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Question
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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Solution
| 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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Define Time Reversal Test
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 |
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 |
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 |
State with reasons whether you agree or disagree with the following statement:
Index number measures changes in the price level only.
