184 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK 
13314 and F3 120 or 150. Even so, the formule slightly modified 
would apply if the statistics for F; and F; were separately 
available. 
(e) Constant ratio between the income and expenditure, of any 
family, i.e., either exact equality of income and expenditure or 
more generally, a slight excess of income over expenditure, that 
excess being the same percentage for all Cases. This assumption 
is chiefly for convenience in order that for the budget ratios, the 
¢’s and p's may, except for a constant factor, be applied inter- 
changeably to expenditure or income. Most actual budget sta- 
tistics conform approximately to this assumption (in its second 
form) of a slight excess of income over expenditure. 
These five assumptions—of (a) adjustment, (b) comparability, 
(c) dependence of each want only on the provision for that want, 
(d) equality of price indexes (F1=F3 and Ri=R;), and (e) con- 
stant ratio between income and expenditure, include all we need 
in order to solve our problem, provided, of course, that, as first 
stated, our statistics are reliable. The method merely interprets 
budget behavior under these five assumptions. 
If the underlying assumptions just discussed are correct and 
if the statistical data employed are accurate, the method here 
presented and its results are unassailable. 
Perhaps more space has been consumed in setting forth the 
problem and the method of solving it than may seem necessary to 
some of my readers. But I am anxious, in thus breaking new 
ground, not to conceal or overlook any possible difficulty. If the 
method here proposed is some day to be practically utilized, as I 
hope it may be, those using the method need to know exactly what 
are the possible pit-falls and sources of error. 
Some General Formule Derived 
Thus far only two formule, or two pairs of formule, (1) and 
(2), have been reached. 
More important are certain formule derivable from these four. 
Dividing the lower of the equations (1) by the upper, just as they 
stand, we get: 
Ssps Sep2 
Bs _ BE. 
Sir Sate 
Fy Fy