Suppose that the resident of vegopia spend all of their income on cauliflower,broccoli and carrots.in 2006 they buy 100 heads of cauliflower for $200,50 bunches of broccoli for $75 and 500 carrots for $50.in 2007 they buy 75 heads of cauliflower for $225,80 bunches of broccoli for $120 and 500 carrots for $100. a.Calculate the price of each vegetable in each year. b.Using 2006 as the base year,calculate the cpi for each year. c.What is the inflation rate in 2007
To calculate the price of each vegetable in each year, we need to divide the total expenditure for each vegetable by the quantity bought.
In 2006:
- Price of cauliflower = $200 / 100 heads = $2 per head
- Price of broccoli = $75 / 50 bunches = $1.50 per bunch
- Price of carrots = $50 / 500 carrots = $0.10 per carrot
In 2007:
- Price of cauliflower = $225 / 75 heads = $3 per head
- Price of broccoli = $120 / 80 bunches = $1.50 per bunch
- Price of carrots = $100 / 500 carrots = $0.20 per carrot
Now, let's calculate the CPI (Consumer Price Index) for each year using 2006 as the base year. The formula for CPI is (Expenditure in current year / Expenditure in base year) * 100.
In 2006:
- CPI = (($200 + $75 + $50) / ($200 + $75 + $50)) * 100 = 100
In 2007:
- CPI = (($225 + $120 + $100) / ($200 + $75 + $50)) * 100 = 157.14
To calculate the inflation rate in 2007, we use the formula:
- Inflation rate = ((CPI in current year - CPI in previous year) / CPI in previous year) * 100
Inflation rate in 2007 = ((157.14 - 100) / 100) * 100 = 57.14%
Therefore, the inflation rate in 2007 is 57.14%.
a. To calculate the price of each vegetable in each year, we need to divide the total cost by the quantity for each vegetable.
In 2006:
Price of cauliflower = $200 / 100 = $2 per head
Price of broccoli = $75 / 50 = $1.50 per bunch
Price of carrots = $50 / 500 = $0.10 per carrot
In 2007:
Price of cauliflower = $225 / 75 = $3 per head
Price of broccoli = $120 / 80 = $1.50 per bunch
Price of carrots = $100 / 500 = $0.20 per carrot
b. To calculate the CPI (Consumer Price Index) for each year, we need to use the formula:
CPI = (Total cost of the basket in the current year / Total cost of the basket in the base year) x 100
In 2006:
Total cost of the basket = $200 + $75 + $50 = $325
CPI(2006) = ($325 / $325) x 100 = 100
In 2007:
Total cost of the basket = $225 + $120 + $100 = $445
CPI(2007) = ($445 / $325) x 100 ≈ 136.92
c. To calculate the inflation rate in 2007, we can use the formula:
Inflation rate = (CPI(2007) - CPI(2006)) / CPI(2006) x 100
Inflation rate(2007) = (136.92 - 100) / 100 x 100 ≈ 36.92%
Therefore, the inflation rate in 2007 is approximately 36.92%.