# Methods of Consumer Price Index Numbers

There are two methods to compute consumer price index numbers: (a) Aggregate Expenditure Method (2) Family Budget Method

Aggregate Expenditure Method

In this method, the quantities of commodities consumed by the particular group in the base year are estimated and these figures or their proportions are used as weights. Then the total expenditure of each commodity for each year is calculated. The price of the current year is multiplied by the quantity or weight of the base year. These products are added. Similarly, for the base year the total expenditure of each commodity is calculated by multiplying the quantity consumed by its price in the base year. These products are also added. The total expenditure of the current year is divided by the total expenditure of the base year and the resulting figure is multiplied by $100$ to get the required index numbers. In this method, the current period quantities are not used as weights because these quantities change from year to year.
${P_{on}} = \frac{{\sum {P_n}{q_o}}}{{\sum {P_o}{q_o}}} \times 100$

Here,
${P_n}$ Represent the price of the current year,
${P_o}$ Represents the price of the base year and
${q_o}$ Represents the quantities consumed in the base year.

Family Budget Method

In this method, the family budgets of a large number of people are carefully studied and the aggregate expenditure of the average family for various items is estimated. These values are used as weights. The current year’s prices are converted into price relatives on the basis of the base year’s prices, and these price relatives are multiplied by the respective values of the commodities in the base year. The total of these products is divided by the sum of the weights and the resulting figure is the required index numbers.
${P_{on}} = \frac{{\sum WI}}{{\sum W}}$

Here, $I = \frac{{{P_n}}}{{{P_0}}} \times 100$   and   $W = {P_o}{q_o}$

Example:

Construct the consumer price index number for $1988$ on the basis of $1987$ from the following data using: (1) Aggregate Expenditure Method (2) Family Budget Method.

 Commodities Quantity consumed in $1987$ Unit Prices $1987$ $1988$ $A$ 6 quintal quintal $315.75$ $316.00$ $B$ 6 quintal quintal $305.00$ $308.00$ $C$ 1 quintal quintal $416.00$ $419.00$ $D$ 6 quintal quintal $528.00$ $610.00$ $E$ 4 kg kg $12.00$ $11.50$ $F$ 1 quintal quintal $1020.00$ $1015.00$

Solution:
(1) The consumer price index number of $1988$ by Aggregate Expenditure Method:

 Commodities Quantity Consumed $1987$ ${q_o}$ Unit Prices ${P_1}{q_o}$ ${P_o}{q_o}$ $1987$ ${P_o}$ $1988$ ${P_1}$ $A$ 6 quintal quintal $315.75$ $316.00$ $1896$ $1894.5$ $B$ 6 quintal quintal $305.00$ $308.00$ $1848$ $1830.0$ $C$ 1 quintal quintal $416.00$ $419.00$ $419$ $416.0$ $D$ 6 quintal quintal $528.00$ $610.00$ $3660$ $3168.0$ $E$ 4 kg kg $12.00$ $11.50$ $46$ $48.0$ $F$ 1 quintal quintal $1020.00$ $1015.00$ $1015$ $1020.0$ $\begin{gathered} \sum {P_1}{q_o} \\ = 8884 \\ \end{gathered}$ $\begin{gathered} \sum {P_o}{q_o} \\ = 8376.5 \\ \end{gathered}$

The consumer price index number of $1988$ is

${P_{on}} = \frac{{\sum {P_n}{q_o}}}{{\sum {P_o}{q_o}}} \times 100 = \frac{{8884}}{{8376.5}} \times 100 = 106.06$

(2) The consumer price index number of $1988$ by Family Budget Method:

 Commodities Quantity Consumed $1987$ ${q_o}$ Prices $\begin{gathered} W = \\ {P_o}{q_o} \\ \end{gathered}$ $\begin{gathered} I = \\ \frac{{{P_1}}}{{{P_o}}} \times 100 \\ \end{gathered}$ Product $WI$ $1987$ ${P_o}$ $1988$ ${P_1}$ $A$ $6$ quintal $315.75$ $316.00$ $1894.5$ $100.08$ $189601.56$ $B$ $6$ quintal $305.00$ $308.00$ $1830.0$ $100.98$ $184793.40$ $C$ $1$ quintal $416.00$ $419.00$ $416.0$ $100.72$ $41899.52$ $D$ $6$ quintal $528.00$ $610.00$ $3168.0$ $115.53$ $365999.04$ $E$ $4$ kg $12.00$ $11.50$ $48.0$ $95.83$ $4599.84$ $F$ $1$ quintal $1020.00$ $1015.00$ $1020.0$ $99.51$ $101500.20$ $\begin{gathered} \sum W \\ = 8376.5 \\ \end{gathered}$ $\begin{gathered} \sum WI = \\ 888393.56 \\ \end{gathered}$

The consumer price index number of $1988$ is

${P_{on}} = \frac{{\sum WI}}{{\sum W}} \times 100 = \frac{{888393.56}}{{8376.5}} \times 100 = 106.06$