From the following data calculate Price Index numbers by using
i) Laspeyre's method
ii) Paasche's method
iii) Bowler's method
| Commodities | Base Year Price (Rs.) | Base Year Quantity | Current Year Price (Rs.) | Current Year Quantity |
|---|---|---|---|---|
| A | 5 | 25 | 6 | 30 |
| B | 10 | 5 | 15 | 4 |
| C | 3 | 40 | 2 | 50 |
| D | 6 | 30 | 8 | 35 |
Answer (1)
To calculate the Price Index numbers using Laspeyre's, Paasche's, and Bowley's methods, we need to follow specific formulas for each method:
1. Laspeyre's Method:
Laspeyre's Price Index (LPI) is given by the formula: L P I = ( ∑ ( P 0 × Q 0 ) ∑ ( P 1 × Q 0 ) ) × 100 where:
P 0 and Q 0 are the base year prices and quantities.
P 1 and Q 1 are the current year prices and quantities.
Calculation: L P I = ( ( 5 × 25 ) + ( 10 × 5 ) + ( 3 × 40 ) + ( 6 × 30 ) ( 6 × 25 ) + ( 15 × 5 ) + ( 2 × 40 ) + ( 8 × 30 ) ) × 100 = ( 125 + 50 + 120 + 180 150 + 75 + 80 + 240 ) × 100 = ( 475 545 ) × 100 = 114.74
2. Paasche's Method:
Paasche's Price Index (PPI) is given by the formula: PP I = ( ∑ ( P 0 × Q 1 ) ∑ ( P 1 × Q 1 ) ) × 100
Calculation: PP I = ( ( 5 × 30 ) + ( 10 × 4 ) + ( 3 × 50 ) + ( 6 × 35 ) ( 6 × 30 ) + ( 15 × 4 ) + ( 2 × 50 ) + ( 8 × 35 ) ) × 100 = ( 150 + 40 + 150 + 210 180 + 60 + 100 + 280 ) × 100 = ( 550 620 ) × 100 ≈ 112.73
3. Bowley's Method:
Bowley's formula for index number is an average of Laspeyre's and Paasche's indices: BP I = 2 L P I + PP I
Calculation: BP I = 2 114.74 + 112.73 ≈ 113.74
In summary:
Laspeyre's Price Index: 114.74
Paasche's Price Index: 112.73
Bowley's Price Index: 113.74
These indices help measure the general change in prices by evaluating the cost of purchasing a fixed basket of goods or a set volume of goods in a base year compared to the current year.
