Question

For the data

Variable	Price		Weights
	Base Year	Current Year
X	30	50	8
Y	10	15	7
Z	25	30	4

The weighted price index number is:

• A. 152.44
• B. 150.44
• C. 154.44
• D. 156.44

Answer 1

The Correct Option is A

To calculate the weighted price index, we will use the formula for the Laspeyres Price Index:

\( PI_L = \frac{\sum (P_1 \times Q_0)}{\sum (P_0 \times Q_0)} \times 100 \)

Where:

• \( P_0 \) is the price in the base year.
• \( P_1 \) is the price in the current year.
• \( Q_0 \) is the weight, acting as the quantity in the base year.

Using the provided data:

Variable	\( P_0 \)	\( P_1 \)	\( Q_0 \)
X	30	50	8
Y	10	15	7
Z	25	30	4

Calculate the numerator \(\sum (P_1 \times Q_0)\):

\( (50 \times 8) + (15 \times 7) + (30 \times 4) = 400 + 105 + 120 = 625 \)

Calculate the denominator \(\sum (P_0 \times Q_0)\):

\( (30 \times 8) + (10 \times 7) + (25 \times 4) = 240 + 70 + 100 = 410 \)

Compute the Laspeyres Price Index:

\( PI_L = \frac{625}{410} \times 100 \approx 152.44 \)

Thus, the weighted price index number is:

152.44