Question

Taking an example, examine the process of calculating an index number and show the changes.

Answer 1

The standard formula used to compute a simple aggregate price index number is:

`"Index Number" = ("Value in the Current Period" (p_1))/("Value in the Base Period"(p_0))`

The process of calculating an index number involves comparing the value of a variable in the current period with its value in a standard base period. To find this, the current period’s value is divided by the base period’s value, then multiplied by 100 to express the change as a percentage. In this process, the base year’s index number is always treated as a fixed benchmark of 100. For example, if we compare rice prices over time or across different cities, this method clearly shows whether the value has increased or decreased relative to the baseline.

Example A: Price Index Over Time

Suppose rice is sold at ₹ 4.50/kg in Bhubaneswar in the base year 1985 (p₀), and its price rose to ₹ 9.00/kg in the current year 2005 (p₁).

Price Index = `(9.00/4.52) xx 100`

= 200

The Change: An index value of 200 indicates a net 100% increase (200 − 100) in the price of rice over the twenty-year period.

Example B: Price Index Across Locations

Suppose during the same year (2005), rice sold at ₹ 12.00/kg in Delhi. To compare the price at Bhubaneswar relative to Delhi (making Delhi the base):

Spatial Index = `(9.00/12.00) xx 100`

= 75

The Change: An index value of 75 indicates that the price of rice in Bhubaneswar is 25% lower (100 − 75) than the price in Delhi.

Example C: Quantity Index Number

Rice production in Odisha was 36,000 metric tons in the base year 2001 (Q₀), and it reached 42,000 metric tons in the current year 2012 (Q₁).

Quantity Index = `((42,000)/(36,000)) xx 100`

= 116.66

The Change: An index value of 116.66 indicates a net 16.66% increase (116.66 − 100) in agricultural production volume between 2001 and 2012.