The Cost of Living Index Number by Aggregate Expenditure Method is given by …………

Answer

To find the Cost of Living Index Number by the Aggregate Expenditure Method, we can follow these steps:

### Step 1: Understand the Variables
- Let \( P_0 \) be the price of commodities in the base year.
- Let \( Q_0 \) be the quantity of commodities in the base year.
- Let \( P_1 \) be the price of commodities in the current year.
- Let \( Q_1 \) be the quantity of commodities in the current year.

### Step 2: Calculate Expenditure in Both Years
- **Expenditure in the Base Year**: This is calculated as:
\[ \text{Expenditure}_{\text{base}} = P_0 \times Q_0 \]

- **Expenditure in the Current Year**: This is calculated as:
\[ \text{Expenditure}_{\text{current}} = P_1 \times Q_1 \]

### Step 3: Set Up the Formula for Cost of Living Index Number
The Cost of Living Index Number (CLIN) can be calculated using the following formula:
\[ \text{CLIN} = \left( \frac{\sum (P_1 \times Q_1)}{\sum (P_0 \times Q_0)} \right) \times 100 \]

### Step 4: Summation of Expenditures
- Calculate the summation of expenditures for all commodities:
\[ \sum (P_1 \times Q_1) \quad \text{and} \quad \sum (P_0 \times Q_0) \]

### Step 5: Substitute Values into the Formula
- Substitute the calculated values from Step 4 into the CLIN formula.

### Step 6: Calculate the Cost of Living Index Number
- Finally, perform the calculation to find the Cost of Living Index Number.

### Final Answer
The Cost of Living Index Number by the Aggregate Expenditure Method is given by:
\[ \text{CLIN} = \left( \frac{\sum (P_1 \times Q_1)}{\sum (P_0 \times Q_0)} \right) \times 100 \]

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