1. Find Laspeyre's index number, Paasche's index number, Dorbish-Bowley's index number
| Item | Price0 | Quantity0 | Price1 | Quantity1 |
| Rice | 39 | 1 | 40 | 1.5 |
| Milk | 40 | 12 | 44 | 10 |
| Bread | 45 | 2 | 50 | 1.5 |
| Banana | 30 | 2 | 36 | 1.5 |
Solution:
| Item | `p_0` | `q_0` | `p_1` | `q_1` | `p_1q_0` | `p_0q_0` | `p_1q_1` | `p_0q_1` |
| Rice | 39 | 1 | 40 | 1.5 | 40 | 39 | 60 | 58.5 |
| Milk | 40 | 12 | 44 | 10 | 528 | 480 | 440 | 400 |
| Bread | 45 | 2 | 50 | 1.5 | 100 | 90 | 75 | 67.5 |
| Banana | 30 | 2 | 36 | 1.5 | 72 | 60 | 54 | 45 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Total | | | | | `740` | `669` | `629` | `571` |
1. Laspeyre's index number
`I_L=(sum p_1q_0)/(sum p_0q_0) xx 100`
`=(740)/(669) xx 100`
`=110.61`
Thus, there is a rise of `(110.61-100)=10.61%` in prices
2. Paasche's index number
`I_P=(sum p_1q_1)/(sum p_0q_1) xx 100`
`=(629)/(571) xx 100`
`=110.16`
Thus, there is a rise of `(110.16-100)=10.16%` in prices
3. Dorbish and Bowley's price index
`I_D=(I_L + I_P)/2`
`=(110.6129+110.1576)/2`
`=(220.7705)/2`
`=110.39`
Thus, there is a rise of `(110.39-100)=10.39%` in prices
2. Find Dorbish-Bowley'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. Dorbish and Bowley's price index
`I_D=((sum p_1q_0)/(sum p_0q_0) + (sum p_1q_1)/(sum p_0q_1))/2 xx 100`
`=((456)/(406) + (506)/(451))/2 xx 100`
`=(2.2451)/2 xx 100`
`=1.1226 xx 100`
`=112.26`
Thus, there is a rise of `(112.26-100)=12.26%` in prices
3. Find Dorbish-Bowley's index number
| Item | Price0 | Quantity0 | Price1 | Quantity1 |
| A | 3 | 25 | 5 | 28 |
| B | 1 | 50 | 3 | 60 |
| C | 2 | 30 | 1 | 30 |
| D | 5 | 15 | 6 | 12 |
Solution:
| Item | `p_0` | `q_0` | `p_1` | `q_1` | `p_1q_0` | `p_0q_0` | `p_1q_1` | `p_0q_1` |
| A | 3 | 25 | 5 | 28 | 125 | 75 | 140 | 84 |
| B | 1 | 50 | 3 | 60 | 150 | 50 | 180 | 60 |
| C | 2 | 30 | 1 | 30 | 30 | 60 | 30 | 60 |
| D | 5 | 15 | 6 | 12 | 90 | 75 | 72 | 60 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Total | | | | | `395` | `260` | `422` | `264` |
1. Dorbish and Bowley's price index
`I_D=((sum p_1q_0)/(sum p_0q_0) + (sum p_1q_1)/(sum p_0q_1))/2 xx 100`
`=((395)/(260) + (422)/(264))/2 xx 100`
`=(3.1177)/2 xx 100`
`=1.5589 xx 100`
`=155.89`
Thus, there is a rise of `(155.89-100)=55.89%` in prices
This material is intended as a summary. Use your textbook for detail explanation.
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