A STATISTICAL METHOD FOR MEASURING ‘MARGINAL UTILITY’ 167 
two supposed Cases in Oddland, they value the dollar differently 
in the ratio of 100 to 44 4/9. 
Calculating S; and Ss from Ss 
Evidently this contrast in the valuation of the dollar is not 
due to any contrast between the two families, since by hypothesis 
they are as like as two peas, but is due entirely to the contrast 
between their economic circumstances. But, up to this point, 
the only signs of this contrast in their circumstances are indirect ; 
the hypotheses as made, imply differences in their circumstances 
in prescribing that Case 1 chose the same food as Case 2 at food 
prices only a third greater, while Case 3 chose the same housing 
as Case 2 at housing prices three times as great. If, as compared 
with Case 2, Case 3 could thus afford to pay much more for the 
very same sort of tenement while Case 1 could only afford to pay 
a little more for the very same sort of food, it certainly looks 
as though Case 3 were richer than Case 1. What we want to 
know next is: How much richer is Case 3 than Case 1? Our 
next problem, then, is to find out what were the total incomes’ 
or expenditures, S; and S; of Case 1 and Case 3. 
We can calculate S; and S; from S, by chains of reasoning 
analogous to the two chains of reasoning by which we have just 
calculated W; and W3 from Ws, although our new pair of chains 
consists of a larger number of links. 
Our first link is assumed. It is that S.=$600. 
The second link is ¢s, the percentage of Ss spent by Case 2 for 
food. This percentage is readily found from the budget tables. 
Suppose it to be 50%. That is, the budget tables of Evenland 
show that in a family there which has an income and annual 
expenditure of only $600, 50% thereof is spent for food. 
Our third link is the same thing—the food expenditure of 
Case 2,—but expressed in actual dollars. We find this, of course, 
simply by multiplying S, by $2. The result is S; ¢, or, in 
figures, $600} .50=$300, spent for food by Case 2. 
The next step is to ascertain the number of food units 
(“pounds”) thus bought for S.¢, dollars. This is found by divid- 
RT assumed, that budgets balance in all cases, income being equal 
to expenditures or, if we wish to be more realistic, that income exceeds 
expenditures in all cases by a fixed percentage, say 10%, as savings.