All Terrain Thinking

A Compendium of things I think are Important

Economics: It's not just whats' in your wallet

Quantitative significance of growth

How much does growth matter? Should we be worried about a difference of 1 or 2 percentage points in the growth rate? To answer this question you can return to the simple mathematics of growth that is at the center of present value analysis. The equation of growth is:

FV = PV*(1 + g)^T

• PV = Present Value ( value at beginning of the period)
• FV = Future Value ( value at the end of the period)
• g = Average growth rate per period
• T = Number of time periods

To demonstrate the quantitative significance of the growth rate on the levels of future income, you simply substitute alternative values for g into the equation.  For example, let's look at future income of someone aged 20 earning $1,000 every two weeks. If we look only three years into the future, the difference between a 1 and 3 percent per year growth rate is approximately 6 percent (9.3 vs. 3.03 percent). At a growth rate of 1 percent, the $1000 will grow to $1030 while a 3 percent growth rate will result in an income level of $1090.  The $60 difference is a difference of 6 percent.

FV = 1000*(1.01)³ = 1000* 1.0303   = $1030
FV = 1000*(1.03)³  = 1000*1.0930 = $1090

When we move the time frame back to 30 years, however, the gap widens to more than 100 percent. If we expect income to grow at 1 percent, the $1,000 will reach $1,348 in 30 years, substantially less than the $2,427 which we would have at a three percent growth rate.

FV = 1000*(1.01)³⁰  = 1000* 1.348  = $1348
FV = 1000*(1.03)³⁰  = 1000*2.427 = $2427

The significance of small differentials can thus be rather significant when we take the long view.  One section is devoted to a brief review of the mathematics of present value.    This will be followed by a review of the 'facts' concerning where growth has occurred and a discussion of the determinants of growth - why countries grow at different rates.

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