consider the simple economy that produces only three products. use the information in the following table to…

consider the simple economy that produces only three products. use the information in the following table to calculate the (annual rate of) inflation for 2025 as measured by the consumer price index (cpi).\n\n| product | base year (2015) quantity | base year (2015) price | 2024 price | 2025 price |\n| :--- | :--- | :--- | :--- | :--- |\n| haircuts | 1 | $10.00 | $11.00 | $16.20 |\n| hamburgers | 10 | 2.00 | 2.45 | 2.40 |\n| movies | 2 | 15.00 | 15.00 | 14.00 |\n\nusing the information in the table, the cpi for 2024, with 2015 as the base year, is ____. (enter your response rounded to one decimal place.)

consider the simple economy that produces only three products. use the information in the following table to calculate the (annual rate of) inflation for 2025 as measured by the consumer price index (cpi).\n\n| product | base year (2015) quantity | base year (2015) price | 2024 price | 2025 price |\n| :--- | :--- | :--- | :--- | :--- |\n| haircuts | 1 | $10.00 | $11.00 | $16.20 |\n| hamburgers | 10 | 2.00 | 2.45 | 2.40 |\n| movies | 2 | 15.00 | 15.00 | 14.00 |\n\nusing the information in the table, the cpi for 2024, with 2015 as the base year, is ____. (enter your response rounded to one decimal place.)

Answer

Explanation:

Step1: Calculate the cost of the basket in the base year (2015)

$$Cost_{2015} = (1 \times $10.00) + (10 \times $2.00) + (2 \times $15.00) = $10.00 + $20.00 + $30.00 = $60.00$$

Step2: Calculate the cost of the basket in 2024

$$Cost_{2024} = (1 \times $11.00) + (10 \times $2.45) + (2 \times $15.00) = $11.00 + $24.50 + $30.00 = $65.50$$

Step3: Calculate the CPI for 2024

$$CPI_{2024} = \left( \frac{Cost_{2024}}{Cost_{2015}} \right) \times 100 = \left( \frac{$65.50}{$60.00} \right) \times 100 \approx 109.1667$$

Step4: Calculate the cost of the basket in 2025

$$Cost_{2025} = (1 \times $16.20) + (10 \times $2.40) + (2 \times $14.00) = $16.20 + $24.00 + $28.00 = $68.20$$

Step5: Calculate the CPI for 2025

$$CPI_{2025} = \left( \frac{Cost_{2025}}{Cost_{2015}} \right) \times 100 = \left( \frac{$68.20}{$60.00} \right) \times 100 \approx 113.6667$$

Step6: Calculate the inflation rate for 2025

$$Inflation\ Rate = \left( \frac{CPI_{2025} - CPI_{2024}}{CPI_{2024}} \right) \times 100 = \left( \frac{113.6667 - 109.1667}{109.1667} \right) \times 100 \approx 4.122%$$

Answer:

The CPI for 2024 is 109.2. The annual rate of inflation for 2025 is 4.1%.