176 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK 
to be independent of all variables other than housing itself, and 
so as to Ws, R.. 
Such independence of food and housing would clearly not 
hold true of an individual item within the food group or the 
housing group. We know, for instance, that the desirability of, 
or want-for-one-more loaf of bread depends on many other vari- 
ables besides the quantity of bread. Especially does it depend 
on the quantity of, say, butter as a complementary or “complet- 
ing” * article, and on the quantity of, say, cake, as a substitute or 
“competing” * article. 
But these interrelations within the food group would probably 
not appreciably affect the want for food as a whole, especially as, 
in the two Cases 1 and 2, such interrelations within the food 
group are assumed to be very similar in Oddland and Evenland. 
Certainly slight internal differences within the food groups,— 
such differences as we find between, say, England and the United 
States,—could be neglected. One country may emphasize jam 
more than marmalade on its tables and the other vice versa with- 
out appreciably influencing the comparative desirability of the 
food régimens as a whole. 
Such interrelations, therefore, merely affect the adjustments 
within the food group. There is practically no corresponding 
relationship outside the group. That is, there is no substitute for 
food and no complementary group. Only in extreme cases can 
we say that clothing, for instance, can even partially take the 
place of food in keeping one warm or that flowers on the table are 
a complement to the food important enough to appreciably inter- 
fere with the equation WiF;—W,F,. Any such extreme cases 
will scarcely cast doubt on the truth of the proposition that 
similar families having similar food rations in two countries— 
though differing in housing conditions and (perhaps) other cir- 
cumstances—will equally crave a given improvement in that 
ration. 
In short, it is here assumed—and the assumption seems to be 
reasonable—that, taking food as a group, there is no other group 
of importance—neither housing, nor clothing, nor anything else 
—which is sufficiently a “complementary” or a “substitute” group 
to vitiate the equality of the want-for-more or better food, given 
physically equal or corresponding rations. 
1 See my Mathematical Investigations, D. 65.