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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
Features of index numbers:
- It is useful in framing suitable economic policies.
- It is useful to present financial data in real terms
- Index numbers are statistical devices.
- Index numbers are specialized averages.
Index number which is computed from a single variable called is a ______.
Define family budget method
Calculate by a suitable method, the index number of price from the following data:
| Commodity | 2002 | 2012 | ||
| Price | Quantity | Price | Quantity | |
| A | 10 | 20 | 16 | 10 |
| B | 12 | 34 | 18 | 42 |
| C | 15 | 30 | 20 | 26 |
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 |
Using the following data, construct Fisher’s Ideal Index Number and Show that it satisfies Factor Reversal Test and Time Reversal Test?
| Commodities | Price | Quantity | ||
| Base Year | Current Year | Base Year | Current Year | |
| Wheat | 6 | 10 | 50 | 56 |
| Ghee | 2 | 2 | 100 | 120 |
| Firewood | 4 | 6 | 60 | 60 |
| Sugar | 10 | 12 | 30 | 24 |
| Cloth | 8 | 12 | 40 | 36 |
Compute the consumer price index for 2015 on the basis of 2014 from the following data.
| Commodities | Quantities | Prices in 2015 | Prices in 2016 |
| A | 6 | 5.75 | 6.00 |
| B | 6 | 5.00 | 8.00 |
| C | 1 | 6.00 | 9.00 |
| D | 6 | 8.00 | 10.00 |
| E | 4 | 2.00 | 1.50 |
| F | 1 | 20.00 | 15.00 |
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.
Complete the correlation:
P0 : ______ : : P1 : Current year price.
