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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
APPEARS IN
संबंधित प्रश्न
______ : Base year prices :: P1 : Current year prices.
Complete the Correlation:
__________ : Single variable :: Composite index : Group of variables
Assertion (A): Index numbers are statistical devices.
Reasoning (R): Index numbers measure only changes in the price level over a period of time.
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.
Explain factor reversal test
Calculate price index number for 2005 by (a) Laspeyre’s (b) Paasche’s method
| Commodity | 1995 | 2005 | ||
| Price | Quantity | Price | Quantity | |
| A | 5 | 60 | 15 | 70 |
| B | 4 | 20 | 8 | 35 |
| C | 3 | 15 | 6 | 20 |
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 |
Calculate the cost of living index by aggregate expenditure method:
| Commodity | Weight 2010 |
Price (Rs.) | |
| 2010 | 2015 | ||
| P | 80 | 22 | 25 |
| Q | 30 | 30 | 45 |
| R | 25 | 42 | 50 |
| S | 40 | 25 | 35 |
| T | 50 | 36 | 52 |
Choose the correct alternative:
Cost of living at two different cities can be compared with the help of
Read the given passage and answer the questions:
|
Index Number is a technique of measuring changes in a variable or group of related variables with reference to time, geographical location and other characteristics. Index Number is very useful for economists, farmers, traders, government, educationalists and trade union leaders for planning and implementing the plans according to their sector. The scope of index number is not limited to only one subject but it extends to many subjects such as Economics, Educational science, Psychology, History, Sociology, Geography etc. While framing index number its objective must be determined. To attain the objective the information is collected in various ways and this information is used for comparing two different time periods. For this purpose, the base year’s index is assumed as 100 and accordingly the value of the current year is calculated. Laspeyre, Paasche and Fisher have suggested different methods for constructing index numbers. |
- Explain the meaning of Index Number.
- To whom the Index Number is useful?
- Express your opinion about the given passage.
