CPI (12 points)

In the base month of November 2020, the price of a pound of tomatoes was $1.65, and the quantity purchased was 7 pounds. In November 2022, the price of the tomatoes increased to $2.25 per pound.

In the base month of November 2020, the price of a gallon of gas was $2.45, and the quantity purchased was 40 gallons. In November 2022, the price of a gallon of gas increased to $3.70 per gallon.

Complete parts a and b.

a. Using these values, solve for the CPI, assuming that November 2020 is the base month.

b. Solve for the CPI growth rate between November 2020 and November 2022.

To calculate the CPI, we need to compare the prices of tomatoes and gasoline in November 2020 and November 2022. The formula for calculating the CPI is as follows:

CPI = (Price of Basket in Current Year / Price of Basket in Base Year) * 100

where the "Price of Basket" represents the total cost of the goods in the basket (in this case, tomatoes and gasoline) and the base year is November 2020.

a) Calculating the CPI:

Price of the tomato basket in November 2020:

Price per pound of tomatoes: $1.65

Quantity purchased: 7 pounds

Total cost = Price per pound * Quantity = $1.65 * 7 = $11.55

Price of the tomato basket in November 2022:

Price per pound of tomatoes: $2.25

Quantity purchased: 7 pounds

Total cost = Price per pound * Quantity = $2.25 * 7 = $15.75

Price of the gasoline basket in November 2020:

Price per gallon of gas: $2.45

Quantity purchased: 40 gallons

Total cost = Price per gallon * Quantity = $2.45 * 40 = $98.00

Price of the gasoline basket in November 2022:

Price per gallon of gas: $3.70

Quantity purchased: 40 gallons

Total cost = Price per gallon * Quantity = $3.70 * 40 = $148.00

Now we can calculate the CPI using the formula mentioned earlier:

CPI in November 2020 = (Total cost of tomato basket in November 2020 + Total cost of gasoline basket in November 2020) = ($11.55 + $98.00) = $109.55

CPI in November 2022 = (Total cost of tomato basket in November 2022 + Total cost of gasoline basket in November 2022) = ($15.75 + $148.00) = $163.75

b) Calculating the CPI growth rate:

The CPI growth rate indicates the percentage change in the CPI over the given period. It is calculated using the following formula:

CPI growth rate = ((CPI in November 2022 - CPI in November 2020) / CPI in November 2020) * 100

Substituting the values into the formula:

CPI growth rate = (($163.75 - $109.55) / $109.55) * 100 = 49.44%

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