A STATISTICAL METHOD FOR MEASURING ‘MARGINAL UTILITY’ 171 
wantabs), and the other for Case 3, the corresponding 
coordinates, or “latitude” and “longitude,” of which are 
S;—=$1440, W3=.3314 wantabs. 
These two points are only two out of an indefinite number 
of points which may be supposed to constitute, or lie on, a 
curve expressing the law by which the want-for-one-more dollar 
diminishes in relation to the increase of the number of dollars of 
income available. This curve is none other than the curve of 
“marginal utility” of money in relation to the size of one’s income, 
often described in text books of economics but never, hitherto, 
envisaged as, even theoretically, derivable from statistics. The 
slope of such a curve, if ever reliably ascertained, would enable us 
to determine a juster system of income taxation than that now in 
vogue based purely on arbitrary judgment or guesswork. 
Important Equations 
The nub of the matter lies in the equations signifying that 
Cases 1 and 2 are alike as to food, while Cases 2 and 3 are alike 
as to housing. These equations (in the opposite order in which 
they were found) constitute the following two sets: 
Sigs 
F 
S-- 
h 
NS 
WF, = WF) 
WiR;, = JIE 
2) 
What has been done is to solve these four equations to obtain 
the four unknowns, W,, Ws, S;, Ss, assuming S, and W, as known, 
the former in dollars and the latter being, for convenience, taken 
as the standard for measuring wantability since no other unit 
has previously been established. 
Equations (1) signify that the physical food rations of Cases 1 
and 2 are alike and that the physical housing accommodations of 
Cases 2 and 3 are alike. 
Equations (2) signify that the marginal wants for like food 
rations are alike (for Cases 1 and 2) and that those for like 
housing accommodations are alike (for Cases 3 and 2). 
A, 
Ro 
Assumptions Underlying Equation (1) Re-exzamined 
But, before going further, it will be well to review critically 
the hypotheses on which the foregoing reasoning fundamentally