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?
So, take a shot. Remember, the CPI is a weighted average of the percentage change in prices. Hint: I get CPI in 1999 as 146.2
To calculate the Consumer Price Index (CPI), we need to follow a few steps:
1. Determine the quantities and prices of the goods in the base year (1998 in this case).
In 1998:
- Heads of cauliflower purchased: 100
- Price per head of cauliflower: $200
- Total expenditure on cauliflower in 1998: 100 * $200 = $20,000
- Bunches of broccoli purchased: 50
- Price per bunch of broccoli: $75
- Total expenditure on broccoli in 1998: 50 * $75 = $3,750
- Carrots purchased: 500
- Price per carrot: $0.10 (since $50/500 = $0.10)
- Total expenditure on carrots in 1998: 500 * $0.10 = $50
2. Calculate the total expenditure on all goods in the base year:
Total expenditure in the base year (1998) = $20,000 + $3,750 + $50 = $23,800
3. Determine the quantities and prices of the goods in the given year (1999 in this case).
In 1999:
- Heads of cauliflower purchased: 75
- Price per head of cauliflower: $225
- Total expenditure on cauliflower in 1999: 75 * $225 = $16,875
- Bunches of broccoli purchased: 80
- Price per bunch of broccoli: $120
- Total expenditure on broccoli in 1999: 80 * $120 = $9,600
- Carrots purchased: 500 (same as in 1998)
- Price per carrot: $0.20 (since $100/500 = $0.20)
- Total expenditure on carrots in 1999: 500 * $0.20 = $100
4. Calculate the total expenditure on all goods in the given year (1999):
Total expenditure in the given year (1999) = $16,875 + $9,600 + $100 = $26,575
5. Calculate the CPI in both years:
CPI in 1998 = (Total expenditure in 1998 / Total expenditure in base year) * 100
CPI in 1998 = ($23,800 / $23,800) * 100 = 100
CPI in 1999 = (Total expenditure in 1999 / Total expenditure in base year) * 100
CPI in 1999 = ($26,575 / $23,800) * 100 ≈ 111.46
6. Calculate the inflation rate in 1999:
Inflation rate = (CPI in 1999 - CPI in 1998) / CPI in 1998 * 100
Inflation rate = (111.46 - 100) / 100 * 100 ≈ 11.46%
Therefore, the CPI in 1998 is 100, the CPI in 1999 is approximately 111.46, and the inflation rate in 1999 is approximately 11.46%.