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प्रश्न
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 |
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उत्तर
| Commodity | Base year | Current year | p0q0 | p0q1 | p1q0 | p1q1 | ||
| p0 | q0 | p1 | q1 | |||||
| A | 6 | 10 | 50 | 56 | 300 | 336 | 500 | 560 |
| B | 2 | 2 | 100 | 120 | 200 | 240 | 200 | 240 |
| C | 4 | 6 | 60 | 60 | 240 | 240 | 360 | 360 |
| D | 10 | 12 | 50 | 24 | 500 | 240 | 600 | 288 |
| E | 8 | 12 | 40 | 36 | 320 | 288 | 480 | 432 |
| Total | `sum"p"_0"q"_0` = 1560 | `sum"p"_0"q"_1` = 1344 | `sum"p"_1"q"_0` = 2140 | `sum"p"_1"q"_1` = 1880 | ||||
Fisher’s Price Index Number
`"P"_01^"F" = sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100`
= `sqrt(2140/1560 xx 1880/1344) xx 100`
= `sqrt((40,23,200)/(20,96,640)) xx 100`
= `sqrt(1.92) xx 100`
= `1.385 xx 100`
= 138.5
Time Reversal Test: To prove P01 × P10 = 1
P01 × P10 = `sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1)) xx sqrt((sum"p"_0"q"_1 xx sum"p"_0"q"_0)/(sum"p"_1"q"_1 xx sum"p"_1"q"_0))`
= `sqrt(2140/1560 xx 1880/1344 xx 1344/1880 xx 1560/2140)`
P01 × P10 = 1
Time reversal test is satisfied.
Factor Reversal Test: To prove P01 × Q01 = `(sum"p"_1"q"_1)/(sum"p"_0"q"_0)`
= `sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1)) xx sqrt((sum"q"_1"P"_0 xx sum"q"_1"P"_1)/(sum"q"_0"p"_0 xx sum"q"_0"p"_1))`
= `sqrt(2140 /1560 xx 1880/1344 xx 1344/1560 xx 1880/2140)`
= `sqrt((1880 xx 1880)/(1560 xx 1560)`
= `1880/1560`
⇒ `"P"_01 xx "Q"_01 = (sum"p"_1"q"_1)/(sum"p"_0"q"_0)`
Factor reversal test is satisfied.
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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.
______ : Base year prices :: P1 : Current year prices.
Explain the features of index numbers.
Define Laspeyre’s price index number
Explain Paasche’s price index number
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:
Another name of consumer’s price index number is:
Choose the correct alternative:
Which of the following Index number satisfy the time reversal test?
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 |
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.
