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APPENDIX

amount of the produce which results from the application of
# units of outlay to a given area of land. The unit of outlay
may, as stated before, be conceived of as a definite number
of days of labour by one man aided by a given amount of
capital, or as the labour, etc, purchaseable by a definite
pecuniary outlay, that is, we may conceive of the outlay as
effort or under the form of money outlay. The expression
for the rent-yielding capacity of the land is
J) — xf),
x having the value corresponding to the position of N in
Fig. (xi), or, to express the same fact otherwise, f(#) having
the value CN/ON, the tangent of the angle made by OCE
with Ox.
If we conceive of the outlay as an outlay of actual effort
and sacrifice, labour and capital, in amount measured by the
length of the abscissa of any point on the produce curve,
then the rate at which further outlay would add to the
produce, when the actual outlay is x units of labour and
capital, is f(x) per unit. The payment of labour and
capital at the rate of this marginal productivity requires x. f(z)
units of produce. The remainder f(#)—x.f1(2) is the rentyielding
 capacity of the land.
A striking proposition is that expressed by Mr. Wicksteed
in his discussion of the problem of distribution. We state it
in a partial form as follows. Let P be the value of the product
of / units of land, w units of labour, and ¢ units of capital, so
that

P=e(l.w.c.) . . . . . (vii)
expresses the relation of the product to the factors of production.
 Then, for some kinds of production, the increase of
land, labour, and capital in exactly the same proportion will
result in an increase of product in that same proportion, or
mP=g(ml.mw.mec) . . . . (viii)
where 72 is a numerical multiplier. If # be not far from
unity, this proposition may be true for kinds of production
for which it is not true for all values of #.
Where these conditions (vii) and (viii) hold, a well-known
proposition in Differential Calculus gives the result (since ¢
must be a homogeneous function of /, w, ¢)
7%. dp do
P=/. at? a, te
or, the assignment, to each of the factors of production, of