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