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प्रश्न
Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.
| Commodities | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 170 | 562 | 72 | 632 |
| B | 192 | 535 | 70 | 756 |
| C | 195 | 639 | 95 | 926 |
| D | 1987 | 128 | 92 | 255 |
| E | 1985 | 542 | 92 | 632 |
| F | 150 | 217 | 180 | 314 |
| 7 | 12.6 | 12.7 | 12.5 | 12.8 |
| 8 | 12.4 | 12.3 | 12.6 | 12.5 |
| 9 | 12.6 | 12.5 | 12.3 | 12.6 |
| 10 | 12.1 | 12.7 | 12.5 | 12.8 |
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उत्तर
| Commodities | Base Year | Current Year | p0q0 | p0q1 | p1q0 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 170 | 562 | 72 | 632 | 95540 | 107440 | 40464 | 45504 |
| B | 192 | 535 | 70 | 756 | 102720 | 145152 | 37450 | 52920 |
| C | 195 | 639 | 95 | 926 | 124605 | 180570 | 60705 | 87970 |
| D | 1987 | 128 | 92 | 255 | 23936 | 47685 | 11776 | 23460 |
| E | 1985 | 542 | 92 | 632 | 100270 | 116920 | 49864 | 58144 |
| F | 150 | 217 | 180 | 314 | 32550 | 47100 | 39060 | 56520 |
| 7 | 12.6 | 12.7 | 12.5 | 12.8 | 160.02 | 161.28 | 158.75 | 160 |
| 8 | 12.4 | 12.3 | 12.6 | 12.5 | 152.52 | 155 | 154.98 | 157.5 |
| 9 | 12.6 | 12.5 | 12.3 | 12.6 | 157.50 | 158.80 | 153.75 | 155 |
| 10 | 12.1 | 12.7 | 12.5 | 12.8 | 153.67 | 154.90 | 158.75 | 160 |
| Total | 480244.71 | 645496.98 | 239945.23 | 325150.5 | ||||
Lasperyre’s price Index number
`"P"_01^"L" = (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100`
= `239945.23/480244.71 xx 100`
= 49.96
Passhe's price index number
`"P"_01^"p" = (sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`
= `325150.5/645496.98 xx 100`
= 50.37
Fisher's price index number
`"P"_01^"F" = [sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1))] xx 100`
= `[sqrt((239945.23 xx 325150.5)/(480224.71 xx 645496.98))] xx 100`
= `sqrt((3572000)/(1827840)) xx 100`
= `sqrt(1.9542) xx 100`
= `1.3979 xx 100`
= 139.79
= 139.8
Time reversal test
Test is satisfied when `"P"_01 xx "P"_10` = 1
`"P"_01 = sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1))`
= `sqrt((1900 xx 1880)/(1360 xx 1344))`
`"P"_10 = sqrt((sum"p"_0"q"_1 xx sum"p"_0"q"_0)/(sum"p"_1"q"_1 xx sum"p"_1"q"_0))`
= `sqrt((1344 xx 1360)/(1880 xx 1900))`
`"P"_01 xx "P"_10 = sqrt((1900 xx 1880 xx 1344 xx 1360)/(1360 xx 1344 xx 1880 xx 1900))`
= `sqrt(1)`
Hence Fisher’s Ideal Index satisfies Time reversal test
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संबंधित प्रश्न
Identify & explain the concept from the given illustration.
Agricultural Research Institute constructed an index number to measure changes in the production of raw cotton in Maharashtra during the period 2015-2020.
State the uses of Index Number
Discuss about Cost of Living Index Number
Using the following data, construct Fisher’s Ideal index and show how it satisfies Factor Reversal Test and Time Reversal Test?
| Commodity | Price in Rupees per unit | Number of units | ||
| Basic year | Current year | Base year | Current year | |
| A | 6 | 10 | 50 | 56 |
| B | 2 | 2 | 100 | 120 |
| C | 4 | 6 | 60 | 60 |
| D | 10 | 12 | 50 | 24 |
| E | 8 | 12 | 40 | 36 |
The following are the group index numbers and the group weights of an average working class family’s budget. Construct the cost of living index number:
| Groups | Food | Fuel and Lighting |
Clothing | Rent | Miscellaneous |
| Index Number | 2450 | 1240 | 3250 | 3750 | 4190 |
| Weight | 48 | 20 | 12 | 15 | 10 |
Choose the correct alternative:
Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:
An Enquiry was made into the budgets of the middle class families in a city gave the following information.
| Expenditure | Food | Rent | Clothing | Fuel | Rice |
| Price(2010) | 150 | 50 | 100 | 20 | 60 |
| Price(2011) | 174 | 60 | 125 | 25 | 90 |
| Weights | 35 | 15 | 20 | 10 | 20 |
What changes in the cost of living have taken place in the middle class families of a city?
Assertion and reasoning question:
- Assertion (A): The index number considers all factors.
- Reasoning (R): The index number is based on samples.
Choose the correct pair :
| Group A | Group B | ||
| 1) | Price Index | a) | `(sump_1q_1)/(sump_0q_0) xx100` |
| 2) | Value Index |
b) |
`(sumq_1)/(sumq_0) xx 100` |
| 3) | Quantity Index | c) | `(sump_1q_1)/(sump_0q_1) xx100` |
| 4) | Paasche's Index | d) | `(sump_1)/(sump_0) xx 100` |
The base year's index of a selected variable is assumed as ______.
