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