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 sum of the prices in 1983: \(67.45 + 15.25 + 1.15 + 22.85 = 106.70\).
  • Calculate the sum of the prices today: \(126.85 + 29.95 + 2.25 + 44.25 = 203.30\).
  • Determine the CPI ratio: \(\left( \frac{203.30}{106.70} \right) \times 100 \approx 190.53\).
  • Select the closest provided estimate: \(\boxed{195}\).

Explanation

  1. Calculate Total Costs of the Market Basket

To estimate the current Consumer Price Index (CPI), we first need to determine the total cost of a defined market basket of goods in the base year (1983) and compare it to the total cost of that same basket of goods today. The basket consists of: a pair of boots, a hair dryer, a box of tissues, and a toaster.

The total cost in 1983 is calculated by summing the prices of these four items:
\[C_{1983} = 67.45 + 15.25 + 1.15 + 22.85 = 106.70\]

Next, we calculate the total cost of the same basket today:
\[C_{current} = 126.85 + 29.95 + 2.25 + 44.25 = 203.30\]

  1. Calculate and Estimate the CPI

The CPI is defined as the ratio of the total cost of the market basket today to the total cost in the base year, multiplied by 100:
\[CPI_{current} = \left( \frac{C_{current}}{C_{1983}} \right) \times 100\]
Substituting our calculated totals:
\[CPI_{current} = \left( \frac{203.30}{106.70} \right) \times 100 \approx 1.90534 \times 100 \approx 190.53\]

Given the options provided (a: 208, b: 195, c: 180, d: 173), our calculated estimate of approximately \(190.53\) is closest to \(195\). Therefore, a reasonable estimate of the current CPI is \(195\).

Examples

The Consumer Price Index (CPI) is a vital tool used by economists, businesses, and governments to track inflation and the purchasing power of money. By comparing the cost of a fixed "basket" of goods over time, people can adjust their financial planning, negotiate salaries, and understand how the real value of their income changes. For instance, if you want to know how much money today would be equivalent to a specific amount in 1983, you can multiply that amount by the ratio of today's price level to the 1983 price level (the CPI). This provides a clearer picture of historical economic shifts.

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