Question

The price index as arithmetic mean of Laspeyre's and Paasche's indices was expounded by:

• A. Irving Fisher
• B. Karl Pearson
• C. Kelly
• D. Drobish and Bowley

Hint:

Think of the formula \( \frac{L+P}{2} \); Fisher's index instead takes a geometric mean of L and P.

Answer 1

The Correct Option is D

Step 1: Recall the standard price index formulas. Laspeyre's index uses base year quantities as weights, and Paasche's index uses current year quantities as weights.

Step 2: A simple average of these two indices, \[ P_{01} = \frac{P_{0}^{L} + P_{0}^{P}}{2} \] is called the Drobish-Bowley index number. It was suggested independently by Drobish and Bowley as an easy way to combine the upward bias of Laspeyre's index and the downward bias of Paasche's index.

Step 3: Irving Fisher's index is the geometric mean of the two (called the ideal index), not the arithmetic mean, so it is a different formula. Karl Pearson is associated with correlation and skewness measures, not this index. Kelly's index uses a fixed weight aggregate method, again different from a simple average of Laspeyre's and Paasche's indices.

Step 4: Hence the arithmetic mean of Laspeyre's and Paasche's indices is the Drobish and Bowley index. The answer is Drobish and Bowley.