The following are prices and consumption quantities for three commodities in 2009 and 2019: Commodity 2009 2019 Price Quantity Price Quantity A $2 15 $5 17 B $32 4 $28 3 C $5 20 $7 15 Based on the above information, calculate the Laspeyres aggregate price index for 2019 using 2009 as the base year. Round your final answer to two decimal places.
Question
The following are prices and consumption quantities for three commodities in 2009 and 2019: Commodity 2009 2019 Price Quantity Price Quantity A 5 17 B 28 3 C 7 15 Based on the above information, calculate the Laspeyres aggregate price index for 2019 using 2009 as the base year. Round your final answer to two decimal places.
Solution
The Laspeyres Price Index is a price index that is computed by taking the ratio of the total cost of purchasing a specified group of commodities at the current prices to the cost of purchasing the same group of commodities at base-period prices. The formula for the Laspeyres Price Index is:
Laspeyres Price Index = ∑(P1 * Q0) / ∑(P0 * Q0) * 100
Where: P1 = Price in the current period Q0 = Quantity in the base period P0 = Price in the base period
Let's calculate the Laspeyres Price Index for 2019 using 2009 as the base year for each commodity:
For commodity A: P1 = 2 Laspeyres Price Index for A = (5 * 15) / (2 * 15) * 100 = 250
For commodity B: P1 = 32 Laspeyres Price Index for B = (28 * 4) / (32 * 4) * 100 = 87.5
For commodity C: P1 = 5 Laspeyres Price Index for C = (7 * 20) / (5 * 20) * 100 = 140
The Laspeyres aggregate price index for 2019 using 2009 as the base year is the average of the three indices:
Laspeyres aggregate price index = (250 + 87.5 + 140) / 3 = 159.17
So, the Laspeyres aggregate price index for 2019 using 2009 as the base year is 159.17 (rounded to two decimal places).
Similar Questions
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