The people on Coral Island buy only juice and cloth. The CPI basket contains the quantities bought in 2013 (the reference base year).
The average household spent $60 on juice and $30 on cloth in 2013 when the price of juice was $2 a bottle and the price of cloth was $5 a yard.
In 2014, juice is $4 a bottle and cloth is $6 a yard.
Calculate the CPI and the inflation rate in 2014.
Thanks!!
To calculate the CPI (Consumer Price Index) and the inflation rate in 2014, we will follow these steps:
1. Calculate the expenditure in 2013:
- The average household spent $60 on juice, so the quantity of juice bought can be found by dividing the expenditure by the price: $60 / $2 = 30 bottles.
- Similarly, the quantity of cloth bought can be found by dividing the expenditure by the price: $30 / $5 = 6 yards.
2. Calculate the expenditure in 2014:
- The price of juice in 2014 is $4 a bottle, so the expenditure on juice can be found by multiplying the price by the quantity: $4 * 30 = $120.
- Likewise, the expenditure on cloth can be found by multiplying the price by the quantity: $6 * 6 = $36.
3. Calculate the CPI in 2014:
- The CPI compares the cost of the basket of goods in different years, with the reference base year (in this case, 2013) set to 100.
- The formula for calculating the CPI is (Expenditure in the current year / Expenditure in the base year) * 100.
- In 2014, the expenditure is $120 on juice and $36 on cloth, and in 2013, the expenditure was $90 ($60 on juice + $30 on cloth).
- Thus, the CPI for 2014 is ($120 + $36) / $90 * 100 = 160.
4. Calculate the inflation rate:
- The inflation rate measures the percentage change in the CPI from the base year to the current year.
- The formula for calculating the inflation rate is (CPI in the current year - CPI in the base year) / CPI in the base year * 100.
- In our case, the CPI in 2014 is 160, and in 2013 (base year) it was 100.
- Therefore, the inflation rate is (160 - 100) / 100 * 100 = 60%.
So, in 2014, the CPI is 160, and the inflation rate is 60%.