A STATISTICAL METHOD FOR MEASURING ‘MARGINAL UTILITY” 173
Fy and F, as an average of prices. These concepts were make-
shifts to simplify the statement. Index numbers properly are
averages of price relatives.” The equation does not, of course,
imply that, as between Cases 1 and 2, the families will find all
food prices differing in the same ratio, nor that the family will
have absolutely identical rations in the two Cases. It may find the
two food markets different in many details. But, on the average,
the food prices in Evenland are three-fourths the food prices in
Oddland; and, since the family in Evenland also spent three-
fourths as much for food as the corresponding family in Oddland,
it must, in that sense, be considered as having substantially the
same quantity and quality of food. If the assumed budget tables
and price indexes are correct, the $1000 Oddland family and the
$600 Evenland family certainly do have substantially the same
food rations. If we wish some term more strictly appropriate than
“pounds” of food we may say “index of food consumption.”
Likewise, the $1440 Oddland family and the $600 Evenland
family, although their dwellings may not be exactly alike in
every detail, must, if the budget price tables be correct, have
substantially the same sort of housing, since rents (of the same
quality) are three times as high in Oddland as in Evenland and
Case 3 in Oddland pays said three times as much for his rent as
Case 2 pays for his in Evenland.
In other words, while we cannot measure food by the pound
nor housing by the square foot nor their prices in those terms,
we can use index numbers and expenditures for food and housing
in such a way as to enable us to substitute, for strict physical
equality, an equality between the ratio of food expenditure to
index number of food prices for Case 1 and the corresponding
ratio for Case 2; as well as an equality between the ratio of hous-
ing expenditure to index number of housing costs for Case 3
and the corresponding ratio for Case 2. For short, I shall call
such equality “physical” equality, since it is the nearest approach
to strict physical equality we can get and would be absolute
equality if the price relatives which are averaged to make the
index numbers, F’s and R’s, were all equal. In short, we have
selected our two Oddland families so that, so far as is possible in
the two different markets, they match the Evenland family Case
2 (Case 1 matching it as to food and Case 3, as to housing).
*See my The Making of Index Numbers, Appendix III.