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प्रश्न
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 |
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उत्तर
| Commodities | Base Year | Current Year | p0q0 | p0q1 | p1q0 | p1q1 | ||
| Price (p0) |
Quantity (q0) |
Price (p1) |
Quantity (q1) |
|||||
| Wheat | 6 | 10 | 50 | 56 | 300 | 336 | 500 | 560 |
| Ghee | 2 | 2 | 100 | 120 | 200 | 240 | 200 | 240 |
| Firewood | 4 | 6 | 60 | 60 | 240 | 240 | 360 | 360 |
| Sugar | 10 | 12 | 30 | 24 | 300 | 240 | 360 | 288 |
| Cloth | 8 | 12 | 40 | 36 | 320 | 288 | 480 | 432 |
| Total | 1360 | 1344 | 1900 | 1880 | ||||
Fisher's ideal index number = `sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100`
`"P"_01^"F" = sqrt((1900 xx 1880)/(1360 xx 1344)) xx 100`
= `sqrt((3,572,000)/(1,827,840)) xx 100`
= `sqrt(1.9542) xx 100`
Factor reversal test
Test is satisfied when `"P"_01 xx "Q"_01 = (sum"p"_1"q"_1)/(sum"p"_0"q"_0)`
`"Q"_01 = sqrt((sum"p"_0"q"_1 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_1"q"_0))`
= `sqrt((1344 xx 1880)/(1360 xx 1900))`
`"P"_01 xx "Q"_01 = sqrt((1900 xx 1880)/(1360 xx 1344) xx (1344 xx 1880)/(1360 xx 1900)`
= `sqrt((1880 xx 1880)/(1360 xx 1360))`
= `1880/1360`
= `(sum"p"_1"q"_1)/(sum"p"_0"q"_0)`
Hence Fisher’s Ideal Index satisfies Factor reversal test.
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संबंधित प्रश्न
Statements that are incorrect in relation to index numbers:
- An index number is a geographical tool.
- Index numbers measure changes in air pressure.
- Index numbers measure relative changes in an economic variable.
- Index numbers are specialized averages.
Complete the Correlation:
__________ : Single variable :: Composite index : Group of variables
State with reason whether you agree or disagree with the following statement:
Index numbers measure changes in the price level only.
Device that measures changes in an economic variable or a group of variables 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.
Mention the classification of Index Number
Explain Paasche’s price index number
Explain factor reversal test
State with reasons whether you agree or disagree with the following statement:
Index number measures changes in the price level only.
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.
