Use the following table to answer question. The table shows the prices and the quanti­ties consumed in Carnivore Country. Suppose the base year is 2017. Also, suppose that 2017 is the year the typical consumption basket was determined, so the quantities consumed in 2017 are the only quantities needed to calculate the CPI in each year.

Question

Year Price of Beef Quantity of Beef Price of Pork Quantity of Pork
2017 $2.00 100 $1.00 100
2018 2.50 90 0.90 120
2019 2.75 105 1.00 130

What is the inflation rate for 2019?
a. 0 percent
b. 10.3 percent
c. 11 percent
d. 13.3 percent
e. none of the above

Answer 1

To calculate the inflation rate for 2019 using the Consumer Price Index (CPI), we first need to determine the CPI for both 2018 and 2019 based on the fixed quantities of the consumption basket from the base year (2017).

Step 1: Calculate the total cost of the basket in the base year (2017)

2017:

• Price of Beef: $2.00, Quantity: 100
• Total cost of Beef = $2.00 × 100 = $200
• Price of Pork: $1.00, Quantity: 100
• Total cost of Pork = $1.00 × 100 = $100
• Total cost of basket in 2017 = $200 + $100 = $300

Step 2: Calculate the total cost of the basket in 2018

2018:

• Price of Beef: $2.50, Quantity: 100
• Total cost of Beef = $2.50 × 100 = $250
• Price of Pork: $0.90, Quantity: 100
• Total cost of Pork = $0.90 × 100 = $90
• Total cost of basket in 2018 = $250 + $90 = $340

Step 3: Calculate the total cost of the basket in 2019

2019:

• Price of Beef: $2.75, Quantity: 100
• Total cost of Beef = $2.75 × 100 = $275
• Price of Pork: $1.00, Quantity: 100
• Total cost of Pork = $1.00 × 100 = $100
• Total cost of basket in 2019 = $275 + $100 = $375

Step 4: Calculate the CPI for each year

• CPI in 2017 = (Total cost in 2017 / Total cost in 2017) × 100 = ($300 / $300) × 100 = 100
• CPI in 2018 = (Total cost in 2018 / Total cost in 2017) × 100 = ($340 / $300) × 100 = 113.33
• CPI in 2019 = (Total cost in 2019 / Total cost in 2017) × 100 = ($375 / $300) × 100 = 125

Step 5: Calculate the inflation rate for 2019

The inflation rate is calculated as follows:

\[ \text{Inflation Rate} = \frac{\text{CPI in Current Year} - \text{CPI in Previous Year}}{\text{CPI in Previous Year}} \times 100 \]

Using 2018 as the previous year:

\[ \text{Inflation Rate in 2019} = \frac{125 - 113.33}{113.33} \times 100 \]

\[ = \frac{11.67}{113.33} \times 100 \approx 10.3% \]

Conclusion

The inflation rate for 2019 is approximately 10.3 percent.

Thus, the answer is b. 10.3 percent.