**Another in my WWWTF series (What in the world will I ever use this for?)**

**Math Concept**: Percentage Change

Percentage changes are a way to compare changes in numbers relative to the starting value. To calculate a percentage change you take the new value of the number (Ending Point) and subtract the starting value (Starting Point), then divide this difference by the starting point:

(Ending Point-Starting Point)/(Starting Point)

This will give the the change in decimal form. To express the change as a percent, just multiply the decimal form by 100.

For example, if a number increases from 50 to 52, we can calculate the percentage change as:

=(52-50)/50

=0.04

This is the decimal form. To put it in percentage form, multiply by 100:

percentage change = 0.04*100

=4%

So when the number increased from 50 to 52, the number increased by 4%.

What in the world will you ever use this for?

**Application**: Price Elasticity of Demand

If you are running your own business, it can be important to understand how sensitive your customers are to changes in the price of your product.

For example, we know that if you raise your price, you are going to lose some sales (people buy less when prices rise). But, the people who still buy your stuff at the new higher price are paying more. Now you are selling less but getting more money for each sale. Has the amount of money you made increased or decreased?

The answer is, it depends on how sensitive your customers are to the price change. If you raise your price and you don't lose many customers, you might increase the money you make. But if you raise your price and you lose a lot of customers, you might lose money.

To understand how sensitive customers are to price changes, economists use a number known as the Elasticity of Demand. The Elasticity of Demand (E) is defined as:

E=(Percentage Change in Quantity)/(Percentage Change in Price)

To see how to calculate the Elasticity of Demand suppose last month, the price of your product was $10 and you sold 100 units. This month you raised your price to $11 and sold 90 units.

In this case, the percentage change in the price is ($11-$10)/($10). Doing the math, the percentage change in price is 0.10 (or a 10% increase).

Using similar calculations, the percentage change in quantity is (90-100)/100. Again doing the math, the percentage change in quantity is -0.10 (or a 10% decrease).

Using these percentage changes, the Elasticity of Demand is:

E=(Percentage Change in Quantity)/(Percentage Change in Price)

E=(-0.10)/(0.10)

E = -1

An economist would say that, in this case, the Elasticity of Demand is equal to negative one. The interpretation is that every time the price increases by 1%, the quantity demanded decreases by 1%.

Why are elasticities important? Knowing elasticities can help different decision makers make decisions about changing prices. For example, a local government might be considering increasing the tax on liquor, hoping to increase tax receipts for the local goverment. But if the Elasticity of Demand for alcohol is less than negative 1, increasing the tax on alcohol (raising the price) might end up decreasing the tax revenue.

## Recent Comments