Chapter 7: Index Numbers

An Index Number is a statistical device designed to measure changes in a variable or a group of related variables with respect to time, geographic location, or other characteristics.

Important Types of Index Numbers

1. Wholesale Price Index (WPI): Measures the relative changes in the prices of commodities traded in wholesale markets. It broadly indicates general inflation in an economy.
2. Consumer Price Index (CPI): Also known as the Cost of Living Index, it measures changes in the prices of a basket of consumer goods and services purchased by households.
3. Index of Industrial Production (IIP): Measures changes in the volume of industrial production over a given period.

Uses of Index Numbers

• Formulating government and business policies.
• Measuring trends and tendencies (like inflation or output growth).
• Deflating macroeconomic variables (e.g., converting nominal GDP to real GDP).

Inflation and Index Numbers

Inflation refers to a general and persistent rise in the price level. It is conventionally measured using price index numbers (mainly CPI in many countries, though WPI also plays a role). $$ \text{Rate of Inflation} = \frac{A_2 - A_1}{A_1} \times 100 $$ Where \(A_1\) is the price index in year 1 and \(A_2\) is the price index in year 2.

Simple Aggregative Method

The simplest way to calculate an index number is to express the aggregate price of all commodities in the current year as a percentage of the aggregate price of the same commodities in the base year.

$$ P_{01} = \frac{\sum P_1}{\sum P_0} \times 100 $$

Where:

• \(P_{01} \) = Price index of the current year relative to the base year.
• \(\sum P_1 \) = Sum of prices of commodities in the current year.
• \(\sum P_0 \) = Sum of prices of commodities in the base year.

Competency-Based Questions

Application-Based Question

Q1. Suppose the sum of the prices of a basket of goods in the base year (2015) was ₹5,000. In the current year (2024), the price of the exact same basket is ₹7,500. Calculate the price index number using the Simple Aggregative Method.

Answer: Given:

• \(\sum P_0 \) = 5000
• \(\sum P_1 \) = 7500

Using the formula: $$ P_{01} = \frac{\sum P_1}{\sum P_0} \times 100 $$ $$ P_{01} = \frac{7500}{5000} \times 100 = 1.5 \times 100 = 150 $$

The Price index number is 150, which indicates that prices have risen by 50% since the base year.

Analytical Question

Q2. How does the Consumer Price Index (CPI) help employers design wage contracts for their employees in times of high inflation?

Answer: The CPI accurately reflects the cost of living by measuring the prices of essential goods and services consumed by households. In times of high inflation, the purchasing power of money falls. Employers utilize the CPI to adjust wages and calculate the Dearness Allowance (DA). By indexing salaries to the CPI, employers grant wage increases that match the inflation rate, thereby safeguarding the real income and standard of living of their employees against rising prices.