Construct Laspeyre's price index number for the year 2005 from the following table. Commodity 2004 2005 : : : : : Price Quantity Price Quantity A 5 60 12 50 B 4 40 10 45 C 3 20 8 30 D 2 50 7 40

Price Index Number Using Laspeyre’s Method

Laspeyre’s price index is calculated using the base year quantities and current year prices. The formula is:

$$\text{Laspeyre’s Index}=\left(\frac{\sum (P_1\times Q_0)}{\sum (P_0\times Q_0)}\right)\times 100$$

Where:

• $P_0$ = Base year (2012) price
• $P_1$ = Current year (2015) price
• $Q_0$ = Base year (2012) quantity

Step 1: Calculate the total expenditure in the base year (2012)

$$\sum (P_0\times Q_0)=(10\times 80)+(4\times 150)+(6\times 120)+(20\times 70)$$ $$=800+600+720+1400=3520$$

Step 2: Calculate the total expenditure in the current year (2015) using base year quantities

$$\sum (P_1\times Q_0)=(15\times 80)+(4\times 150)+(10\times 120)+(25\times 70)$$ $$=1200+600+1200+1750=4750$$

Step 3: Compute the Laspeyre’s Price Index

$$\text{Laspeyre’s Index}=\left(\frac{4750}{3520}\right)\times 100=134.94$$

Step 4: Interpretation

The price index of 134.94 indicates that the price level in 2015 has increased by 34.94% compared to 2012.

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Explanation of the figure:

• The bar chart shows the price index for each commodity using Laspeyre’s method.
• Commodity A has a price index of 134.94 (indicating a price increase).
• Commodity B remains unchanged (index = 100).
• Commodity C shows the highest increase (166.67%).
• Commodity D has a moderate increase (125%).

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Calculation of Individual Price Indices (Optional but useful for understanding)