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