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.