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
$${P_{on}} = \frac{{{P_n}}}{{{P_o}}} \times 100$$ 
$$1980$$

$$40$$

$$\frac{{40}}{{40}} \times 100 = 100$$

$$1981$$

$$50$$

$$\frac{{50}}{{40}} \times 100 = 125$$

$$1982$$

$$60$$

$$\frac{{60}}{{40}} \times 100 = 150$$

$$1983$$

$$70$$

$$\frac{{70}}{{40}} \times 100 = 175$$

$$1984$$

$$80$$

$$\frac{{80}}{{40}} \times 100 = 200$$

$$1985$$

$$100$$

$$\frac{{100}}{{40}} \times 100 = 250$$

$$1986$$

$$90$$

$$\frac{{90}}{{40}} \times 100 = 225$$

$$1987$$

$$110$$

$$\frac{{110}}{{40}} \times 100 = 275$$

Arpit
December 1 @ 8:18 pm
What if base year is not given in the sum??