Methods of Consumer Price Index Numbers

There are two methods for the compute of 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 on 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 total expenditure on 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 by100 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


            Where,
                        {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 on various items is estimated. These values are used as weights. Current year’s price are converted into price relatives on the basis of base year’s prices and these prices 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}}


Where 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) 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}

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) Consumer price index number of1988 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}

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

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