Question

Suppose a basket of goods and services has been selected to calculate the consumer price index. In 2005, the basket of goods cost $108.00; in 2006, it cost $135.00; and in 2007, it cost $168.75. Which of the following statements is correct

Answer 1

If the CPI is 156.25 in 2007, then 2005 is the base year.

Step-by-step explanation:

There are 4 statements:

1. Using 2005 as the base year, the economy's inflation rate was higher in 2007 than it was in 2006.

2. Using 2005 as the base year, the economy's inflation rate for 2006 was 27 percent.

3. If the CPI is 156.25 in 2007, then 2005 is the base year.

4. If 2007 is the base year, then the CPI is 33.75 in 2006.

If 2005 is the base year, the consumer price index (CPI) of 2005 is calculated:

+)
`CPI_(2015) = (Basket_Cost_(2015) )/(Basket_Cost_(base year) ) * 100 = (108)/(108) * 100 = 100`%

Consumer price index of 2006 and 2007 are calculated:

+)
`CPI_(2006) =(Basket_Cost_(2006) )/(Basket_Cost_(2005) ) * 100 = (135)/(108) * 100 = 125`%

+)
`CPI_(2007) =(Basket_Cost_(2007) )/(Basket_Cost_(2005) ) * 100 = (168.75)/(108) * 100 = 156.25\\`%

=> Answer 3 - correct

The inflation rate of year X can be calculated by the formula:
`I_(Year X) = (CPI_(X) - CPI_(X-1))/CPI_(X-1)`

+) The inflation rate of 2006:
`I_(2006) = (CPI_(2006) - CPI_(2005) )/CPI_(2005) = (125 - 100)/100 = 0.25 = 25%`%

=> Answer 2 - wrong

+) The inflation rate of 2007:

`I_(2007) = (CPI_(2007) - CPI_(2006) )/CPI_(2006) = (156.25 - 125)/125 = 0.25 = 25%`%

=> Answer 1 - wrong

If 2007 is the base year, the consumer price index (CPI) of year X is calculated:

`CPI_(X) = (Basket_Cost_(X) )/(Basket_Cost_(base year)) * 100\\= (Basket_Cost_(X) )/(Basket_Cost_(2007)) * 100`

=>
`CPI_(2006) = (135)/(168.75) * 100 = 80%`%

=> Answer 4 - wrong

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