APPENDIX

315

payment at the marginal rate of its contribution to the
product, exhausts the total product.
Where increase of production proceeds by the increase of
different factors of production in differing proportions, the
above proposition does not cease to have importance, The
assumption of unchanged modes of production, if made, may
be held to include the association of different factors of
production in uniform proportions wherever that is possible.
But the advance from less to more intensive cultivation of
land, under pressure of growing demand for raw products,
implies the increase of other factors of production in greater
degree than the land to which they are applied is increased.
Thus the amounts of labour and capital, mw and wc, are
associated, not with #/ units of land, but with units, If mis
greater thanunity,e(/. mw . mc) will be less than g(m/. maw . mc),
unless land is so plentiful in relation to the available labour
and capital that additions to the latter are needed to
develop the full powers of the land actually in use. Hence,
in new countries, increasing returns to labour and capital
applied to land are found, and, in old countries, decreasing
returns.
The expression f(x) ~x. f(z), obtained above as a representation
 of rent, states rent as a residue. The expression
7 2 in equation (ix) is equated to terms representing just

what the f(x) —x. f(x) represented in the preceding. Thus
an expression for rent, representing it in similar form to the
remuneration of other factors in production, is secured. Now
a .
2 represents the rate of decrease of product resulting from
concentrating on a smaller area the productive efforts
applicable to a larger area. Hence the statement, that
the rent of / units of land is / 2 merely means that production

 is supposed to be so organised that the reduction of
output, caused by such concentration, is just balanced by the
consequent saving in cost of hire of land.
The problem of joint supply may be expressed conveniently
 in algebraic terms. Let x be the amount of
commodity A which is produced in the same process as
the amount z of commodity B, and let y be the joint
expenses of production of these amounts. The demand
price for the amount x of A being y,, and the demand price