Question

A typical family on Sandy Island consumes only juice and cloth.Last​ year, which was the base​ year, the family spent ​$12 on juice and ​$42 on cloth. In the base​ year, juice was ​$4 a bottle and cloth was ​$6 a length.This​ year, juice is ​$3 a bottle and cloth is ​$7 a length.

What is the CPI​ basket? What is the CPI and the inflation rate in the current​ year?

Answer 1

The CPI basket for the family on Sandy Island consists of juice and cloth purchased in the base year. The CPI for the current year is 107.4, indicating the total cost of the CPI basket increased from the base year, which leads to an inflation rate of 7.4% in the current year.

Step-by-step explanation:

To calculate the Consumer Price Index (CPI) for the current year, we use the information provided about a family on Sandy Island. The CPI basket consists of the goods and services that were consumed by the family in the base year, which in this case includes juice and cloth. In the base year, the family spent $12 on juice and $42 on cloth, with juice costing $4 a bottle and cloth costing $6 a length. Thus, they bought 3 bottles of juice (12/4) and 7 lengths of cloth (42/6). To find the CPI for the current year, we need to calculate the total cost of the CPI basket at the current year's prices. That would be 3 bottles of juice at $3 per bottle plus 7 lengths of cloth at $7 per length, which amounts to ($3*3)+($7*7)=$9+$49=$58.Then, we calculate the cost of the CPI basket in the base year, which was $12+$42=$54. The formula for CPI in the current year is (Current Year Cost / Base Year Cost) * 100, giving us ($58/$54) * 100 = 107.4, suggesting a CPI of 107.4. To find the inflation rate, we compare this year's CPI to the base year's CPI of 100 and find the percentage increase: (107.4 - 100) / 100 = 0.074 or 7.4% inflation rate.