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Chapter 4: Problem 137

In 1933, the Consumer Price Index was \(38.3(1967=100)\) and Babe Ruth received a salary of $$\$ 80,000$$, his highest ever. Near the end of the 1978 baseball season, the Consumer Price Index hit 200 . Using this information, what would Ruth's salary be in \(1978 ?\)

Short Answer

Expert verified
Babe Ruth's salary in 1978, adjusted for inflation using the given CPI values, would be approximately $417,600.

Step by step solution

01

Understand the concept of CPI

Consumer Price Index (CPI) is a measure that examines the weighted average of prices of a basket of consumer goods and services, such as transportation, food, and medical care. It is calculated by taking price changes for each item in the predetermined basket of goods and averaging them. Changes in the CPI are used to assess price changes associated with the cost of living. In this exercise, we will use the CPI values to adjust Babe Ruth's salary for inflation.
02

Calculate the CPI ratio

The first step is to calculate the ratio of the CPI in 1978 to the CPI in 1933, which will give us the rate at which we need to adjust Babe Ruth's salary. The formula we can use for this is: CPI ratio = \( \frac{CPI_{1978}}{CPI_{1933}} \) Plug in the given values: CPI ratio = \( \frac{200}{38.3} \)
03

Calculate Babe Ruth's adjusted salary

To find Babe Ruth's adjusted salary in 1978, multiply his 1933 salary by the CPI ratio. The formula we can use for this is: Adjusted salary = Salary in 1933 × CPI ratio Plug in the given values: Adjusted salary = $80,000 × \( \frac{200}{38.3} \)
04

Solve for the adjusted salary

Now we just need to solve for the adjusted salary: Adjusted salary = \(80,000 × \( \frac{200}{38.3} \) ≈ \)80,000 × 5.22 Adjusted salary ≈ $417,600 In conclusion, if Babe Ruth's 1933 salary of \(80,000 were adjusted for inflation using the given CPI values, his salary in 1978 would be approximately \)417,600.

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