Mill and Keynes and tradition hold (4.2) and (4.2a) as logical certitudes which hold
constant over time. I agree if we imagine the asterisks. Constancy over time would
imply
change in growth = change in output - change in consumption. (4.3)
I take the trouble to derive this as a road | haven't preferred to follow. | will reason instead in rates rather than flows. Rates, or ratios of flows to capital, effectively cancel capital from numerator and denominator. That frees them to show comparison between smaller and larger economies among the eight | test. Mill’s idea, or anyhow mine, is that the ratio of consumption to capital in all those countries can
hold constant. That is what the charts and tables show.
To follow that lead, divide (4.2a) by capital. This finds
growth — output consumption
at canteal ; (4.4) capital capital capital That can be put more compactly as growth rate = capital productivity - consumption rate, (4.4a)
where rate always means ratio to capital. That needs a caveat because consumption rate in macro means ratio to output. Capital productivity in this sense is also called rate of return.
For more compactness still, define
thrift rate = - consumption rate,
allowing (4.4a) to be restated as
Chapter 4 Mill’s Idea 1/11/16 12
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