Let's solve this step by step using the **CPI (Consumer Price Index) method**: ### Step 1: CPI Formula CPI for a given year is calculated as: \[ \text{CPI}_{\text{year}} = \frac{\text{Cost of basket in current year prices}}{\text{Cost of basket in base year prices}} \] where the "basket" is based on quantities from a base year (here, 2021, since we are measuring inflation/deflation from 2021 to 2022). ### Step 2: Find the cost of the 2021 basket at 2021 and 2022 prices #### Quantities used (from 2021): - Pizza Q = 12 - Shoes Q = 11 #### 2021 Prices: - Pizza P = $11.00 - Shoes P = $150.00 \[ \text{Cost of 2021 basket at 2021 prices} = (12 \times 11) + (11 \times 150) = 132 + 1650 = 1782 \] #### 2022 Prices: - Pizza P = $12.00 - Shoes P = $100.00 \[ \text{Cost of 2021 basket at 2022 prices} = (12 \times 12) + (11 \times 100) = 144 + 1100 = 1244 \] ### Step 3: Calculate CPI for 2021 and 2022 (using 2021 as the base year) \[ \text{CPI}_{2021} = \frac{1782}{1782} = 1 \] \[ \text{CPI}_{2022} = \frac{1244}{1782} = 0.6982 \] ### Step 4: Calculate Inflation/Deflation Rate \[ \text{Inflation/Deflation Rate} = \frac{\text{CPI}_{2022} - \text{CPI}_{2021}}{\text{CPI}_{2021}} = \frac{0.6982 - 1}{1} = -0.3018 \] The closest value in the options is **-0.2931**. --- ## **Final Answer:** \[ \boxed{-0.2931} \] This indicates a **deflation** (decrease in price level) from 2021 to 2022.

Certainly! Let's go through the detailed, step-by-step calculation process for finding the inflation/deflation from 2021 to 2022 using the CPI method. --- ### **Step 1: Understand the Data** | Year | Pizza Quantity (Q) | Pizza Price (P) | Shoes Quantity (Q) | Shoes Price (P) | |--------|----------------------|-----------------|---------------------|----------------| | 2020 | 10 | $10.00 | 7 | $125.00 | | 2021 | 12 | $11.00 | 11 | $150.00 | | 2022 | 13 | $12.00 | 8 | $100.00 | --- ### **Step 2: Determine the basket quantities** Since we are calculating inflation from **2021 to 2022**, and using the **CPI method**, **the basket quantities are based on the base year (2021)**. **Basket quantities (from 2021):** - Pizza Q = 12 - Shoes Q = 11 --- ### **Step 3: Calculate the total cost of the basket in 2021 (base year prices)** Using 2021 prices: \[ \text{Cost of 2021 basket at 2021 prices} = (Q_{Pizza} \times P_{Pizza,2021}) + (Q_{Shoes} \times P_{Shoes,2021}) \] \[ = (12 \times \$11.00) + (11 \times \$150.00) \] \[ = \$132 + \$1650 = \$1782 \] --- ### **Step 4: Calculate the total cost of the same basket at 2022 prices** Using the **2022 prices** (since CPI compares the basket at different year prices): \[ \text{Cost of 2021 basket at 2022 prices} = (12 \times P_{Pizza,2022}) + (11 \times P_{Shoes,2022}) \] \[ = (12 \times \$12.00) + (11 \times \$100.00) \] \[ = \$144 + \$1100 = \$1244 \] --- ### **Step 5: Calculate the CPI for 2021 and 2022** - **CPI for 2021 (base year):** \[ \text{CPI}_{2021} = \frac{\text{Cost of basket at 2021 prices}}{\text{Cost of basket at 2021 prices}} = \frac{\$1782}{\$1782} = 1 \] - **CPI for 2022:** \[ \text{CPI}_{2022} = \frac{\text{Cost of basket at 2022 prices}}{\text{Cost of basket at 2021 prices}} = \frac{\$1244}{\$1782} \approx 0.6982 \] --- ### **Step 6: Calculate the inflation/deflation rate** \[ \text{Inflation/Deflation} = \frac{\text{CPI}_{2022} - \text{CPI}_{2021}}{\text{CPI}_{2021}} = \frac{0.6982 - 1}{1} = -0.3018 \] Expressed as a decimal, this is approximately **-0.3018**, indicating deflation. ### **Step 7: Match with the options** The options provided are: - -0.1590 - 0.1590 - 0.1595 - 0.1595 - 0.2931 - 0.2931 Our calculated value is **-0.3018**, which is closest to **-0.2931** among the options. --- ## **Final Answer:** \[ \boxed{\textbf{-0.2931}} \] This indicates a **deflation of approximately 29.31%** from 2021 to 2022 using the CPI method.