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The problem asks you to compute the Consumer Price Index (CPI) for two periods using the given data. The CPI measures changes in the price level of a market basket of consumer goods and services over time.

Here's how to approach the solution:

### 1. **Market Basket in Base Year (2010):**
   - **Price of chocolate (2010):** $2
   - **Quantity of chocolate (2010):** 80
   - **Price of cookies (2010):** $4
   - **Quantity of cookies (2010):** 4

### 2. **Market Basket in Comparison Year (2012):**
   - **Price of chocolate (2012):** $4
   - **Quantity of chocolate (2012):** 7
   - **Price of cookies (2012):** $4
   - **Quantity of cookies (2012):** 4

The formula to compute the CPI is:

\[
\text{CPI} = \frac{\text{Cost of Basket in Current Year}}{\text{Cost of Basket in Base Year}} \times 100
\]

### Step-by-Step Calculation:

1. **Cost of the basket in the base year (2010):**
   \[
   \text{Cost}_{2010} = (\text{Price of chocolate in 2010} \times \text{Quantity of chocolate in 2010}) + (\text{Price of cookies in 2010} \times \text{Quantity of cookies in 2010})
   \]
   \[
   = (2 \times 80) + (4 \times 4) = 160 + 16 = 176
   \]

2. **Cost of the basket in the current year (2012):**
   \[
   \text{Cost}_{2012} = (\text{Price of chocolate in 2012} \times \text{Quantity of chocolate in 2010}) + (\text{Price of cookies in 2012} \times \text{Quantity of cookies in 2010})
   \]
   **Note**: We use the base year quantities (80 chocolates and 4 cookies) when computing the cost in the comparison year.
   \[
   = (4 \times 80) + (4 \times 4) = 320 + 16 = 336
   \]

3. **Calculate CPI for 2012:**
   \[
   \text{CPI}_{2012} = \frac{\text{Cost}_{2012}}{\text{Cost}_{2010}} \times 100 = \frac{336}{176} \times 100 = 190.91
   \]

Thus, the CPI for 2012 is **190.91**, which shows that the price level has increased by 90.91% compared to the base year 2010.

Would you like to go through additional details or have any specific questions on the steps?

Here are five follow-up questions that expand on this topic:

1. How would the CPI change if the price of chocolate in 2012 was $3 instead of $4?
2. Can CPI ever be less than 100, and if so, under what conditions?
3. How does inflation relate to changes in CPI?
4. What are the limitations of using CPI as a measure of cost of living?
5. How can changes in the quantity of goods consumed affect the calculation of CPI?

**Tip:** When computing CPI, remember that you always use the quantities from the base year, not the current year, for consistency across time periods.

Suppose that people consume only two goods as shown in the table: Year 2010, Price of Chocolate: $2, Quantity of Chocolate: 80; Price of Cookies: $4, Quantity of Cookies: 4. Year 2012, Price of Chocolate: $4, Quantity of Chocolate: 7; Price of Cookies: $4, Quantity of Cookies: 4. Compute the Consumer Price Index (CPI) for the two years.

Learn how to calculate the Consumer Price Index (CPI) for two periods using price and quantity data. This example compares the cost of a market basket in 2010 and 2012 to compute the CPI and understand inflation.

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