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Mb0040 Q6. Construct index numbers of price for the following data by applying: i) Laspeyre’s method ii) Paasche’s method iii) Fisher’s Ideal Index number


Commodity
Base year
Current year

Price
Quantity
Price
Quantity
A
2
8
4
6
B
5
10
6
5
C
4
14
5
10
D
2
19
2
13

Answer : 
Commodity
Base year
Current year





Price  
P0
Quantity Q0
Price P1
Quantity Q1
P0Q0
P1Q1
P1Q0
P0Q1
A
2
8
4
6
16
24
32
12
B
5
10
6
5
50
30
60
25
C
4
14
5
10
56
50
70
40
D
2
19
2
13
38
26
38
26





160
130
200
103

Laspeyre’s price index Laspeyre’s method is based on fixed weights of the base year. Base year’s quantities are used as weights. The formula given by Laspeyre is given below.

Laspeyre’s price index P01= (∑P1Q0 / ∑P0Q0 ) *100
Where, P1 = Current year price
P0 = Base year price
Q0 = Quantity used for weight in the base years

P01      = (200/160)*100
                                                = 1.25 *100
                                                = 125

ii) Paasche’s method
Paasche’s method is based on current year’s quantities. Current year’s quantities are used as weights. Paache’s Price Index is given by:

                            
Where, P1 = Current year price;
P0 = Base year price
Q1 = Current year quantity which are taken as weights.

P01= (130/103)*100
            = 1.26*100
            = 126

iii) Fisher’s Ideal Index number


This is the geometric mean of Laspeyre’s and Paasche’s index numbers. It is –

                = √[(200/160)*(130/103)]*100
= √[1.25*1.26]*100
= √1.575 * 100
= 1.255*100
            = 125.5


Answers taken from www.smuHelp.com

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