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Glossary
Levels of GDP Vs. Percentage Change in GDP

Knowing your pulse rate before and after exercising gives you two pulse rates but limited information for comparison. Knowing the percentage change in your pulse rate from before exercise to after exercise gives you much more useful information for comparing how hard your heart is working from one exercise period to another. In a similar way, economists can measure real GDP at various times each year. Real GDP tells economists the amount of final goods and services being produced each time the economists measure, but it won't tell them what they really need to know—at what rate the economy is growing or slowing. To determine whether the economy is healthy and growing, and at what rate the economy is growing, economists must compare the percentage change in real GDP numbers over time.

Let's see how Mr. Kliesen explains this topic to the student visitors.

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Let's do some practice exercises around this topic.

Practice 1

Suppose you have a friend named Rao who has been receiving an allowance since he was in middle school. His allowance was $4 a week in sixth grade, $7 a week in eighth grade and is now $10 a week in tenth grade. Rao's allowance increased in each of those years by $3 per week. Do you think that means that his allowance grew at the same rate between sixth grade and eighth grade as it did between eighth grade and tenth grade?

One way to describe the change in Rao's allowance from sixth to eighth grade, and from eighth grade to tenth grade, is to say that his weekly allowance increased by $3 per week, each time. This goes back to measuring pulse before and after exercise. It tells us some information (what the allowance was before and what it was after), but it doesn't tell us whether the change is healthy or not. Therefore, another way to describe the change and get more information is to indicate the rate of change, which is the percentage by which the allowance increased each time. Let's determine this for Rao's allowance change from sixth grade to eighth grade.

 

Sixth-Grade to Eighth-Grade Rate of Change for Rao's Allowance
What is the rate of change between $4 and $7?
To calculate this, follow these steps:

1. Subtract his sixth-grade allowance ($4) from his eighth-grade allowance ($7).

$7 - $4 = $3

2. Divide the result ($3) by his starting allowance ($4).

$3 ÷ $4=.75

3. Multiply the resulting decimal by 100 to convert the decimal to a percentage.

.75 x 100=75%

Rate of Change: 75%

Now, using the same process, let's determine by what percentage Rao's allowance increased from eighth grade to tenth grade. Do you think it will be the same, more or less?

 

Eighth-Grade to Tenth-Grade Rate of Change for Rao's Allowance
What is the rate of change between $7 and $10?
To calculate this, follow these steps:

1. Subtract his eighth-grade allowance ($7) from his tenth-grade allowance ($10).

$10 - $7 = $3

2. Divide the result ($3) by his starting allowance ($7).

$3 ÷ $7=.428 (round up to .43)

3. Multiply the resulting decimal by 100 to convert the decimal to a percentage.

.43 x 100=43%

Rate of Change: 43%

Even though Rao's allowance increased by the same dollar amount each time, it did not increase by the same percentage rate. His first increase represented a 75 percent rate of change. His second increase represented a 43 percent rate of change. How could Rao use this information to ask his parents for an additional increase in his allowance?

Practice 2

Suppose you are the producer of a show called, "The Fastest Loser." This is a competition in which men and women work to lose weight. They don't necessarily win by losing the most weight each week. A contestant wins by losing weight at the fastest rate. To know who won, the producers must compare the amount of weight a contestant lost to the contestant's starting weight. For example:

Female contestant: starting weight is 190 lbs.; weight at the end of a week is 184 lbs.
Male contestant: starting weight is 350 lbs.; weight at the end of a week is 340 lbs.

Here is the set of formulas to consider as you make your calculations:

Ending point - starting point = amount of change
Amount of change ÷ starting point = decimal amount
Decimal amount x 100 = percentage rate of change
Round your answer to the nearest tenth.

Using each contestant's information and the formulas above, determine the rate of weight loss for each contestant. Who is losing at a faster rate?
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Practice 3

Tami has a part-time job. Her starting salary was $6.30 an hour. After one year, she received a raise and was earning $6.61 per hour. She has been working two years, and her boss just told her that she is going to receive another 31 cents per hour increase in pay. Answer the following two questions regarding Tami's pay:

At what percentage rate did Tami's salary increase during the first year? (Round your answer to the nearest hundredth.)
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At what rate did Tami's salary increase the second year? (Round your answer up to the nearest hundreth.)
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Even though the numerical amount of Tami's raise was the same each year—31 cents—the percentage change was different for years one and two because Tami's base wage was different in each year ($6.30 in year 1 and $6.61 in year 2). So, although Tami's wage increased by the same amount each year (31 cents per hour), her wages actually grew at a slower rate—or percentage—in year two, compared with year one.

Just as Tami's salary increased over time and Rao's allowance grew over time, economies usually grow over time. Economic growth is defined as an increase in real GDP over a period of time. But, just as with Tami's salary and Rao's allowance, it isn't the absolute change that tells us what we need to know. We have to determine how fast or how slowly the economy is growing by measuring the rate of change—the percentage change in real GDP over a period of time.

Why is economic growth even important? Go to our next section, and find out!