A STATISTICAL METHOD FOR MEASURING ‘MARGINAL UTILITY’ 169
Given Sa: = $600 = Total dollars spent by Case 2.
From tables ¢; = 509, = 9 for food by Case 2.
Multiplying, S:¢2 = $300 = dollars spent for food by Case 2.
Given Fy; = $1 per “Ib.” = Index No. of food prices,
Case 2.
Measure of food, Case 2.
Dividing,
S58 _ 300 “Ibs.”
5
Nn _ 300 “Ibs.
$1.33 per “r
2400
409,
$1000
Same as
= Measure of food, Case 1.
= Index No. of food prices, Case 1.
= dollars spent for food by Case 1.
% for food by Case 1.
Total dollars spent by Case 1.
Likewise, to get Ss, the total spent in Case 3, we proceed as
follows:
Given S; = $600
From tables ps = 209,
Multiplying, Sap» — $120
Given R; — $1 per sq. ft.
Sapa
Dividing ~~ “p-= 120 sq. ft
Same as = 2. = 120 sq. ff
3
$3 per sq. ft.
Tay
7
= Total dollars spent by Case 2.
= 9, for rent by ro 2.
dollars spent for rent by Case 2.
Index No. of rent prices,
Case 2.
Measure of Housing, Case 2.
= Measure of Housing, Case 3.
Given
Multiplying,
From tables,
Dividing,
= Index No. of rent, Case 3.
= dollars spent for rent by Case 3.
9 for rent, Case 3.
ral dollars spent, Case 3.
||
Comparison of Case 1 and Case 3
We have now found S; and S; through the intermediation
of S;. We note that both 8; and Sz are in the same country,
Oddland, and under the same prices, F; (or its equal F3) of
food and R; (or its equal R3) of house rent.
Thus we have four results from our four chains of cal-
culations:
S:=$1,000;
Sa=—81.440:
a}
LE
Wi=.75
Ws— 331k
According to these figures (which, of course, are based on
hypothetical rather than actual statistics for the F's, R’s, ¢’s,
p’s), if one family in Oddland has an income of $1,000 and
another has 449% more, the latter's valuation of each dollar
is 55 5/9% less.
Chart IT shows this result by two points, one for Case 1, the
“latitude” and “longitude” of which are respectively income
and want-for-one-more dollar (namely S:=8$1000, W,=.75