Question

Use the price of apples and oranges to calculate a price index called the Apple and Oranges Price Index (AOPI). Apples cost $0.50 in 2002 and $1 in 2009, whereas oranges cost $1 in 2002 and $0.50 in 2009. If 10 apples and 5 oranges were purchased in 2002, and 5 apples and 10 oranges were purchased in 2009, the AOPI for 2009, using 2002 as the base year, is:

Answer 1

2009 AOPI is 125

Step-by-step explanation:

The question is to determine the Apples and Oranges Price Index (AOPI) for 2009 with 2002 as the base year

First step: For the base year 2002, the goods were bundled as 10 apples and 5 oranges

Therefore, we calculate the cost of these two in 2002 as follows

= 10 apples x $0.5 + 5 oranges x $1 = $10

Second step: For the 2009, the goods were 5 apples and 10 oranges however, since we are using 2002 as the base year, we will calculate the cost of this same 10 aples and 5 oranges using the 2009 value.

= 10 apples x $1 + 5 oranges x $0.25

= $12.5

Step 3: Based on these calculations with 2002 as the base year

The consumer price index = (12.5/10) x 100

The AOPI (Apple and Oranges Price Index) for 2009 assuming that of 2002 is 100 will be 125