growth rate = capital productivity + thrift rate. (4.4b)
Notice that we must change the sign before “consumption rate” to find thrift. Change
downward in consumption rate is change upward in thrift rate, and conversely. Further
change in growth rate = change in capital productivity — change in consumption rate, (4.5)
by the same logic as with (4.3). Save space again by reexpressing (4.5) as acceleration = productivity gain + thrift gain. (4.5a) Finally divide by acceleration to reach
1= productivity gain + thrift gain
; — (4.6) acceleration acceleration if acceleration is nonzero. Reexpress as 1 = free growth index + thrift index, (4.6a)
where indexes are undefined if acceleration is zero.
I think this gets at what Mill meant, and anyhow what I mean. We both describe acceleration as well as growth. One night think that his “whatever increases the productive power of labor” is the opposite from my “change in capital productivity.” But they are about the same. Better machines make their operators more productive
whether skills have changed or not.
Chapter 4 Mill’s Idea 1/11/16 13
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