An Index Number is a statistical measure that expresses the relationship between two variables or groups of variables. For the purpose of computing the Index numbers, we use one variable or the group of variables as the base. There are various methods in use to calculate the Index numbers. Aggregate Expenditure Method is one of such methods which we shall study in detail here.

**Aggregate Expenditure Method**

Under this method, we take the quantities of consumption of various commodities by a particular section of the people in the base year as weights. We then calculate the total expenditure of each commodity for each year.

For this, we need to multiply the price of the current year with the quantity or weight of the base year and add these products. Similarly, we have to calculate the total expenditure for the base year of each commodity.

Thus, in order to calculate the index numbers, we have to divide the total expenditure of the current year by the total expenditure of the base year and multiply the resulting figure by 100.

This method is somewhat like the Laspeyresâ€™ Method.

Consumer Price Index = \(\frac{âˆ‘p_{1}q_{0}}{âˆ‘p_{0}q_{0}}\) x 100

Here,

p_{1} = prices of the current year

p_{0 }= prices of the base year

q_{0} = quantity consumed in base year.

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**Family Budget Method**

Under this method, we study the family budgets of a large number of people and estimate the aggregate expenditure of the average family for various items. These values are used as weights. We then convert the current yearâ€™s prices into price relatives on the basis of the base yearâ€™s prices.

We then multiply these price relatives by the respective values of the commodities of the base year. Now, we need to divide the total of these products by the sum of the weights.

This method is similar to the weighted average of price relative method. Its formula is:

Consumer Price Index = \(\frac{âˆ‘PW}{âˆ‘W}\)

Where,

P = \(\frac{p_{1}}{p_{0}}\) x 100

V = Value weights or p_{0}q_{0}

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**Uses of Consumer Price Index Number**

- We use it to develop economic policy and also to evaluate the real earnings.
- It is also helpful in measuring the purchasing power of the consumer. The formula for measuring the purchasing power is:

Purchasing Power = \(\frac{1}{ Consumer Price Index}\) x 100

- It is also used in the process of deflating. The formula to express the process of deflating is:

Real Wage = \(\frac{Money Value}{ Consumer Price Index}\) x 100

- It is also useful in the negotiation of wages and wage contracts. It is also used in the calculation of Dearness Allowance.

**SolvedÂ Example onÂ Aggregate Expenditure**

From the following information calculate the changes in the cost of living of people of Indore in 2018 in comparison with 2017.

Food | Clothing | Rent | Education | Others | |

Expenses | 40% | 20% | 10% | 15% | 15% |

Price in 2017 | 200 | 120 | 70 | 100 | 50 |

Price in 2018 | 220 | 150 | 80 | 120 | 70 |

**Answer:**

**Calculation of Cost of Living**

Items | Expenses%Â Â Â Â Â Â Â (W) | Price in 2017Â Â Â (p_{0}) |
Price in 2018Â Â Â (p_{1}) |
P = \(\frac{p_{1}}{p_{0}}\) x 100 |
PW |

Food | 40 | 200 | 220 | \(\frac{220}{200}\) x 100 | \(\frac{220}{200}\) x 100 x 35 = 3850 |

Clothing | 20 | 120 | 150 | \(\frac{150}{120}\) x 100 | \(\frac{150}{120}\) x 100 x 20 = 2500 |

Rent | 10 | 70 | 80 | \(\frac{80}{70}\) x 100 | \(\frac{80}{70}\) x 100 x 10 = 1143 |

Education | 15 | 100 | 120 | \(\frac{120}{100}\) x 100 | \(\frac{120}{100}\) x 100 x 15 = 1800 |

Others | 15 | 50 | 70 | \(\frac{70}{50}\) x 100 | \(\frac{70}{50}\) x 100 x 15 = 2100 |

âˆ‘W = 100 | âˆ‘PW = 11393 |

Consumer Price Index = Â \(\frac{âˆ‘PW}{âˆ‘W}\)

= \(\frac{11393}{100}\)

= 113.93

We can hence conclude that the cost of living has increased by 13.93% in 2018 as compared to 2017.

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