Using the following data, compute Fisher's Ideal Price Index Numbers for the current year:
|
Commodity |
Base Year |
Current Year |
||
|
Price |
Qty. |
Price |
Qty. | |
|
(₹) |
(Kg.) |
(₹) |
(Kg.) |
|
|
A |
12 |
20 |
15 |
25 |
|
B |
10 |
08 |
16 |
10 |
|
C |
15 |
02 |
12 |
01 |
|
D |
60 |
01 |
65 |
01 |
|
E |
03 |
02 |
10 |
01 |
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 129.60
|
Commodity |
$p_0$ |
$q_0$ |
$p_1$ |
$q_1$ |
$p_1q_0$ |
$p_0q_0$ |
$p_1q_1$ |
$p_0q_1$ |
|
A |
12 |
20 |
15 |
25 |
300 |
240 |
375 |
300 |
|
B |
10 |
08 |
16 |
10 |
128 |
80 |
160 |
100 |
|
C |
15 |
02 |
12 |
01 |
24 |
30 |
12 |
15 |
|
D |
60 |
01 |
65 |
01 |
65 |
60 |
65 |
60 |
|
E |
03 |
02 |
10 |
01 |
20 |
06 |
10 |
03 |
|
Total |
|
|
|
|
$\sum p_1q_0 = 537$ |
$\sum p_0q_0 = 416$ |
$\sum p_1q_1 = 622$ |
$\sum p_0q_1 = 478$ |
Fisher's Price Index Number ($P_{01}$):
$P_{01} = \sqrt{\frac{\sum p_1q_0}{\sum p_0q_0} \times \frac{\sum p_1q_1}{\sum p_0q_1}} \times 100$
$P_{01} = \sqrt{\frac{537}{416} \times \frac{622}{478}} \times 100$
$P_{01} = \sqrt{\frac{334014}{198848}} \times 100 \approx 129.60$