APPENDIX

[ dealing with the relation of the amount of a commodity
for which there is a demand at any particular price, and
that price, reference was made on p. 25 to what constitutes a
complete knowledge of the state of demand. Expressing
the matter in a symbolic form, let x be the number of units
of a commodity for which there is a demand when the price
is measured by » units of purchasing power. Then,
corresponding to each possible value of y, there will be a
definite value of x A complete knowledge of demand
would comprise a knowledge of all such pairs of values of x
and py. The changes in the value of x which result from
small changes in the value of y are, at any rate when the
demand of a large market is under consideration, small.
The fact that the value of x is in some way connected with
the value of ¥ can be expressed in the form
=f . . . . . ..@
If the amount demanded increased in precise proportion
to the fall of price from some definite level, the equation (i)
would take the form
VY =C— ML.

As a rule, however, we cannot assume that the relation
is so simple as this. Nor can we obtain exact knowledge
of the form of the function indicated by f(x) in equation (i).
If we had that knowledge, the complete expression of the
state of demand, referred to above, would be provided.
Though unable to state the form of the relation between
y and x with precision, we can state two things about the
equation (i). For each value of one of the variables there
is only one real value of the other, to each x there is only
one appropriate value of y, and wice versd. Further, the
larger x is, the smaller will y be. The value of f(x) decreases
as x increases. In the language of the Differential Calculus,
2 or f}(x) is negative for all values of x. This is the expression
 of the principle enunciated in the middle of p. 22,