1. Find Cost of living Index number by the Family budget method
| Item | Quantity | Price0 | Price1 |
| A | 35 | 16 | 18 |
| B | 25 | 40 | 45 |
| C | 20 | 60 | 120 |
| D | 10 | 80 | 90 |
| E | 20 | 30 | 45 |
| F | 15 | 28 | 35 |
Solution:
Family budget method :
| Item | Quantity
`q_0` | Price
`p_0` | Price
`p_1` | Price relatives
`I=p_1/p_0 xx 100` | `W=p_0q_0` | `IW` |
| A | 35 | 16 | 18 | 112.5 | 560 | 63000 |
| B | 25 | 40 | 45 | 112.5 | 1000 | 112500 |
| C | 20 | 60 | 120 | 200 | 1200 | 240000 |
| D | 10 | 80 | 90 | 112.5 | 800 | 90000 |
| E | 20 | 30 | 45 | 150 | 600 | 90000 |
| F | 15 | 28 | 35 | 125 | 420 | 52500 |
| --- | --- | --- | --- | --- | --- | --- |
| Total | | | | | `sum W=4580` | `sum IW=648000` |
Consumer price index number by family budget method
`I=(sum IW)/(sum W)`
`=(648000)/(4580)`
`=141.48`
Thus, there is a rise of `(141.48-100)=41.48%` in family budget
2. Find Cost of living Index number by the Family budget method
| Item | Quantity | Price0 | Price1 |
| A | 40 | 160 | 200 |
| B | 25 | 400 | 600 |
| C | 5 | 50 | 70 |
| D | 20 | 10 | 18 |
| E | 10 | 2 | 3 |
Solution:
Family budget method :
| Item | Quantity
`q_0` | Price
`p_0` | Price
`p_1` | Price relatives
`I=p_1/p_0 xx 100` | `W=p_0q_0` | `IW` |
| A | 40 | 160 | 200 | 125 | 6400 | 800000 |
| B | 25 | 400 | 600 | 150 | 10000 | 1500000 |
| C | 5 | 50 | 70 | 140 | 250 | 35000 |
| D | 20 | 10 | 18 | 180 | 200 | 36000 |
| E | 10 | 2 | 3 | 150 | 20 | 3000 |
| --- | --- | --- | --- | --- | --- | --- |
| Total | | | | | `sum W=16870` | `sum IW=2374000` |
Consumer price index number by family budget method
`I=(sum IW)/(sum W)`
`=(2374000)/(16870)`
`=140.72`
Thus, there is a rise of `(140.72-100)=40.72%` in family budget
3. Find Cost of living Index number by the Family budget method
| Item | Quantity | Price0 | Price1 |
| A | 40 | 2 | 2.50 |
| B | 20 | 3 | 3.25 |
| C | 10 | 1.5 | 1.75 |
Solution:
Family budget method :
| Item | Quantity
`q_0` | Price
`p_0` | Price
`p_1` | Price relatives
`I=p_1/p_0 xx 100` | `W=p_0q_0` | `IW` |
| A | 40 | 2 | 2.5 | 125 | 80 | 10000 |
| B | 20 | 3 | 3.25 | 108.3333 | 60 | 6500 |
| C | 10 | 1.5 | 1.75 | 116.6667 | 15 | 1750 |
| --- | --- | --- | --- | --- | --- | --- |
| Total | | | | | `sum W=155` | `sum IW=18250` |
Consumer price index number by family budget method
`I=(sum IW)/(sum W)`
`=(18250)/(155)`
`=117.74`
Thus, there is a rise of `(117.74-100)=17.74%` in family budget
This material is intended as a summary. Use your textbook for detail explanation.
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