To determine the relative change in the real wage, we need to compare the wage in 2010 to the wage in 2015 after adjusting for changes in the cost of living, often represented by the Consumer Price Index (CPI). However, the problem does not provide the actual CPI values for 2010 and 2015, so we'll work with the given wages and analyze the change.
Here’s the step-by-step solution:
1. Identify the initial wage and the final wage:
- Initial wage in 2010: \$19.59
- Final wage in 2015: \$19.59
2. Determine the change in the wage:
- Since the wage did not change from 2010 to 2015, the change in wage is \$0.
3. Calculate the relative change:
- The formula for relative change is:
[tex]\[
\text{Relative change} = \frac{\text{Final value} - \text{Initial value}}{\text{Initial value}} \times 100
\][/tex]
- Substituting the given values, we get:
[tex]\[
\text{Relative change} = \frac{19.59 - 19.59}{19.59} \times 100
\][/tex]
- Simplifying the numerator:
[tex]\[
\frac{0}{19.59} \times 100 = 0 \times 100 = 0
\][/tex]
4. Result:
- The relative change in the real wage is 0%.
Thus, if there was no change in their wage from 2010 to 2015, the relative change in their real wage is 0.0%.
