SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 
In order to make use of this expression we should have to 
assign a form to ®. The simple thing to do is to put ®=log; in 
this case we maximise a weighted sum of the logarithms of the 
excesses of the consumption of the various commodities in the 
different years over the quantities that enter into the basic 
standard of living. This form is only possible if at all times 
each element in round brackets in (V. 10) is positive. As even 
simpler practical alternative would be to replace v by , that 
is to maximise not utility but consumption itself. 
As I have stated them, these relationships apply to an eco- 
nomy which is not only closed but stationary, that is has a 
fixed technology and fixed preferences. The way to remove 
these limitations is described in [40]. 
The maximisation of (V. 10) subject to (V. 1), (V. 2), 
(V. 5), (V. 7) and (V. 8) is, for practical purposes, a problem 
in dynamic programming. If the terminal stock requirements 
are set too high there will be no solution: we cannot meet these 
requirements and have a consumption in excess of * through- 
out the transitional period. If we insist on p* as a minimum, 
then we must reduce our terminal stock requirements. If we 
insist on the rate of growth originally intended for the steady 
state, we must reduce the level of consumption in the first year 
of the steady state. By experimenting with different initial 
consumption levels for the steady state, and perhaps also with 
different forms of the maximand, we may hope to obtain a 
complete path for consumption that is acceptable as an object 
of policv 
2] Stone - pag. 79