Find Laspeyre's index number, Paasche's index number, Fisher's index number
| Item | Price0 | Quantity0 | Price1 | Quantity1 |
| A | 10 | 20 | 12 | 22 |
| B | 8 | 16 | 8 | 18 |
| C | 5 | 10 | 6 | 11 |
| D | 4 | 7 | 4 | 8 |
Solution:
| Item | `p_0` | `q_0` | `p_1` | `q_1` | `p_1q_0` | `p_0q_0` | `p_1q_1` | `p_0q_1` |
| A | 10 | 20 | 12 | 22 | 240 | 200 | 264 | 220 |
| B | 8 | 16 | 8 | 18 | 128 | 128 | 144 | 144 |
| C | 5 | 10 | 6 | 11 | 60 | 50 | 66 | 55 |
| D | 4 | 7 | 4 | 8 | 28 | 28 | 32 | 32 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Total | | | | | `456` | `406` | `506` | `451` |
1. Laspeyre's index number
`I_L=(sum p_1q_0)/(sum p_0q_0) xx 100`
`=(456)/(406) xx 100`
`=112.32`
Thus, there is a rise of `(112.32-100)=12.32%` in prices
2. Paasche's index number
`I_P=(sum p_1q_1)/(sum p_0q_1) xx 100`
`=(506)/(451) xx 100`
`=112.2`
Thus, there is a rise of `(112.2-100)=12.2%` in prices
3. Fisher's index number
`I_F=sqrt(I_L xx I_P)`
`=sqrt(112.3153 xx 112.1951)`
`=112.26`
Thus, there is a rise of `(112.26-100)=12.26%` in prices
This material is intended as a summary. Use your textbook for detail explanation.
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