172 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK
rests, in order to make sure whether those hypotheses are true or
reasonable.
The hypotheses have already been stated, but the equations
help us to see more clearly what they involve, and one cannot see
too clearly when trying to peer into a region supposed to be dark,
and filled with elusive will-o-the-wisps of thought.
If the equations for food, rely Soa = Ss and W, F1—
Ws F,, are correct (and also the corTesrending fale for rent), all
the rest follows indubitably. Any critic, in order to discredit the
method, must discredit one or another of these four equations.
Certainly no criticism of the first equation is possible, except
as to the statistical accuracy of the numerical data. The equa-
tion merely describes the two families enjoying the same, or
equivalent, food rations. That is, if we locate in the statistical
tables of budgets two groups of families, one in Oddland having
a total budget of S;, or $1000, and the other in Evenland having
a total budget of S., or $600, and if it be true, as the statistical
tables are here assumed to state, that in Oddland a $1000 family
averages ¢1, or 40%, (of his income and expenditure) on food,
making S; ¢;, or $400, while a $600 Evenland family averages
¢2, or 50%, on food, making $300; and if, furthermore, the rela-
tive food prices in the two countries (for food of the same
quality) are as F;—F,, or as 1.3313--1.00, then these two
families certainly do have the relationship
Boy
Sits _ Sut (;, 1000 X 40% _ 600 X 0%)
Fone 7% Eas 331 1.00
For convenience we have described this relationship by saying
that the two families are selected to have the same food rations.
But if we prefer meticulous exactitude, we should say, instead,
that they are selected such that their food expenditures are pro-
portional to the food price indexes. This is evident if the first
equation hh = hh is written oh = > . This states that the
expenditures for food in Cases 1 and 2 are proportional to their
prices. It is only in this specific sense that the food can be
said to be “the same” in the two Cases.
We need, therefore, no longer picture this sameness as same-
ness in “pounds,” nor need we longer conceive of the index number
