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If someone was hired at a wage of [tex]$19.59 per hour in 2010, and in 2015 they were still making $[/tex]19.59 per hour (no raises), what is the relative change in their real wage?

Hint: Consider the CPI. Round to the tenth of a percent.



Answer :

GinnyAnswer
To understand the effect of inflation on a person's wage over the years, we need to consider the Consumer Price Index (CPI). The CPI measures changes in the price level of a market basket of consumer goods and services purchased by households. Here's a step-by-step solution to determine the relative change in real wage from 2010 to 2015:

1. Determine the initial wage and CPI values:
- Initial hourly wage in 2010: $19.59
- CPI in 2010: 218.056
- CPI in 2015: 237.017

2. Calculate the real wage in 2010:
- The real wage adjusts for inflation and represents the purchasing power of the wage.
- Formula: Real Wage = Nominal Wage / (CPI / 100)
- Real wage in 2010 = [tex]$19.59 / (218.056 / 100) ≈ $[/tex]8.98

3. Calculate the real wage in 2015:
- Using the same formula, we calculate the real wage in 2015.
- Real wage in 2015 = [tex]$19.59 / (237.017 / 100) ≈ $[/tex]8.27

4. Determine the relative change in the real wage:
- The relative change measures the percentage change in purchasing power.
- Formula: Relative Change = ((Real Wage in 2015 - Real Wage in 2010) / Real Wage in 2010) 100
- Relative Change = (([tex]$8.27 - $[/tex]8.98) / $8.98) 100 ≈ -8.0%

Therefore, the relative change in their real wage from 2010 to 2015 was approximately -8.0%, indicating a decrease in purchasing power despite the nominal wage staying the same.

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