When a quantity changes we

**define** the

percent of change to be:

`
(Change in quantity)/(original quantity)`

So, if a metro card cost $1.50 in 2002 and it costs $2.00 in 2006 then the percent change would be:

`
$0.50/ $1.50 = 1/3 = 33 and 1/3 percents`

Since the change was an increase, we can say "the price of a metro card increased by 33 and 1/3 percent." If, magically, in 2007 they changed the price of a metro card back to $1.50 we could find the percent of decrease from 2006 to 2007. Again, we use the change in price: $0.50 --but this time the original price is the 2006 price: $2.00

`
0.50/2.00 = 1/4 = 25 percents`

This is a decrease so we’d say "the price fell by 25 percent since 2006." Part of the confusion some people have with percents of change arises from the fact that the

percent of increase from 1.50 to 2.00 is not the same as the

percent of decrease from 2.00 to 1.50. The percents are not the same because whenever you have a percent it must be a percent

*of* something. In the case of percent of change we think of it as a percent of the original number.

This tends to mess people up when they are asked question such as: "

*If the price of a metro card has increased 50% since 1972 and the current price is $3.00 what was the price in 1972?*"

`
(1972 price) + (fifty percent increase on 1972 price) = (current price)`

x + 0.50x = 3.00

1.5x = 3.00

x = 3.00/1.5

x=$2.00 in 1972

The major trouble is the fact that a percent is pretty

meaningless unless it is a percent of something. The key in the pervious problem is realizing that 50% applies to the

unknown price in 1972. However, a change in

wording changes the entire problem:

"

*The current price $3.00 would have to decrease by 50% to return to the 1972 level. What was the 1972 price?*"

In this case the 50% will apply to the

*$3.00* and the 1972 price would have been

*$1.50*. There are a few

wags out

on the fringe who think that

the way we calculate percent change is inherently deceptive. They may or may not have a point. Percent change is used in

finance and various

statistics.

Pure mathematicians tend to avoid them—if mentioned at all the wording has a precision and clarity that I’d like to see in

economic statistics more often.

However, understanding and avoiding the simple but dangerous errors is an essential survival skill that could probably land you a pretty

high power job. Most

high school seniors are unable to solve these problem correctly. (I’ve met people with

MBAs who get lost in these

simple calculations.)