I also modeled human capital as three fourths of total capital. My tag for the two ideas together was the “three fourths rule.” The agreement of the two ratios as modeled is a convenient coincidence. If they differed, this book would have to be a
few sentences longer. Each is first-order approximation only.
The Free Growth Index for Total Capital
Given the three fourths rule, the free growth index for total capital is derived by reading “pure” and “total” before the words consumption and capital in the
equations of Chapter 4.
Now back to the charts and tables. The free growth index for total capital is tracked in the red line and labeled (Kt). It too fluctuates around one in each country, but in a much narrower range than does the blue line g(K). The reason is the three fourths rule. The thrift index, not shown in the charts and tables, is one minus the free growth index. It is derived in Chapter 4 as thrift rate over acceleration, where thrift rate is change in consumption/capital ratio times minus one. By the three fourths rule, where pure consumption is three fourths of all consumption while total capital is four times physical capital, the pure consumption/total capital ratio is only 3/16 (3/4 divided by 4) the size of the consumption/physical capital ratio. The yearly changes in these ratios reflected in the numerator of the thrift index will hold to the same proportion. The denominator is acceleration, which is always the same for physical as total capital by the assumption that they hold in 1:4 proportion throughout. This explains why the unshown thrift index, or numerator over denominator, is automatically 3/16 as large for total as for physical capital, and why
the shown free growth index runs nearer one in consequence.
I have just given an idea why it can be worthwhile to brush up the algebra we all learned in high school or before, and to suffer the nuisance of mathematical notation.
| have made a very simple truth, obvious in hindsight, seem complicated by making
Chapter 5 Bringing Human Capital In 1/13/16 13
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