Suppose that the residents of Veggieland spend all of their income on cauliflower, broccoli, and carrots. In 1998 they buy 100 heads of cauliflower for $200, 50 bunches of broccoli for $75, and 500 carrots for $50. In 1999 they buy 75 heads of cauliflower for $225, 80 bunches of broccoli for $120, and 500 carrots for $100. If the base year is 1998, what is the CPI in both years? What is the inflation rate in 1999
To calculate the CPI in both years, we need to follow these steps:
Step 1: Determine the market basket for the base year (1998) and the prices of each item in the market basket.
Market basket in 1998:
- 100 heads of cauliflower for $200
- 50 bunches of broccoli for $75
- 500 carrots for $50
Step 2: Calculate the cost of the market basket in the base year (1998):
Cost of the market basket in 1998:
(100 * $200) + (50 * $75) + (500 * $50) = $20,000 + $3,750 + $25,000 = $49,750
Step 3: Determine the market basket for the current year (1999) and the prices of each item in the market basket.
Market basket in 1999:
- 75 heads of cauliflower for $225
- 80 bunches of broccoli for $120
- 500 carrots for $100
Step 4: Calculate the cost of the market basket in the current year (1999):
Cost of the market basket in 1999:
(75 * $225) + (80 * $120) + (500 * $100) = $16,875 + $9,600 + $50,000 = $76,475
Step 5: Calculate the CPI in both years:
CPI in 1998 = (Cost of the market basket in 1998 / Cost of the market basket in 1998) x 100
CPI in 1998 = ($49,750 / $49,750) x 100 = 100
CPI in 1999 = (Cost of the market basket in 1999 / Cost of the market basket in 1998) x 100
CPI in 1999 = ($76,475 / $49,750) x 100 = 153.63 (approx)
Step 6: Calculate the inflation rate in 1999:
Inflation rate in 1999 = ((CPI in 1999 - CPI in 1998) / CPI in 1998) x 100
Inflation rate in 1999 = ((153.63 - 100) / 100) x 100 = 53.63% (approx)
Therefore, the CPI in 1998 is 100, the CPI in 1999 is 153.63, and the inflation rate in 1999 is approximately 53.63%.
To calculate the Consumer Price Index (CPI), we need to compare the prices of the same basket of goods between two different periods. In this case, we will compare the prices of cauliflower, broccoli, and carrots between 1998 and 1999.
Step 1: Calculate the cost of the basket of goods in each year.
- In 1998, the cost of the basket is $200 for cauliflower, $75 for broccoli, and $50 for carrots. Adding these up, we get $200 + $75 + $50 = $325.
- In 1999, the cost of the basket is $225 for cauliflower, $120 for broccoli, and $100 for carrots. Adding these up, we get $225 + $120 + $100 = $445.
Step 2: Calculate the CPI for each year.
- The CPI is calculated by dividing the cost of the basket in a given year by the cost of the same basket in the base year (1998 in this case) and multiplying by 100.
- The CPI in 1998 is (325/325) x 100 = 100 (since it is the base year).
- The CPI in 1999 is (445/325) x 100 = 136.92 (rounded to two decimal places).
So, the CPI in 1998 is 100, and the CPI in 1999 is 136.92.
To calculate the inflation rate in 1999, we need to compare the CPI in 1999 with the CPI in the previous year.
Step 3: Calculate the inflation rate.
- The inflation rate is calculated by subtracting the CPI of the previous year from the CPI of the current year, dividing by the CPI of the previous year, and multiplying by 100.
- The inflation rate in 1999 is ((136.92 - 100) / 100) x 100 = 36.92%.
Therefore, the inflation rate in 1999 is 36.92%.