If Laspeyre’s and Paasche’s Price Index Numbers are 50 & 72 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Numbers

Answer

To find Dorbish-Bowley's and Fisher's Price Index Numbers given Laspeyre’s and Paasche’s Price Index Numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Laspeyre’s Price Index Number (P01 of L) = 50
- Paasche’s Price Index Number (P01 of P) = 72

2. **Calculate Dorbish-Bowley’s Price Index Number:**
- The formula for Dorbish-Bowley’s Price Index Number (P01 of D) is:
\[ P01 of D = \frac{P01 of L + P01 of P}{2} \]
- Substitute the given values:
\[ P01 of D = \frac{50 + 72}{2} \]
- Calculate:
\[ P01 of D = \frac{122}{2} = 61 \]

3. **Calculate Fisher’s Price Index Number:**
- The formula for Fisher’s Price Index Number (P01 of F) is:
\[ P01 of F = \sqrt{P01 of L \times P01 of P} \]
- Substitute the given values:
\[ P01 of F = \sqrt{50 \times 72} \]
- Calculate the product:
\[ 50 \times 72 = 3600 \]
- Now, take the square root:
\[ P01 of F = \sqrt{3600} = 60 \]

### Final Answers:
- Dorbish-Bowley’s Price Index Number = 61
- Fisher’s Price Index Number = 60

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