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