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 by Laspeyre’s Method

Laspeyre’s price index is calculated using the formula:

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

where:

• $P_0$ = Price in the base year (2012)
• $P_1$ = Price in the current year (2015)
• $Q_0$ = Quantity in the base year (2012)

Step 1: Calculate $P_0\times Q_0$ (Base Year Value)

We use the base year (2012) quantities and prices to compute the total expenditure in the base year.

$$\sum (P_0\times Q_0)=800+600+720+1400=3520$$

Step 2: Calculate $P_1\times Q_0$ (Current Year Price × Base Year Quantity)

We use the current year (2015) prices but keep the base year quantities.

$$\sum (P_1\times Q_0)=1200+600+1200+1750=4750$$

Step 3: Compute Laspeyre’s Price Index

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

Interpretation

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