Meaning, Features and Uses of Index Numbers

Prices, production, wages and the cost of living do not stay fixed — they rise and fall from year to year. To describe such a change in a group of related items by a single figure, statisticians use an index number. An index number is a specialised average that measures the relative change in a variable, or a group of variables, between two different situations — usually two time periods. This chapter of the Maharashtra Std XII (HSC) commerce Mathematics and Statistics course builds price index numbers by several standard methods and then applies them to the cost of living. These are the same, well-established index-number principles set out in the national mathematics-and-statistics curriculum, so the methods carry over directly to commerce and economics.

The period we compare against is the base year (its values are subscripted $0$: price $p_0$, quantity $q_0$); the period we are studying is the current year (subscripted $1$: $p_1$, $q_1$). The base-year index is always taken as 100, and the current-year index tells us the percentage change. An index of $125$ means prices are, on the whole, $25\%$ higher than in the base year; an index of $90$ means they are $10\%$ lower.

Features (characteristics) of index numbers.

• They are specialised averages — unlike a simple average of like items, an index number averages changes in items that may be in different units (kg, litre, metre) by first reducing them to ratios or values.
• They are expressed as percentages but the $\%$ sign is not written.
• They measure changes not directly measurable, such as the general 'price level' or the 'cost of living', which have no single physical unit.
• They compare two situations — two time periods (time series) or two places / groups.

Uses of index numbers.

1. They act as economic barometers — they signal the general trend of prices, trade and business activity.
2. They measure and help control inflation / deflation by tracking the general price level.
3. The cost of living index is used to fix wages, grant dearness allowance (DA), and measure changes in the purchasing power of money and in real wages.
4. Governments use them to frame economic policy (taxation, price control, planning).
5. Producers and businesses use production and price indices for forecasting and comparison.