A STATISTICAL METHOD FOR MEASURING ‘MARGINAL UTILITY’ 163 
1, and similarly as to W; in Case 2, and W3 in Case 3, thus add- 
ing three more symbols to the previous list, namely: 
Want-for-one-more dollar: Wy, W., W3 
Pa 
Ra J 
The larger the income available, the more and better will be 
the food and shelter obtained. Changes in quality will, under all 
ordinary circumstances, accompany changes in quantity so that 
to designate the quantity would practically be sufficient to com- 
pletely determine the entire character—quality as well as quan- 
tity—of the ration used. For convenience, therefore, we need 
pay no attention to the accompanying changes in quality but may 
give attention only to changes in quantity,—the number of 
pounds of food used; likewise we may describe housing by a 
quantitative index, say the number of square feet of floor space. 
These somewhat naive methods of picturing the matter can be 
revised later, as we approach the practical statistical problem. 
All that is meant here is that, for convenience in thought, we may 
distinguish the housing conditions of our three families exclusively 
on the basis of floor space. A family of five occupying a tene- 
ment of 2000 square feet has, naturally, a better, as well as a 
larger, housing accommodation than one occupying a 1000 square 
feet tenement; but the housing conditions for such a family are 
sufficiently specified and determined by specifying the number of 
square feet used. 
Again, to fix our ideas, let us think (also somewhat 
inaccurately) of the index number Fy, or its equal Fj, as the 
average price of food per pound in Oddland, and likewise Fs, as 
the average price of food per pound in Evenland. Similarly R; 
(or its equal Rj) is taken as rent per square foot in Oddland, and 
R, rent per square foot in Evenland. 
Since we shall only need the relative magnitudes of Fy (or Fs) 
and Fs, we shall, for simplicity and convenience, assume that the 
Evenland average price of food, Fs, is $1 per pound, while, 
similarly, R,, is $1 per square foot. 
Calculating Wy and Ws from Ws 
It is now possible to calculate S; from S, or vice uersa; and Ss 
from S, or vice versa. 1 shall start with S, and from it calculate 
S: and Ss, and likewise, starting with Ws, calculate W; and Ws. 
We thus measure Oddland’s four magnitudes in terms of Even-