f Fisher’s index = 150 and Paasche’s Index = 144, then Laspeyre’s index is ____(a) 147(b) 156.25(c) 104.17(d) 138

1. Break Down the Problem

We need to find Laspeyres’s index given Fisher’s index and Paasche’s index. We can use the relationship between these indices to derive the solution.

2. Relevant Concepts

The relationship among the indices can be expressed through the formula: $L = \frac{F \times P}{\sqrt{F \times P}}$ where:

• $L$ is Laspeyres's index,
• $F$ is Fisher’s index,
• $P$ is Paasche’s index.

3. Analysis and Detail

Given:

• $F = 150$
• $P = 144$

We plug in the values into the formula to calculate $L$:

$L = \frac{150 \times 144}{\sqrt{150 \times 144}}$

First, we calculate $150 \times 144$: $150 \times 144 = 21600$

Next, we calculate $\sqrt{150 \times 144}$: $\sqrt{21600} \approx 147$

So, we now have: $L = \frac{21600}{147}$

Calculating $\frac{21600}{147}$: $\frac{21600}{147} \approx 147.06$

4. Verify and Summarize

After double-checking the calculations, we confirm that the approximate result is about 147.06. In the context of the given multiple-choice options, Laspeyres's index rounds down closely to 147.

Final Answer

Laspeyres’s index is approximately 147 (option a).