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 (\$)

Shower curtain		8.8515.66

Floor rug		71.25119.75

T-shirt		13.9523.99

Oscillating fan		22.7537.50






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


A164
B170
C185
D199

Verified Answer :

  • Calculate the total cost of the basket of goods in 1983: \(116.80\).
  • Calculate the total cost of the basket of goods currently: \(196.90\).
  • Determine the CPI ratio: \(\left(\frac{196.90}{116.80}\right) \times 100 \approx 168.58\).
  • Compare to given choices to find the best estimate, which is \(\boxed{170}\) (choice b).

Explanation

  1. Calculate Total Costs for the Basket of Goods

To estimate the current Consumer Price Index (CPI), we first need to determine the total cost of the specified basket of goods in the base year (1983) and compare it to the total cost of the same basket today.

The total cost in 1983 is the sum of the prices provided for that year:
\[ C_{1983} = 8.85 + 71.25 + 13.95 + 22.75 = 116.80 \]

The total current cost is the sum of the current prices provided:
\[ C_{now} = 15.66 + 119.75 + 23.99 + 37.50 = 196.90 \]

  1. Determine the CPI and Select the Best Estimate

The CPI is a measure that reflects the price change of a representative basket of goods over time, relative to a base year. Using the calculated totals, the CPI is determined by dividing the current total cost by the base year total cost, and then multiplying the result by 100 to represent it as an index:
\[ \text{CPI} = \left(\frac{C_{now}}{C_{1983}}\right) \times 100 \]
\[ \text{CPI} = \left(\frac{196.90}{116.80}\right) \times 100 \approx 1.6858 \times 100 \approx 168.58 \]

Comparing this result to the given options (164, 170, 185, 199), the value 168.58 is closest to 170. Therefore, 170 is a reasonable estimate for the current CPI based on these items.

Examples

Understanding the Consumer Price Index (CPI) is essential for grasping how inflation affects the purchasing power of money over time. In everyday life, this helps in analyzing price trends for household expenses, planning budgets, and understanding wage adjustments. For instance, if an individual tracks their grocery spending over several years, they can create their own "mini-CPI" to see if their cost of living is rising faster or slower than the national inflation rate, allowing for more informed financial decisions.

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