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APPENDIX

may be determined, and then the corresponding y may be
found from either of the equations (i) and (ii).
The above deals with the equilibrium of aggregate supply
and demand. A brief consideration of the relation of
individual producers to the aggregate supply will be of
interest.
Let us take the case of three producers for illustration.
The method may be applied to any number whatever. Let
the supply equations of the individual producers be
y=o)h y=02), y=04x) . . . (iv)
Let the amounts supplied at the price y be #, z, Zs,
respectively in the case of these three. The supply equations
may be solved in the form
“=F(9), =F), =F») . .
The aggregate supply x=, +,+;, or
=F (0)+FnN+F(p) . . . . (vi)
This equation may, in turn, be solved for y in terms of x,
yielding the result
y=0(1),

the aggregate-supply equation, which is to be taken with the
demand equation to determine the equilibrium. When, by
means of the equations of aggregate supply and aggregate
demand, the equilibrium value of y has been determined, the
values of x, x, 2; are given by the equations (v), that is,
the individual contributions of the separate producers are
determined.
It is clear that the method may be extended to any
number of producers, and may be applied to the demand
side of the problem as well as to the supply side, that is, a
composite demand may be handled as well as a supply by
many competitors. It will be observed that the price y
secured by each producer has been taken as the same, in
accordance with the assumption of free competition in open
market. Where the separate producers supply separate
markets, they have independent demand equations to be
associated with their individual supply equations.
In Fig. (v), the above is presented in the diagrammatic
form. The curves Ss, S,5,, S,s; are taken to represent the
supply conditions of the three producers. Across the three
a line 1p, p,4,P is drawn parallel to Ox, cutting the three
curves in gy, py, p, respectively. On this line a point P is taken