Advertisements
Advertisements
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 |
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
______ : Base year prices :: P1 : Current year prices.
Complete the Correlation:
__________ : Single variable :: Composite index : Group of variables
Index numbers that measure changes in the level of output or physical volume of production in the economy −
Index number which is computed from a single variable called is a ______.
Identify & explain the concept from the given illustration.
Bombay Stock Exchange has developed “Sensex” as a stock market index for reflecting the share prices of listed companies.
Explain Paasche’s price index number
Define true value ratio
Calculate Fisher’s index number to the following data. Also show that it satisfies Time Reversal Test.
| Commodity | 2016 | 2017 | ||
| Price (Rs.) | Quantity (kg) | Price (Rs.) | Quantity (kg) | |
| Food | 40 | 12 | 65 | 14 |
| Fuel | 72 | 14 | 78 | 20 |
| Clothing | 36 | 10 | 36 | 15 |
| Wheat | 20 | 6 | 42 | 4 |
| Others | 46 | 8 | 52 | 6 |
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?
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.
