162 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK 
In order to extract from the figures for prices and budgets 
some of the want schedules of our imaginary typical families, I 
allot to the three Cases such incomes as will result in (a) the 
selection of the same, or equally desirable, food rations in Cases 
1 and 2 and (b) the selection of the same, or equally desirable, 
housing accommodations in Cases 2 and 3. Thus Case 2, in 
Evenland, resembles Case 1, as to food (but not as to housing) 
and resembles Case 3 as to housing (but not as to food). By 
means of these interrelationships, Case 2 acts as a go-between 
connecting Case 1 and Case 3. These interrelations afford the 
essential basis for the method employed. 
Notation 
Let the total expenses or sums of money spent on the family 
budget in Cases 1, 2 and 3 be respectively S;, Sz, Sz (the letter S 
standing for Spent or Sums). Let the percentages of these sums 
spent for food be ¢i1, pa, $s the letter ¢ suggesting food and 
Greek letters being used for all budget percentages. Similarly 
let the percentages spent for rent be pi, ps2, ps. Similarly, let 
the price index of food in Oddland, 7.e., for Cases 1 and 3, be F; 
or its equal F;3 (since, of course, being in the same market, they 
are assumed to be the same) and in Evenland, F,. Likewise let 
the price index of rent be RR, or its equal Rj, in Oddland and R. 
in Evenland.® 
Thus, in short tabular form, we have the following symbols to 
consider: 
Lol Tents Si, Ss, Ss 
% for food: ¢1, ds, ¢3 
Food Price Index: Fi, Fs, Fj; (Fy, = Fs) 
% for rent: pi, pz, ps 
Eo it Price Tadee: 22. I, I, (Ris Ih) 
The Problem 
Our chief problem is to measure, or compare, the families’ 
want-for-one-more dollar in the three Cases. We shall also 
measure the want-for-one-more unit of food, and the want-for- 
one-more unit of shelter. 
Let us designate by W;, the want-for-one-more dollar in Case 
t I realize that it seems a wasteful notation to use two symbols F. and 
Fs to mean the same thing, as also R, and Rs, as the same price levels 
apply to both Cases 1 and 3. But after trying other notations, I con- 
cluded that there was a valuable mnemonic advantage in using a sub- 
seript 1 for every symbol associated with Case 1 and likewise 2 and 3 
for Case 2 and Case 3 respectively.