Question

Edna is living in a retirement home where most of her needs are taken care of, but she has some discretionary spending. Based on the basket of goods in Table \(22.5,\) by what percentage does Edna's cost of living increase between time 1 and time 2? $$\begin{array}{l|l|l|l} \hline {\text { Items }} & {\text { Quantity }} & {\text { (Time 1) Price }} & {\text { (Time 2) Price }} \\ \hline \text { Gifts for grandchildren } & 12 & \$ 50 & \$ 60 \\ \hline \text { Pizza delivery } & 24 & \$ 15 & \$ 16 \\ \hline \text { Blouses } & 6 & \$ 60 & \$ 50 \\ \hline \text { Vacation trips } & 2 & \$ 400 & \$ 420 \\ \hline \end{array}$$

Short answer

The percentage increase in Edna's cost of living between Time 1 and Time 2 is approximately \(5.85\%\).

Step-by-step solution

Calculate the total cost at Time 1

To find the total cost for Edna at Time 1, we need to multiply the quantity of each item with its corresponding price at Time 1, and then sum up these costs. Total cost at Time 1: - Gifts for grandchildren: \(12 \times \$50 = \$600\) - Pizza delivery: \(24 \times \$15 = \$360\) - Blouses: \(6 \times \$60 = \$360\) - Vacation trips: \(2 \times \$400 = \$800\) Now we can sum up these costs: \(\$600 + \$360 + \$360 + \$800 = \$2120\)

Calculate the total cost at Time 2

To find the total cost for Edna at Time 2, we need to multiply the quantity of each item with its corresponding price at Time 2, and then sum up these costs. Total cost at Time 2: - Gifts for grandchildren: \(12 \times \$60 = \$720\) - Pizza delivery: \(24 \times \$16 = \$384\) - Blouses: \(6 \times \$50 = \$300\) - Vacation trips: \(2 \times \$420 = \$840\) Now we can sum up these costs: \(\$720 + \$384 + \$300 + \$840 = \$2244\)

Calculate the percentage increase

Now that we have the total costs at Time 1 and Time 2, we can find the percentage increase in Edna's cost of living between these times. Percentage Increase = \(\frac{\text{Increase in cost}}{\text{Initial Cost}}\times 100\) Increase in cost = Total cost at Time 2 - Total cost at Time 1 = \(\$2244 - \$2120 = \$124\) Percentage Increase = \(\frac{\$124}{\$2120}\times 100 = 5.85\%\) The percentage increase in Edna's cost of living between Time 1 and Time 2 is approximately \(5.85\%\).

Key concepts

Consumer Price Index

The Consumer Price Index (CPI) is a vital tool that helps us understand the cost of living by measuring the average change over time in the prices paid by consumers for a fixed basket of goods and services. This index is critical because it reflects the spending habits and costs experienced by typical households. To create a CPI, economists select a representative "basket of goods," which includes a variety of items such as food, clothing, transportation, and medical care, similar to the list seen in Edna's case. The prices of these items are then tracked over time. CPI allows us to see how inflation affects purchasing power. If the index rises, it indicates that general prices are increasing, suggesting that with the same amount of money, consumers can buy fewer goods and services than before.

Inflation Rate Calculation

Calculating the inflation rate is key to understanding how the cost of living changes. The inflation rate is the percentage increase in prices over a specific period.In Edna's exercise, we can see this calculation in action. First, calculate the total cost of all items at two different times. Then, determine the increase in costs. This is done by subtracting the initial total cost at Time 1 from the total cost at Time 2. In the case of Edna's goods, the cost increased by \(124 from Time 1 to Time 2.To find the inflation rate or percentage increase:

• Divide the increase in cost by the initial cost (Time 1 total).
• Multiply by 100 to convert it to a percentage: \[\text{Percentage Increase} = \frac{\\)124}{\$2120} \times 100 \approx 5.85\%\]

This result indicates the general increase in costs between the two periods.

Basket of Goods Analysis

The "basket of goods" is a compilation of various items that are usually purchased by consumers. This basket is used as a representative example to measure how prices change over time, which is crucial for calculating both CPI and inflation. In Edna's scenario, her basket includes gifts, pizza, blouses, and vacation trips. Each item's quantity is multiplied by its price at specific times to find the total costs. This basket reflects the spending pattern of a typical consumer, helping economists and analysts gauge the cost of living. Observing how each item's price changes between time periods showcases how inflation impacts different items. For instance, Edna's pizza expenses went up from $15 to $16. Though the change might seem minor, when calculated over many items and users, it collectively raises the cost of living. This analysis helps develop policies to maintain economic stability and manage inflation effectively.