684 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
slows down the growth of the whole system (4). Empirically 
this is absurd. If that commodity, for example, happens to 
be one that consumers do not want to increase, there is no 
reason why the growth of the whole system should be kept 
back simply in order to fulfil the unjustified requirement of a 
uniform rate of growth. In practice, the production of that 
commodity may quite well be kept constant or even decreased 
or eliminated altogether if better and cheaper substitutes can 
be invented. All this means that, following consumers’ pre- 
ferences both with regard to the composition of consumption 
and to the rates of expansion of each single production, it 
might quite well be possible to achieve an over-all rate of 
growth which might not only be better, on utility or welfare 
grounds, but which might also be higher than voN NEUMANN’S 
maximum uniform rate. 
To conclude: there is no ground whatsoever for an exten- 
sion of the voN NEUMANN concept of maximum rate of uniform 
growth to an economic system in which there is technical 
progress. In no case would such a maximum rate of uniform 
growth produce an optimum pattern of growth in terms of 
atility and welfare. Moreover it may even turn out to be 
numerically lower than the over-all growth rate achievable 
by following the sectoral rates of expansion indicated by con- 
sumers’ preferences (5). 
Now the reader may better understand why the dynamic 
analysis of the previous pages has been freed since the begin- 
(*) This criticism was already raised by D.G. CHAMPERNOWNE in his 
1 Note on J. V. Neumann's Article on « À Model of General Equilibrium », 
« The Review of Economic Studies », 1945-46. This Note is quite indi- 
cative of the preoccupations of economists at that time. Mr. CHAMPERNOWNE 
does point out the limitations of von NEUMANN’S assumption of constant 
returns to scale but mainlv with referenre to the case of decreasing returns 
to scale. 
(°) It may be useful to add here that the criticism developed in the text 
applies in its entirety to the so-called turn-pike theorem, which was pro- 
posed by DORFMAN-SAMUELSON-SoLOW (op. cit., pp. 320-231) and is now 
so widely discussed in the economic literature 
‘101 Pasinetti - pag. Ia