This is “Percentage Changes and Growth Rates”, section 17.21 from the book Theory and Applications of Microeconomics (v. 1.0). For details on it (including licensing), click here.

For more information on the source of this book, or why it is available for free, please see the project's home page. You can browse or download additional books there. To download a .zip file containing this book to use offline, simply click here.

Has this book helped you? Consider passing it on:
Creative Commons supports free culture from music to education. Their licenses helped make this book available to you. helps people like you help teachers fund their classroom projects, from art supplies to books to calculators.

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.