statistical tools used in economics.

Index numbers cannot be measured directly but are constructed with help of some mathematical formula. Index numbers are not expressed in terms of any units of measurement because they are ratios. Index numbers are usually expressed as percentages.

Maslow describes an index number as a numerical value characterizing the change in a complex economic phenomenon over a period of time. According to Spiegel, an index number is a statistical measure designed to show changes in a variable or a group of related variables with respect to time, geographical location or some other characteristic. Gregory and Ward describe it as a measure designed to show an average change over time, in the price, quantity or value of a group of items. Croxton and Cowden say that an index number is a device that measures differences in the magnitude of a group of related variables. B. L. Bowley describes an index number as a series that reflects in its trend and fluctuations the movements of some quantity to which it is related. Blair puts an index number as a special kind of average.

Let's Learn

5.1 Definition of Index Numbers

Index Numbers are defined in different ways by different experts. Some of the most popular definitions of Index Numbers are given below.

An Index Number is a statistical measure of changes in a variable or a group of variables with respect to time, geographical location, or some other characteristic such as production, income, etc.

An Index Number is used for measuring changes in some quantity that can not be measured directly.

An Index Number is a single ratio, usually expressed as percentage, that measures aggregate (or average) change in several variables between two different times, places, or situations.

Teacher's Note

Index numbers help us understand how prices change over time, just like tracking vegetable prices at your local market month by month. They show us the real change in the value of money that we use every day.

Exam Trick

Remember: Index number = 100 in base year. If index becomes 120 next year, it means prices went up by 20%. Think of 100 as the starting point, like score 0 in a game.

Points to Remember

Index numbers measure changes in price, quantity, or value over time.

Base year always has an index number of 100.

Index numbers are shown as ratios or percentages.

They help compare prices from different years easily.

Index numbers are used in economics to track inflation and cost of living.

Examples of Index Numbers

NIFTY: The NIFTY 50 index is National Stock Exchange of India's benchmark broad based stock market index for the Indian equity market. It represents the weighted average of 50 Indian company stocks in 13 sectors and is one of the two main stock indices used in India, the other being the BSE Sensex.

SENSEX: The BSE SENSEX (also known as the S&P Bombay Stock Exchange Sensitive Index or simply the SENSEX) is a free-float market-weighted stock market index of 30 well-established and financially sound companies listed on Bombay Stock Exchange.

5.2 Types of Index Numbers

Following are three major types of index numbers.

Price Index Number

Price index numbers measure changes in the level of prices in the economy. It compares the price of the current year, with that of the base year to indicate the relative variation. It is a very good measure of inflation in the economy.

Quantity Index Number

As the name suggests, quantity index numbers measure changes in the quantities of goods between the two specified years. This can be the number of goods produced, sold, consumed, etc. It is a good indication of the output of an economy.

Value Index Number

A value index number is the ratio of the aggregate value of a given commodity (or a group of commodities) in the current year and its value in the base year. A value index number combines prices and quantities by taking the product of price and quantity as the value. The value index number thus measures the percentage change in the value of a commodity or a group of commodities during the current year in comparison to its value during the base year.

Teacher's Note

There are three types of index numbers: price, quantity, and value. In your local market, the price index tells if vegetables got costlier, quantity index tells how much you got, and value index tells the total money you spent.

Exam Trick

Remember: Price Index = is it costlier? Quantity Index = is there more stuff? Value Index = did you spend more money total? Think P-Q-V like three questions about shopping.

Points to Remember

Price index measures change in prices only.

Quantity index measures change in amount of goods.

Value index measures change in total cost (price × quantity).

All three types compare base year with current year.

Index number of 100 always means base year value.

5.3 (a): Terminology

Base Period: The base period of an index number is the period against which comparisons are made. For example, the Central Statistical Organisation (CSO) is constructing the Consumer Price Index by taking 2010 as the base year. It means that the prices in 2015 are compared with 2010 prices by taking them as 100. The base period is indicated by subscript Zero.

Current Period: The present period is called the current period of an index number. An index number measures the changes between the base period and the current period. The current period is indicated by subscript 1.

Note: The period used in index numbers can be a day, a month, or a year. We shall use a year as the period in our study.

5.3 (b): Notation

\(p_0\): Price of a commodity in the base year.

\(q_0\): Quantity (produced, purchased, or consumed) of a commodity in the base year.

\(p_1\): Price of a commodity in the current year.

\(q_1\): Quantity (produced, purchased, or consumed) of a commodity in the current year.

\(w\): Weight assigned to a commodity according to its relative importance in the group.

\(I\): Simple index number. It is also called the price relative. It is given by

\(I = \frac{p_1}{p_0} \times 100\)

\(P_{01}\): Price index for the current year with respect to the base year.

\(Q_{01}\): Quantity index for the current year with respect to the base year.

\(V_{01}\): Value index for the current year with respect to the base year.

Teacher's Note

Notation is just shorthand writing. Think of \(p_0\) like "old price" and \(p_1\) like "new price". It makes math easier, like using abbreviations in your notebook.

Exam Trick

Remember: subscript 0 = base year (old), subscript 1 = current year (new). Just like 0 is before 1 in counting, base year comes before current year in time.

Points to Remember

Subscript 0 always means base year data.

Subscript 1 always means current year data.

Weights are shown by letter 'w'.

Price relative 'I' is calculated by dividing current price by base price.

All index numbers multiply by 100 to show as percentage.

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