Index numbers are indicators used in economics and statistics to show the relative changes in the price of a good or the income of an individual over a given period (or over a specified amount of time) when compared to their values in some fixed period known as the base period chosen for comparison. Numerous disciplines, like economics, business management, statistics, etc., have many uses for index numbers.

**What are Index Numbers?**

Index numbers are statistical tools created to assess the relative change in a phenomenon’s level (variable or set of variables) with respect to time, place, or other factors like income, profession, etc. Index numbers are specialized types of rates, ratios, and percentages that indicate the change in magnitude of a collection of variables in two circumstances.

As an example, suppose we are interested in researching the overall shift in the cost of consumer goods, i.e., the items or commodities that members of a specific social group, such as the working class, low-income group, or middle-income group, consume. Since the prices of different commodities are reported in different units, such as quintals or kilograms, it is obvious that these changes are not immediately measurable.

Additionally, during the two periods, the prices of some commodities may be rising while those of others may be falling, and the rates of increase or reduction for various commodities may vary. A statistical tool known as an index number allows us to arrive at a single representative number that indicates the overall level of the price of the phenomenon (commodities) in a large group.

**Types of Index Numbers:**

There are three main kinds of index numbers depending on the phenomena being compared with respect to the base year. They are:

- Price Index Number.
- Quantity Index Number.
- Value Index Number.

#### 1. Price Index Number.

The price index numbers reflect general price changes. The prices of numerous commodities, including consumer products, stocks and shares, bank deposits, government bonds, and so on, are generally reflected in these indices. The price index number can be calculated using the formula, \text{Price Index Number }=\frac{\sum p_1q_1}{\sum p_0q_1}\times 100.

- where p_1 denotes the prices of various commodities in the current year.
- p_0 denotes the prices of various commodities in the previous/base year.
- q_1 denotes the quantities of various commodities consumed in the current year.
- q_0 denotes the quantities of various commodities consumed in the previous year.

#### 2. Quantity Index Number.

Quantity index figures, such as those for agricultural production, industrial production, imports, exports, etc., track changes in the volume of products produced (made), consumed, or distributed. They are quite beneficial when examining the volume of physical output inside an economy. It can be calculated using the formula (notations as above), \text{Quantity Index Number }=\frac{\sum q_1}{\sum q_0}\times 100.

#### 3. Value Index Number.

These are used to analyze changes in the production’s total value (price times output), such as retail sales, profit, or inventory indexes. These indices are less commonly used than price and quantity indices. It can be calculated using the formula (notations as above), \text{Value Index Number }=\frac{\sum p_1q_1}{\sum p_0q_0}\times 100.

**Uses and Purpose of Index Numbers:**

Index numbers are constructed for different purposes such as studying changes in the cost of living, studying the general changes in the price level in a country, etc. Some of the applications of index numbers in business and economics are as follows:

**1. Understanding the Behaviour of the Economy**

The wholesale and retail pricing indexes, output (volume of commerce, import, export, industrial and agricultural production), bank deposits, foreign exchange, reserves, etc., provide insight into the nature and volatility of the nation’s overall economic and commercial activity. We may pretty accurately assess the general commerce, economic development, and business activity of the nation by carefully examining these statistics.

**2. Used to Detect Trends**

The index numbers can be used to identify patterns in the phenomena since they examine current phenomena with respect to historical data. The index numbers for industrial output, for instance, can be used to forecast future outputs. Following that, a businessman can plan and make decisions based on these forecasts.

**3. Formulating Decisions and Policies**

The cost of living index numbers is used by governments when deciding the salaries and pensions of government employees. Taxes on particular commodities can be changed depending on the consumption index of that commodity.

**4. Measuring Purchasing Power of Money**

The cost of living index numbers determine whether the real wages are rising or falling, money wages remaining unchanged. In other words, they help us in computing the real wages which are obtained by dividing the wages by the corresponding price index and multiplying by 100. Real wages help us in determining the purchasing power of money. If the salary of a person increases yearly but the yearly rate of inflation is even higher then it is clear that the real wages of the person have decreased.

**Characteristics of Index Numbers:**

- Index numbers are specialized averages. For instance, the consumer price index, which offers price comparison for a variety of goods like food, clothing, gasoline, rent, and so forth, is stated in several units. By utilizing the method of calculating price index numbers, it is possible to determine the average price of all of these things represented in various units.
- The percentage change in a phenomenon’s level is measured by index numbers. For example, a price index of 200 means that the price of commodities has doubled compared to the base/previous year. An index number of 100 means that the prices of quantities have remained the same in the current year compared to the base year.
- Index numbers track changes in several phenomena that are difficult to assess directly. For instance, the cost of living cannot be explicitly quantified; rather, we can only investigate relative changes in it by examining changes in a few other elements that are related to it.
- The impact of changes relative to time or space is quantified by index numbers. For example, the cost of living might be completely different in one place compared to another.

**Limitations of Index Numbers:**

- Index numbers are just rough indicators because they are based on sample data and might not accurately reflect changes in a phenomenon’s relative level.
- Each step in the process of creating the index numbers has the potential to introduce mistakes, such as when gathering information on the prices and quantities of the commodities.
- The tastes and patterns of consumption of different items among members of a society change quickly. In light of this, index numbers—which rely on the stability of the goods’ attributes over time—may not be able to keep up with changes and hence might not be truly representative.
- There is no accurate or ideal formula for calculating the price change or quantity change of a given set of data. As a result, each index contains an inaccuracy known as a “formula error”. For example, Paasche’s index has a downward bias while Laspeyre’s index has an upward bias.
- Index figures are susceptible to manipulation by unethical and self-serving individuals to achieve the desired results by cleverly selecting the base year, commodities, price, and quantity quotations.

**Consumer Price Index (CPI) Numbers:**

The consumer price index, also known as the cost of living index or retail price index, is created to calculate how much more expensive it is for consumers of a given class to purchase a basket of goods and services at a given moment in comparison to how much they paid in the base year. Construction of consumer price indexes is required because general indexes do not adequately reflect the impact of changes in the cost of living on different classes of consumers of different goods.

**Consumer Price Index Formula:**

The Consumer Price Index can be calculated using the following formula by the weighted aggregate method: \begin{align*}\text{Consumer Price Index}&=\frac{\text{Total Expenditure in Current Period}}{\text{Total Expenditure in Base Period}}\times 100 \\ &= \frac{\sum p_1q_0}{\sum p_0q_0}\times 100\end{align*} Here, p_0 = \text{Price in the Base Period} \\ p_1 = \text{Price in the Current Period} \\ q_0 = \text{Quantities Consumed in the Base Period}

**Uses of Consumer Price Index (CPI) Number:**

- Real earnings are calculated using the CPI, which is also used to increase income payments.
- The CPI is used to calculate a consumer’s buying power index in dollars. The value of a dollar in a given year relative to a base year is known as the buying power of the dollar. The formula for calculating the purchasing power of the dollar is:\text{Purchasing Power}=\frac{1}{\text{Consumer Price Index}}\times 100
- The price index is most typically employed to achieve deflation of such time series when it comes to monetary values such as retail sales quantities or wage rates. The following formula can be used to describe the deflation process. \text{Real Wage}=\frac{\text{Present Wages}}{\text{Consumer Price Index}}\times 100
- In salary discussions and wage contracts, the CPI is used. The consumer price index serves as the basis for the automatic adjustment of wages.