March 22 1981
Dear Tih ,r,
Thanks a 1 t for your letter and especially for your comments.
Let me first deal with your post-script relating to the earlier
paper on evolution and techniques. *our question is easy to answer,
hut unfortunately it has occasioned me to discover that the
equation 6.4 on page 154 is ^rong. This equation is derived from
6.2 ( to which we have to go bafck because I can hot, naturally,
assume constant labour input, as in 6.3 ). The correct result is
N/C N -jO-b)/ a jN b
and the next equation
N/Cjr - constant times exp {oo bt)
and the following sentence must rumproductivity grows at the rate
of CO h which means that its growth rate would be one third of
that of output if b=l/5.
How r s to your questi n X he productivity per yearfis dfi/dt / dCH/dt
Prom 6,2 we get
c nstant x C. T
H
dN/dt = constantx C T
and since C,
Differentiating with respect to time (function of function rule)
we get
-» ^
„ 1-b , the above becomes
N =N
dll/dt •» constant x N b
Ch
which is the same expression as for the average productivity N/C^
and that confirms your last statement on the two exponential rates
being equal.
The mess I have made in 6.4 does not exactly add to my credibility
but at least the correction strengthens my argument. ( If ever
I will, following more erlauchte Vorbilder publish a collection
of essays I shall have a hell of a time correcting all this
bungled arguments and algebra ).
The application of my argument is less interesting for the fiase of
learning than for large scale economies. It rests, of course on