Fixed Base Method

In fixed base method, a particular year is generally chosen arbitrarily and the prices of the subsequent years are expressed as relatives of the price of the base year. Sometimes instead of choosing a single year as the base, a period of a few years is chosen and the average price of this period is taken as the base year’s price. The year which is selected as a base should be a normal year, or in other words, the price level in this year should neither be abnormally low nor abnormally high. If an abnormal year is chosen as the base, the price relatives of the current year calculated on its basis would give misleading conclusions. For example, a year in which war was at its peak, say the year 1965, is chosen as a base year; thus the comparison of the price level of the subsequent years to the price of 1965 is bound to give misleading conclusions as the price level in 1965 was abnormally high.

In order to remove the difficulty associated with the selection of a normal year, the average price of a few years is sometimes taken as the base price. The fixed base method is used by the government in the calculation of national index numbers.

In fixed base,
Price relative for current year {\text{ = }}\frac{{{\text{Price of Current Year}}}}{{{\text{Price of Base Year}}}} \times 100

Or

{P_{on}} = \frac{{{P_n}}}{{{P_o}}} \times 100

 

Example:

Find index numbers for the following data taking 1980 as the base year.

Year
1980
1981
1982
1983
1984
1985
1986
1987
Price
40
50
60
70
80
100
90
110

 

Solution:
           

Year
Price
Index nos 1980 as base
{P_{on}} = \frac{{{P_n}}}{{{P_o}}} \times 100
1980
40
\frac{{40}}{{40}} \times 100 = 100
1981
50
\frac{{50}}{{40}} \times 100 = 125
1982
60
\frac{{60}}{{40}} \times 100 = 150
1983
70
\frac{{70}}{{40}} \times 100 = 175
1984
80
\frac{{80}}{{40}} \times 100 = 200
1985
100
\frac{{100}}{{40}} \times 100 = 250
1986
90
\frac{{90}}{{40}} \times 100 = 225
1987
110
\frac{{110}}{{40}} \times 100 = 275