The Cost of Living Index Number by Aggregate Expenditure Method is same as

Options

A. Fisher’s Price Index Number
B. Laspeyre’s Price Index Number
C. Paasche’s Price Index Number
D. Dorbish-Bowley’s Price Index Number

Answer

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

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The Cost of Living Index Number (COLI) measures the relative cost of living over time or between different locations.
- The Aggregate Expenditure Method calculates the total cost of a basket of goods and services.

2. **Define 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.

3. **Calculate Total Expenditure**:
- The total expenditure in the current year is calculated as:
\[ \text{Total Cost in Current Year} = \sum P_1 Q_1 \]
- The total expenditure in the base year is calculated as:
\[ \text{Total Cost in Base Year} = \sum P_0 Q_0 \]

4. **Formulate the Cost of Living Index Number**:
- The Cost of Living Index Number (COLI) using the Aggregate Expenditure Method is given by:
\[ \text{COLI} = \left( \frac{\sum P_1 Q_1}{\sum P_0 Q_0} \right) \times 100 \]

5. **Relate to Price Index Number**:
- It can be observed that the formula for the Cost of Living Index Number is equivalent to the formula for the Price Index Number (PIN). Therefore, we conclude that:
\[ \text{COLI} = \text{Price Index Number} \]

6. **Final Conclusion**:
- Thus, the Cost of Living Index Number by Aggregate Expenditure Method is the same as the Price Index Number.