Question

The weighted aggregative index number for the following table is given as 166.31 considering Paasche’s method. Find the approx.value of m.

$\begin{array}{ccccc}\text{Commodity}& & \text{Base Period}& & \text{Current Period}\\ & \text{Price (P0) (In dollars)}& \text{Quantity (Q0)}& \text{Price (P1) (In dollars)}& \text{Quantity (Q1)}\\ H& 1& 7& 3& 25\\ I& 10.5& 10& 7& 11\\ J& m& 8& 4& 12\\ K& 7& 25& 14& 30\\ L& 15& 13& 22& 18\end{array}$

• A. 2.5
• B. 1.5
• C. 1
• D. 0.5

Answer 1

The correct option is C

1

Look at the table below:

$\begin{array}{ccccccc}\text{Commodity}& & \text{Base Period}& & \text{Current Period}& P1Q1& P0Q1\\ & \text{Price (P0) (In dollars)}& \text{Quantity (Q0)}& \text{Price (P1) (In dollars)}& \text{Quantity (Q1)}& & \\ H& 1& 7& 3& 25& 75& 25\\ I& 10.5& 10& 7& 11& 77& 115.5\\ J& m& 8& 4& 12& 48& 12m\\ K& 7& 25& 14& 30& 420& 210\\ L& 15& 13& 22& 20& 440& 300\\ & & \text{Total}& & & 1060& 625.5+12m\end{array}$

$P01=\frac{\sum P1Q1}{P0Q1}\ast 100=\frac{1060}{625.5+12m}\ast 100=166.31$
1.6631(625.5 + 12m) = 1060

1040.27 + 19.96m = 1060

19.96m = 19.73

$m=0.988\cong 1.$