- Calculate the total cost of the items in 1983: \(8.85 + 71.25 + 13.95 + 22.75 = 116.80\).
- Calculate the total cost of the items today: \(15.66 + 119.75 + 23.99 + 37.50 = 196.90\).
- Determine the ratio and the CPI: \(\frac{196.90}{116.80} \times 100 \approx 168.58\).
- The closest given estimate is \(\boxed{170}\) (Option b).
Explanation
- Calculating Total Base Price
To estimate the current Consumer Price Index (CPI), we use the provided data for a specific "market basket" of goods. The formula for the index is \(\text{CPI} = \left( \frac{\text{Total Current Price}}{\text{Total Base Price}} \right) \times 100\). First, we need to calculate the total price of the items in 1983 (the base year) and the total price of those same items today.
The base prices in 1983 are:
- Shower curtain: \(\$8.85\)
- Floor rug: \(\$71.25\)
- T-shirt: \(\$13.95\)
- Oscillating fan: \(\$22.75\)
Total Base Price (\(P_{1983}\)) = \(8.85 + 71.25 + 13.95 + 22.75 = \boxed{\$116.80}\).
- Calculating Total Current Price
Next, we calculate the total current price of the same items today:
- Shower curtain: \(\$15.66\)
- Floor rug: \(\$119.75\)
- T-shirt: \(\$23.99\)
- Oscillating fan: \(\$37.50\)
Total Current Price (\(P_{curr}\)) = \(15.66 + 119.75 + 23.99 + 37.50 = \boxed{\$196.90}\).
- Determining the Estimated CPI
Now, we compute the ratio of the total current price to the total 1983 base price:
\[\text{Ratio} = \frac{P_{curr}}{P_{1983}} = \frac{196.90}{116.80} \approx 1.6858\]
Finally, we estimate the CPI by multiplying this ratio by 100:
\[\text{CPI} \approx 1.6858 \times 100 = 168.58\]
Comparing this result to the given options (a: 164, b: 170, c: 185, d: 199), the value \(168.58\) is closest to 170. Therefore, 170 is the most reasonable estimate of the current CPI.
Examples
Understanding the Consumer Price Index (CPI) is essential for grasping how inflation impacts everyday life. By comparing the cost of a fixed "basket" of goods over time, economists can measure changes in the purchasing power of money. For instance, if you track the prices of your weekly grocery list over several years, you are essentially calculating your own personal CPI. This helps in budgeting, negotiating salaries, and making informed financial decisions in an economy where prices fluctuate.