Suppose the residents of Vegopia spend all of their income on cauliflower, broccoli, and carrots. In 2006, they buy 100 heads of cauliflower for $2 each, 50 bunches of broccoli for $1.50 each, and 500 carrots for $0.10 each. In 2007, they buy 100 heads of cauliflower for $3 each, 50 bunches of broccoli for $1.50 each, and 500 carrots for $0.20 each.
a. Calculate the price of the basket for each year.
b. Using 2006 as the base year, calculate the CPI for each year.
c. What is the inflation rate for 2007?
a. To calculate the price of the basket for each year, we need to multiply the quantity of each item by its respective price and then add them together.
In 2006:
Price of 100 heads of cauliflower = 100 x $2 = $200
Price of 50 bunches of broccoli = 50 x $1.50 = $75
Price of 500 carrots = 500 x $0.10 = $50
Total price of the basket in 2006 = $200 + $75 + $50 = $325
In 2007:
Price of 100 heads of cauliflower = 100 x $3 = $300
Price of 50 bunches of broccoli = 50 x $1.50 = $75
Price of 500 carrots = 500 x $0.20 = $100
Total price of the basket in 2007 = $300 + $75 + $100 = $475
b. To calculate the Consumer Price Index (CPI) for each year, we need to compare the total price of the basket for each year to the base year, which is 2006 in this case.
CPI for 2006 = (Total price of the basket in 2006 / Total price of the basket in 2006) x 100 = (325 / 325) x 100 = 100
CPI for 2007 = (Total price of the basket in 2007 / Total price of the basket in 2006) x 100 = (475 / 325) x 100 = 146.15
c. The inflation rate for 2007 can be calculated by subtracting the CPI for 2006 from the CPI for 2007, dividing the result by the CPI for 2006, and then multiplying by 100.
Inflation rate for 2007 = ((CPI for 2007 - CPI for 2006) / CPI for 2006) x 100 = ((146.15 - 100) / 100) x 100 = 46.15%