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When you compare wages from different periods of time, for example across decades, inflation must be taken into account.

Theory

Your real wages measures your purchasing power as a consumer. That means it’s a measure of the quantity of goods and services your wages can buy for you.

$$\begin{array}{llll}\hfill \text{Realwages}& =\text{wages}\cdot \text{currencyvalue}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\text{wages}\cdot \frac{100}{\text{CPI}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

$$\text{Realwages}=\text{wages}\cdot \text{currencyvalue}=\text{wages}\cdot \frac{100}{\text{CPI}}$$ |

Example 1

**Donald Duck earned $\text{\$}\text{}32\phantom{\rule{0.17em}{0ex}}000\text{}$ in 2010. If the CPI was $\text{}128.8\text{}$ in 2010, what were his real wages that year? **

First, you have to find the currency value for 2010. In this case, that’s the value of the dollar. $$\begin{array}{llll}\hfill \text{Dollarvalue2010}& =\frac{100}{\text{CPI2010}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{100}{128.8}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \approx 0.78\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

Then you can find the real wages like this:

$$\text{Realwages2010}=32\phantom{\rule{0.17em}{0ex}}000\cdot 0.78=24\phantom{\rule{0.17em}{0ex}}960.$$ |

We find out that Donald Duck’s real wages were $$24\phantom{\rule{0.17em}{0ex}}960$ in 2010.

Example 2

**Mr. Duck received a $\text{}1.5\text{}\phantom{\rule{0.17em}{0ex}}\text{\%}$ raise in 2011. How much did his real wages increase from 2010 to 2011 when the CPI was $\text{}130.4\text{}$ in 2011? **

First, you need to find the wages for 2011, so we can compare them to the wages of 2010.

$$\text{Wages2011}=32\phantom{\rule{0.17em}{0ex}}000\cdot 1.015=32\phantom{\rule{0.17em}{0ex}}480$$ |

You get the number $1.015$ by converting the $1.5$ % raise into a growth factor.

Next you need to find the dollar value of Mr. Duck’s 2011 wages. Then you can use the formula for real wages.

$$\begin{array}{llll}\hfill \text{Dollarvalue2011}& =\frac{100}{\text{CPI2011}}=\frac{100}{130.4}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \approx 0.77\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

$$\text{Dollarvalue2011}=\frac{100}{\text{CPI2011}}=\frac{100}{130.4}\approx 0.77$$ |

$$\begin{array}{llll}\hfill \text{Realwages2011}& =32\phantom{\rule{0.17em}{0ex}}480\cdot 0.77\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =25\phantom{\rule{0.17em}{0ex}}009.6\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

$$\text{Realwages2011}=32\phantom{\rule{0.17em}{0ex}}480\cdot 0.77=25\phantom{\rule{0.17em}{0ex}}009.6$$ |

$$\begin{array}{llll}\hfill & \frac{\text{Realwages2011}-\text{realwages2010}}{\text{Realwages2010}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{\rule{0.33em}{0ex}}=\frac{25\phantom{\rule{0.17em}{0ex}}009.6-24\phantom{\rule{0.17em}{0ex}}960}{24\phantom{\rule{0.17em}{0ex}}960}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{\rule{0.33em}{0ex}}=0.0020\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{\rule{0.33em}{0ex}}=0.2\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

$$\begin{array}{llll}\hfill \frac{\text{Realwages2011}-\text{realwages2010}}{\text{Realwages2010}}& =\frac{25\phantom{\rule{0.17em}{0ex}}009.6-24\phantom{\rule{0.17em}{0ex}}960}{24\phantom{\rule{0.17em}{0ex}}960}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =0.0020\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =0.2\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

Even though Donald’s wages increased by $1.5$ % from 2010 to 2011, his real wages, and therefore also his purchasing power, only increased by $0.2$ %. That’s not much at all! **Note!** During salary negotiations, real wages are the important thing. That’s what actually decides how much your own personal economic situation will improve. It might be smart to let Uncle Scrooge take care of salary negotiations in the future.