Question

If \(P_{01}(L)=90\) and \(P_{01}(P)=40\), then \(P_{01}(D-B)\) is ..............

• A. 65
• B. 50
• C. 25
• D. 130

Hint:

Remember the three main "averaged" index numbers:
{Dorbish-Bowley}: Arithmetic Mean of L & P.
{Fisher}: Geometric Mean of L & P (\(\sqrt{L \times P}\)).
{Marshall-Edgeworth}: Uses the sum of base and current year quantities.

Answer 1

The Correct Option is A

The question asks for the Dorbish-Bowley Price Index, \(P_{01}(D-B)\), given Laspeyres' Price Index, \(P_{01}(L)\), and Paasche's Price Index, \(P_{01}(P)\). The formula for the Dorbish-Bowley index is the arithmetic mean of the Laspeyres and Paasche indices: \[ P_{01}(D-B) = \frac{P_{01}(L) + P_{01}(P)}{2} \] Given:
\(P_{01}(L) = 90\)
\(P_{01}(P) = 40\)
Substitute the values into the formula: \[ P_{01}(D-B) = \frac{90 + 40}{2} = \frac{130}{2} = 65 \] Therefore, the Dorbish-Bowley Price Index is 65.