Answered

The prices of consumer goods do not always exactly follow the CPI. The following chart shows several consumer items, along with their respective prices in 1983 and today.




Item		Price in 1983 (\$)Current Price (\$)

Pair of boots		67.45126.85

Hair dryer		15.2529.95

Box of tissues		1.152.25

Toaster		22.8544.25






Using the prices shown on this chart, which of the following is a reasonable estimate of the current CPI?


A208
B195
C180
D173

Verified Answer :

  • Calculate the total cost of the basket in 1983: \(\$106.70\).
  • Calculate the total cost of the basket currently: \(\$203.30\).
  • Determine the CPI ratio: \(\frac{203.30}{106.70} \times 100 \approx 190.53\).
  • Select the closest estimate: \(\boxed{b}\).

Explanation

  1. Calculate the total cost of the basket in 1983 and currently

To estimate the current Consumer Price Index (CPI), we first determine the total cost of the "basket" of goods in both 1983 and at the current time. The basket consists of four items: a pair of boots, a hair dryer, a box of tissues, and a toaster.

The total cost in 1983 is:
\[67.45 + 15.25 + 1.15 + 22.85 = 106.70\]

The total cost at the current time is:
\[126.85 + 29.95 + 2.25 + 44.25 = 203.30\]

  1. Calculate the estimated current CPI

The CPI is defined as the ratio of the current cost of the basket to the cost in the base year, multiplied by 100.
\[\text{CPI} = \left(\frac{\text{Current Cost}}{\text{1983 Cost}}\right) \times 100\]
Substituting the values we calculated:
\[\text{CPI} = \left(\frac{203.30}{106.70}\right) \times 100\]
\[\text{CPI} \approx 1.90534 \times 100 \approx 190.53\]

  1. Compare with given options and identify the best answer

We compare our calculated value of approximately \(190.53\) with the given options:

A208
B195
C180
D173

The calculated value of \(190.53\) is closest to 195 among the given choices. Therefore, the most reasonable estimate for the current CPI is 195. The final answer is \(\boxed{b}\).

Examples

The CPI is a vital economic indicator used to track inflation. For example, a government agency might use it to adjust Social Security payments to ensure they keep up with the rising cost of living. By understanding how the CPI is calculated, students can better appreciate how economic data impacts their own financial future, such as the purchasing power of their savings over time.