time calculation, but when we compute the growth over and over, it makes more sense to define the quantity as

the average quantity over the period in question, which is defined as the quantity halfway between the initial
506 A • The Use of Mathematics in Principles of Economics

quantity and the next quantity. This is harder to explain in words than to show with an example. Suppose a

nation’s GDP was $1 trillion in 2005 and $1.03 trillion in 2006. The growth rate between 2005 and 2006 would

be the change in GDP ($1.03 trillion – $1.00 trillion) divided by the average GDP between 2005 and 2006 ($1.03

trillion + $1.00 trillion)/2. In other words:

Note that if we used the first method, the calculation would be ($1.03 trillion – $1.00 trillion) / $1.00 trillion =

3% growth, which is approximately the same as the second, more complicated method. If you need a rough

approximation, use the first method. If you need accuracy, use the second method.
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