302

APPENDIX

indefinitely, takes the position of the tangent to the demand
curve at the point P. Let this tangent cut Oy at the point
T, and draw PL parallel to Ox.
The elasticity of demand at P is defined as the ratio of
oh to o where Qz is parallel to NM. That is to say, the
elasticity of demand is
Qn PN_PN OQn_PN_ PL_PN
PLP» PL Pz PL TL TL
or the ratio of OL to LT measures the elasticity of demand
at P. If TP be produced to meet Oz in ¢# this ratio is equal
to that of zP to PT.
{n terms of the symbolism of equation (i) this ratio is that
of f(#) to x.fX x). The consideration of changes in the
zlasticity of the demand for different commodities, as supply
changes, referred to on p. 26, may afford useful hints in the
drawing of suitably-shaped demand curves.
Just as the relation of amount demanded and the corresponding
 price is expressed in equation (i), so can the variation
of the amount of supply with corresponding supply price be
=xpressed in a similar equation
y=o(x). . . . . . . (iD

In regard to this equation, however, we cannot lay down
any such universal rule as that relating to the amount demanded
 and its price. To represent a supply price per unit
which is the same whatever the scale of production, the
zquation becomes
ys
 being independent of x,
To represent a supply subject to the conditions of increas-Ing
 cost or decreasing returns, we must have y increasing as
r increases, while, in the case of increasing returns, y decreases
as x increases. In the former case ¢'(#) is positive, in the
.atter negative. In not a few cases, p!(+) will be positive for
some values of x, negative for other values. As with demand,
so also with supply, there may be drawn a curve, to represent
the relation of x to y which is stated in algebraic form in
equation (ii). In Fig. (iv) the curve Ss is drawn representing
conditions of decreasing returns. On the same diagram, a
demand curve D2 is drawn. If these curves present the
conditions of supply and of demand respectively for the same
commodity, and if they intersect in P. and an ordinate PN be