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Question
Explain factor reversal test
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Solution
This is another test for testing the consistency of a good index number.
The product of price index number and quantity index number from the base year to the current year should be equal to the true value ratio.
That is, the ratio between the total value of current period and total value of the base period is known as true value ratio.
Factor Reversal Test is given by
`"P"_01 xx "Q"_01 = (sum"p"_1"q"_1)/(sum"p"_0"q"_0)`
Where, `"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))`
Now interchanging P by Q, we get
`"Q"_01 = sqrt((sum"p"_1"p"_0 xx sum"q"_1"p"_1)/(sum"q"_0"p"_0 xx sum"p"_0"p"_1))`
Where P01 is the relative change in price
Q01 is the relative change in quantity.
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| Commodity | 2002 | 2012 | ||
| Price | Quantity | Price | Quantity | |
| A | 10 | 20 | 16 | 10 |
| B | 12 | 34 | 18 | 42 |
| C | 15 | 30 | 20 | 26 |
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| 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 |
Using Fisher’s Ideal Formula, compute price index number for 1999 with 1996 as base year, given the following:
| Year | Commodity: A | Commodity: B | Commodity: C | |||
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| 1996 | 5 | 10 | 8 | 6 | 6 | 3 |
| 1999 | 4 | 12 | 7 | 7 | 5 | 4 |
Construct the cost of living Index number for 2015 on the basis of 2012 from the following data using family budget method.
| Commodity | Price | Weights | |
| 2012 | 2015 | ||
| Rice | 250 | 280 | 10 |
| Wheat | 70 | 85 | 5 |
| Corn | 150 | 170 | 6 |
| Oil | 25 | 35 | 4 |
| Dhal | 85 | 90 | 3 |
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:
Which of the following Index number satisfy the time reversal test?
State with reasons whether you agree or disagree with the following statement:
Index number measures changes in the price level only.
The base year's index of a selected variable is assumed as ______.
