PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 72}
In order to use (IV. 11) or a similar relationship to deter-
mine the industrial distribution of the labour force and the
associated stocks of assets needed to produce a given vector
of net outputs, we must know how large the total labour force
will be and on what criterion it should be distributed. For the
size of the labour force in 1970 we already have official estim-
ates. For the criterion on which it should be distributed we
have the familiar condition that the marginal physical products
of labour and capital should bear a common ratio to one another
in every industry; this is equivalent to saying that we must
choose a distribution such that it could not be improved by
any redistribution.
On further reflection, however, we have decided not to use
relationships of the form of (IV. 11). Two reasons are perhaps
sufficient to explain this decision. First, technical progress
gets into (IV. 11) by allowing a, to increase with time. This
is not satisfactory because it implies that output will increase
over time for given inputs of labour and capital independently
of the amount of investment that is being carried out. But if
no investment is being carried ‘out the quality of the capital
stock cannot improve, and it is hard to see, therefore, how any
substantial amount of technical progress could take place.
Second, if c,<I it is possible to substitute capital for labour
‘ndefinitely and thus to produce any amount of output with
a given labour force simply by giving it more and more capital
to work with. But we know that this is not true. At any given
time new plant will embody about as much capital as can pro-
fitably be used and it seems doubtful whether much more capital
would be used even if capital were a free good. The reason
is that, typically, techniques do not exist for using much more
capital. Accordingly, there is a limit to the substitution of
capital for labour and we could not, even if we wanted to,
increase output indefinitely with a given labour force.
Our latest ideas on this subject have been set out in [33]
and lead to a production function for industry s at time # which
[1] Stone - pag. 46