168 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK 
ing that number of dollars by Fs, representing the price of food 
in Case 2. The result is Ss, Numerically this result (since we 
2 
suppose Fo, the average price of food in Evenland, to be $1 
a ‘“pound’”’) becomes $300—$1, or 300 “pounds,” or food units. 
We now cross over the sea to “Oddland” and study Case 1. 
As stated in our hypothesis we have assigned to our family, Case 
1, the same number of food units as in Case 2. Or, to be more 
exact, we have allotted to Case 1 such an income as would lead 
it to choose of its own free will (in view of all the costs of living 
for food, clothing, housing, and all the rest obtaining in Oddland), 
the very same (or equally desirable) food as Case 2 buys in 
Evenland (at quite different prices and out of a quite different 
income). It follows that the food of Case 1 must be also 
300 lbs. Algebraically expressed the food of Case 1 is i 80 
1 
that Sir 300 “pounds.” 
From this we can compute S; as soon as we know ¢; and Fi. 
We know that Fi, by hypothesis, is $1.33%5; 1.e. 
F,1=%$1.3314, 
Multiplying this by the last result, namely 
Se — 300 we obtain Sip; = 400. 
which is the money paid for food by Case 1. 
We next find ¢;. The family budget tables in Oddland show, 
let us say, that a family which spends $400 for food is one 
which spends thereon 40% of its total expenditure; that is, 
$1—.40. 
It is now evident that the total expenditure in Case 1 can 
readily be found by dividing the expenditure for food 
Sih; — $400 by ¢1 = 40 giving S; = $1000. 
er 
Thus, beginning with S,—=$600, we have ended our chain of 
calculations with a figure for S;, which was the object of our 
search. That is S;=¥$1000. 
The above process, or chain of calculations by which S; is 
found from S.. may be tabulated as follows: