A price index describes the relationship between the price of a product one year and the price of that product in a base year.

A price index enables us to calculate the change in price over time, or between different parts of the world. It is important to remember that the price index in the chosen base year is 100.

Formula

$$\text{Priceindex}=\frac{\text{price}}{\text{priceinbaseyear}}\cdot 100$$ |

Formula

$$\frac{\text{priceindex1}}{\text{priceindex2}}=\frac{\text{price1}}{\text{price2}}$$ |

Example 1

**The base year price of an item was $\text{\$}\text{}9.80\text{}$. In 2015, the price index was $\text{}235\text{}$. What was the price of the item in 2015? **

The price index of the base year is always 100. You can just insert the given information into the formula, which will give you

$$\begin{array}{llll}\hfill \frac{\text{priceindex2015}}{\text{priceindexbaseyear}}& =\frac{\text{price2015}}{\text{pricebaseyear}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \frac{235}{100}& =\frac{\text{price2015}}{9.80}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \frac{235}{100}\cdot 9.80& =\frac{\text{price2015}}{9.80}\cdot 9.80\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \text{price2015}& =\frac{235}{100}\cdot 9.80=23.30\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$The price of the item was $$23.30$ in $2015$. That means the value of $$1$ has decreased, and stores have raised the price for the same item to compensate.

The consumer price index (CPI) takes various price indices for a number of products and averages them. It is intended to approximate how the whole market has changed in price each year. It’s very useful when calculating inflation and when you negotiate salaries.