Question

From the following data compute Fisher's ideal quantity index.

Items	$2009$	$2009$	$2010$	$2010$
	Price (Rs.) $\left(p_0\right)$	Quantity $\left(q_0\right)$	Price (Rs.) $\left(p_1\right)$	Quantity $\left(q_1\right)$
$A$	$4$	$3$	$6$	$2$
$B$	$5$	$4$	$0$	$4$
$C$	$7$	$2$	$9$	$2$
$D$	$2$	$3$	$1$	$5$

• A. $71.05$
• B. $115.43$
• C. $118.35$
• D. $116.48$

Answer 1

The correct option is A $71.05$

	$p_0{q}_0$	$p_0{q}_1$	$p_1{q}_0$	$p_1{q}_1$
A	12	8	18	12
B	20	20	0	0
C	14	14	18	18
D	6	10	3	5
Sum	52	52	39	35

Fisher's index is given by:

$P_{01}=\sqrt{\frac{\Sigma p_1{q}_0}{\Sigma p_0{q}_0}\times \frac{\Sigma p_1{q}_1}{\Sigma p_0{q}_1}}\times 100$

$P_{01}=\sqrt{\frac{39}{52}\times \frac{35}{52}}\times 100$

$P_{01}=\sqrt{\frac{1365}{2704}}\times 100$

$P_{01}=\sqrt{0.50481}\times 100$

$P_{01}=0.710498\times 100$

$P_{01}=71.05$