Economics: Class 11 (Part 2) — Chapter 7: Index Numbers

• Base Period: The reference period with which comparisons are made. It is conventionally assigned an index value of 100.
• Current Period: The period for which the comparison or change is being calculated.
• Percentage Expression: Index numbers are conventionally expressed as percentages to facilitate easy comparison, though the percentage sign (%) is usually omitted.
• Types of Indices:
  • Price Index: Measures and compares the prices of certain goods over time.
  • Quantity Index: Measures changes in the physical volume of production, construction, or employment.

This method aggregates the prices (or quantities) of various commodities in the current year and compares them with the aggregate in the base year.

1. Simple Aggregative Price Index

Treats all items with equal importance, regardless of their actual economic weight.

Where:

• $P_{01}$ = Price index of the current year (1) relative to the base year (0)
• $\sum P_1$ = Sum of prices of all commodities in the current period
• $\sum P_0$ = Sum of prices of all commodities in the base period

2. Weighted Aggregative Price Index

Assigns weights to different commodities based on their relative importance (usually quantities consumed or produced).

• Laspeyre's Price Index: Uses base period quantities ($q_0$) as weights.
  $$P_{01} = \frac{\sum P_1 q_0}{\sum P_0 q_0} \times 100$$
• Paasche's Price Index: Uses current period quantities ($q_1$) as weights.
  $$P_{01} = \frac{\sum P_1 q_1}{\sum P_0 q_1} \times 100$$

This method computes price relatives for each individual commodity first, and then averages those relatives.

1. Simple Average of Price Relatives

Where $n$ is the number of commodities.

2. Weighted Average of Price Relatives

Where $W_i$ represents the weight (percentage of expenditure or value share) assigned to commodity $i$.

Also known as the Cost of Living Index, CPI measures the average change in retail prices paid by consumers for a specified basket of goods and services.

Where $W$ is the weight and $R = \frac{P_1}{P_0} \times 100$ is the price relative.

Major CPI Series in India:

• CPI for Industrial Workers (CPI-IW)
• CPI for Agricultural Labourers (CPI-AL)
• CPI for Rural Labourers (CPI-RL)
• All-India Rural, Urban, and Combined CPI (Base: 2012 = 100)

The Wholesale Price Index measures changes in the general price level of goods traded at the wholesale stage. Unlike CPI, it does not include services.

• Base Year: 2011-12 = 100
• Major Groups & Weights:

  Major Groups	Weight (%)
  Primary Articles	22.62
  Fuel and Power	13.15
  Manufactured Products	64.23
  All Commodities (Headline Inflation)	100.00

• Core Inflation: A measure of inflation that excludes volatile items like food and fuel (comprising about 55% of the WPI weight).

The IIP is a quantity index that measures changes in the volume of industrial production in the economy.

• Base Year: 2011-12 = 100
• Formula (Laspeyre's variant):
  $$\text{IIP}_{01} = \frac{\sum q_{i1} W_i}{\sum W_i} \times 100$$
• Sectoral Classification: Mining (14.4%), Manufacturing (77.6%), and Electricity (8.0%).
• Eight Core Industries: Coal, crude oil, natural gas, refinery products, fertilizers, steel, cement, and electricity. These have a combined weight of 40.27% in the IIP.

The SENSEX (Bombay Stock Exchange Sensitive Index) is the benchmark stock market index of India. It consists of 30 stocks representing 13 key sectors of the economy, with 1978-79 as its base period.