1. Find Cost of living Index number by the Aggregate expenditure 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:
Aggregate expenditure method :
| Item | Quantity
`q_0` | Price
`p_0` | Price
`p_1` | `p_0q_0` | `p_1q_0` |
| A | 35 | 16 | 18 | 560 | 630 |
| B | 25 | 40 | 45 | 1000 | 1125 |
| C | 20 | 60 | 120 | 1200 | 2400 |
| D | 10 | 80 | 90 | 800 | 900 |
| E | 20 | 30 | 45 | 600 | 900 |
| F | 15 | 28 | 35 | 420 | 525 |
| --- | --- | --- | --- | --- | --- |
| Total | | | | `sum p_0q_0=4580` | `sum p_1q_0=6480` |
Consumer price index number by Aggregate expenditure method
`I_L=(sum p_1q_0)/(sum p_0q_0) xx 100`
`=(6480)/(4580) xx 100`
`=141.48`
Thus, there is a rise of `(141.48-100)=41.48%` in Aggregate expenditure
2. Find Cost of living Index number by the Aggregate expenditure 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:
Aggregate expenditure method :
| Item | Quantity
`q_0` | Price
`p_0` | Price
`p_1` | `p_0q_0` | `p_1q_0` |
| A | 40 | 160 | 200 | 6400 | 8000 |
| B | 25 | 400 | 600 | 10000 | 15000 |
| C | 5 | 50 | 70 | 250 | 350 |
| D | 20 | 10 | 18 | 200 | 360 |
| E | 10 | 2 | 3 | 20 | 30 |
| --- | --- | --- | --- | --- | --- |
| Total | | | | `sum p_0q_0=16870` | `sum p_1q_0=23740` |
Consumer price index number by Aggregate expenditure method
`I_L=(sum p_1q_0)/(sum p_0q_0) xx 100`
`=(23740)/(16870) xx 100`
`=140.72`
Thus, there is a rise of `(140.72-100)=40.72%` in Aggregate expenditure
3. Find Cost of living Index number by the Aggregate expenditure method
| Item | Quantity | Price0 | Price1 |
| A | 40 | 2 | 2.50 |
| B | 20 | 3 | 3.25 |
| C | 10 | 1.5 | 1.75 |
Solution:
Aggregate expenditure method :
| Item | Quantity
`q_0` | Price
`p_0` | Price
`p_1` | `p_0q_0` | `p_1q_0` |
| A | 40 | 2 | 2.5 | 80 | 100 |
| B | 20 | 3 | 3.25 | 60 | 65 |
| C | 10 | 1.5 | 1.75 | 15 | 17.5 |
| --- | --- | --- | --- | --- | --- |
| Total | | | | `sum p_0q_0=155` | `sum p_1q_0=182.5` |
Consumer price index number by Aggregate expenditure method
`I_L=(sum p_1q_0)/(sum p_0q_0) xx 100`
`=(182.5)/(155) xx 100`
`=117.74`
Thus, there is a rise of `(117.74-100)=17.74%` in Aggregate expenditure
This material is intended as a summary. Use your textbook for detail explanation.
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