Question

For an imaginary economy, the consumer price index was 80 in 2014, 100 in 2015, and 140 in 2016. Which of the following statements is correct? a. If the basket of goods that is used to calculate the CPI cost $40 in 2014, then that basket of goods cost $60 in 2015. b. If the basket of goods that is used to calculate the CPI cost $25 in 2015, then that basket of goods cost $35 in 2016. c. The overall level of prices increased by 60 percent between 2014 and 2016. d. All of the above are correct.

Answer 1

b. If the basket of goods that is used to calculate the CPI cost $25 in 2015, then that basket of goods cost $35 in 2016.

Step-by-step explanation:

• According to the changes in the consumer price index given by the stament "the consumer price index was 80 in 2014, 100 in 2015, and 140 in 2016", inflation was of 25% (
  `(100)/(80)-1=25\%`) in the period 2014-2015 and of 40% in the period 2015-2016 (
  `(140)/(100) -1=40\%`). Talking all the period together, inflation in the period 2014-2016 was of 75% (
  `(140)/(80) -1=75\%`).
• This means that on average, prices change in the amount given by inflation each period.
• If the basket of goods that was used to calculate the CPI cost $25 in 2015, in 2016 this basket will cost
  `\$25*(1+inflation2016)=\$25*1.4=\$35`, according to inflation calculated for that period.
• Applying the same reasoning, you can show that the others options are not correct.