Please wait while we create your MIYO...

Study Aids:

Click the Study Aids tab at the bottom of the book to access your Study Aids (usually practice quizzes and flash cards).

Study Pass:

Study Pass is our latest digital product that lets you take notes, highlight important sections of the text using different colors, create "tags" or labels to filter your notes and highlights, and print so you can study offline. Study Pass also includes interactive study aids, such as flash cards and quizzes.

Highlighting and Taking Notes:

If you've purchased the All Access Pass or Study Pass, in the online reader, click and drag your mouse to highlight text. When you do a small button appears – simply click on it! From there, you can select a highlight color, add notes, add tags, or any combination.

Printing:

If you've purchased the All Access Pass, you can print each chapter by clicking on the Downloads tab. If you have Study Pass, click on the print icon within Study View to print out your notes and highlighted sections.

Search:

To search, use the text box at the bottom of the book. Click a search result to be taken to that chapter or section of the book (note you may need to scroll down to get to the result).

View Full Student FAQs

## 17.21 Percentage Changes and Growth Rates

If some variable x (say, the number of gallons of gasoline sold in a week) changes from x1 to x2, then we can simply define the change in that variable as Δx = x2x1. But there are problems with this simple definition. The number that we calculate will change depending on the units in which we measure x. If we measure in millions of gallons, x will be a much smaller number than if we measure in gallons. If we measured x in liters rather than gallons (as it is indeed measured in most countries), it would be a bigger number. So the number we calculate depends on the units we choose. To avoid these problems, we look at percentage changes and express the change as a fraction of the individual value. In what follows, we use the notation %Δx to mean the percentage change in x, and we define it as follows: %Δx = (x2x1)/x1. A percentage change equal to 0.1 means that gasoline consumption increased by 10 percent. Why? Because 10 percent means 10 “per hundred,” so 10 percent 10/100 = 0.1.

Very often in economics, we are interested in changes that take place over time. Thus we might want to compare gross domestic product (a measure of how much our economy has produced) between 2012 and 2013. Suppose we know that gross domestic product in the United States in 2012 was $14 trillion and that gross domestic product in 2013 was$14.7 trillion. Using the letter Y to denote gross domestic product measured in trillions, we write: Y2012 = 14.0 and Y2013 = 14.7. If we want to talk about gross domestic product at different points in time without specifying a particular year, we use the notation Yt. We express the change in a variable over time in the form of a growth rate, which is just an example of a percentage change. Thus the growth rate of gross domestic product in 2013 is calculated as

Y2013 = (Y2013Y2012)/ Y20126 = (14.7 − 14)/14 = 0.05.

The growth rate equals 5 percent. In general, we write %Δ Yt+1 = (Yt+1Yt)/ Yt.

## The Main Uses of This Tool

Close Search Results
Study Aids