Correct Answer - Option 2 : does not satisfy both factor reversal test and circular test of consistency
Explanation:
The Marshall Edgeworth Method for the index number, credited to Marshall (1887) and Edgeworth (1925), is a weighted relative of the current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting.
Factor Reversal Test:
Fisher has described this test in the following words: Just as each formula should permit the interchange of the two items without giving inconsistent results, so it ought to permit interchanging the prices and quantities without giving inconsistent result, i.e., the two results multiplied together should give the true value ratio.”In simple words, the test means that the change in the price multiplied by the change in the quantity should be equal to the total change in the value. The total value of a given commodity in a given year is the product of the quantity and the price per unit (total value = p x q) . The ratio of the total value in one year to the total value in the preceding year is p1q1 / p0q0. Symbolically the test is represented as
P01 x Q01 = Σp1q1 / Σp0q0 V01
Where P01 denotes price index and Q01 , quantity index number.
This test is satisfied by Fisher’s method only.
Circular test
According to this, if indices are constructed for year one based on year zero, for year two based on year one and for year zero based on year two, the product of all the indices should be equal to 1.
Symbolically
P01 × P12 × P20 = 1
This test is satisfied by
2-Simple aggregative method and
1-Kelly’s method.
