SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 
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Prof. KooPMANS’ « golden rule path »), the rate of interest of the 
economic system is determined independently of consumers’ utility 
functions. This theorem follows from Prof. KooPMANS’ own analysis. 
For, on the optimum path, the rate of interest must be equal to the 
natural rate of growth (which, in the particular case of a stationary 
economic system, is equal to zero). 
But this simply means that individuals’ preferences are not a 
determinant of the optimum rate of interest. It does not mean (as 
Prof. KooPMANS seems to fear) that any restriction comes to be im- 
posed on individuals’ preferences. To argue otherwise would sound 
to me rather similar to saying, in the usual case of a one-period pro- 
blem of utility maximization, that the fact that market prices are 
the same for all consumers imposes restrictions on individual prefe- 
rences. Traditional economic theorists have solved this problem a 
long time ago, by referring their analysis only to what happens at 
the margin. Individual preferences are accepted for what they are, 
however different from one individual to another they may be. Yet, 
given these preferences, each individual will push the consumption of 
each commodity to the point at which the ratios of marginal utilities 
are equal to relative market prices. This means that we can make 
definite statements about ratios of marginal utilities, without impos- 
ing any restriction on utility functions. 
Our case is similar. Consumers’ preferences may be quite dif- 
ferent at different levels of consumption, at different times, and for 
different individuals. Any social preference function expressing all 
these preferences may be equally different; and it must be accepted 
for what it is, without any restriction. Yet, if behaviour is to be 
rational, the consumption of each commodity will be distributed over 
time so as to equate marginal intertemporal rates of substitution in 
consumption to the externally given rate of interest. This is all we 
can say. 
Professor KooPMANS’ results have been obtained because he has 
added something else. He has imposed on utility functions at all 
levels (and not only at the margin!) the restriction that utility always 
differs by ¢ at anv two adjacent points of time. This restriction is 
4, Koopmans - pag. 69