Information of sales price per unit of different commodities for two different years is given in following table-
- Information of sales price per unit of different commodities for two different years is given in following table-
Commodities |
2010 | 2016 | ||
Price | Quantity | Price | Quantity | |
A | 20 | 5 | 25 | 3 |
B | 30 | 8 | 45 | 5 |
C | 10 | 12 | 20 | 8 |
D | 15 | 10 | 16 | 10 |
E | 45 | 5 | 50 | 6 |
F | 90 | 10 | 110 | 8 |
Construct the Price Index taking 2010 as the base year and 2016 as the current year by following methods.
- Laspeyre’s Price Index
- Paasche’s Method
iii. Dorbish and Bowley’s method
- Fisher’s Ideal Index Method
- Construction of the Price Index
- Laspeyre’s Price Index
Solution: Base year price and quantity are denoted by P0 and Q0 and current year price and quantity are denoted by P1 and Q1 respectively
Commodity | P0 | Q0 | P1 | Q1 | P0Q0 | P1Q0 | P0Q1 | P1Q1 |
A | 20
30 10 |
5 | 25 | 3 | 100 | 125 | 60 | 300 |
B | 30 | 8 | 45 | 5 | 240 | 360 | 150 | 225 |
C | 10 | 12 | 20 | 8 | 120 | 240 | 80 | 160 |
D | 15 | 10 | 16 | 10 | 150 | 160 | 150 | 160 |
E
|
45 | 5 | 50 | 6 | 225 | 250 | 270 | 300 |
F | 90 | 10 | 110 | 8 | 900 | 1100 | 720 | 880 |
Total | 1735 | 2235 | 1430 | 2025 |
Laspeyre’s price index number is given by= LP01=EP1Q0/EP0Q0*100
Now substituting the values, we get,
LP01=2235/1735*100
LP01=128.818
Laspeyre’s quantity index number is given by= LQ01=EQ1P0/EQ0P0*100
LQ01=1430/1735*100
LQ01=82.42
- Paasche’s Method
Paache’s Price Index is given by: PP01=EP1Q1/EP0Q1*100
PP01=2025/1430*100
PP01=141.60
Paache’s quantity index is given by: PQ01=EQ1P1/EQ0P1*100
PQ01=2025/2235*100
PQ01=90.60
iii. Dorbish and Bowley’s method
DP01=(EP1Q0/EP0Q0+EP1Q1/EP0Q1)*100/2
DP01=(2235/1735+2025/1430)*100/2
DP01=270.4/2
DP01=135
- Fisher’s Ideal Index Method
Fisher’s index number is given by= FP01=SQ ROOT OF (EP1Q0/EP0Q0 X EP1Q1/EP0Q1)*100/2
FP01=SQ ROOT OF (2235/1735 X 2025/1430)*100/2
FP01=SQ ROOT OF (1.288*1416)*100
FP01=SQ ROOT OF 18.2*100 =1820
FP01=42.66
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