(4.5) shows something about “balance” or the state where capital, consumption and output grow at the same rate. It confirms the standard teaching that balance is possible, although not compelled, when growth rate is constant. It also shows that balance is impossible when growth rate changes. No one disputes that capital productivity (output/capital) always leads, and consumption rate (consumption/capital) always lags, in accelerations up and down. Output gets the bad news first and the good news first. What the equations leave unspecified is where capital itself joins the sequence. That is what the evidence in the charts and
tables tells us.
In the case where the free growth index equals one, for example, the above
equations show
thrift gain
thrift index = —=0, implying acceleration — change in consumption rate thrift gain = change in growth rate =0, and
change in consumption rate =0, or equivalently
consumption consumption rate = oo = constant, (4.7) capita
if acceleration is non-zero. (The reason for that qualifier is that zero acceleration
means zero change in growth rate, and division by zero is a no-no.)
In the opposite case where the thrift index is one, the same equations would show
free exerts idles = productivity gain _ changeinproductivtyrate _ acceleration change in growth rate
Chapter 4 Mill’s Idea 1/11/16 14
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