Consider that $p_0, q_0$ represents price and quantity of base year and $p_1, q_1$ represents price and quantity for the current year. Given that $\sum p_0 q_0=584, \sum p_0 q_1=484$. $\sum p_1 q_0=623$ and $\sum p_1 q_1=517$. Which of the following gives Fisher's price Index Number $\left(P_{01}\right)$?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $P_{01}=\sqrt{\frac{623 \times 517}{584 \times 484}} \times 100$
$\text{Laspeyres index} = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100 = \frac{623}{584}\times100$
$\text{Paasche index} = \frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100 = \frac{517}{484}\times100$
$\text{Fisher index} = \sqrt{\left(\frac{623}{584}\times100\right)\left(\frac{517}{484}\times100\right)}$
$= 100\sqrt{\frac{623\times517}{584\times484}}$
$P_{01} = 100\sqrt{\frac{623\times517}{584\times484}}$