depending on the length of the productive process38). It is only with respect to factors of production
which are articles of exchange that the proposed law of remuneration, the “law of marginal
productivity,” is fulfilled in a regime of competition. Thus, in our typical example of black men
assisting white men to catch seals, what the black man gets in a perfect market is an amount of seal
equal to the number of units of service which he supplies, multiplied by the quantity of seal for the
sake of which he is just induced to offer an additional unit of service, the unit employed being a
small quantity. Likewise, what the white man gets in exchange is an amount of service equal to the
amount of seal which he distributes to the black man, multiplied by the quantity of service for the
sake of which he is just induced to offer an additional unit of produce. If the amount of service
rendered may be taken as the measure of the black man's labour (or of some other factor of
production supplied by him), the proposed law holds good for his share of the distributed produce.
But, as the amount of produce given by the white man in exchange for services cannot be taken as
the measure of his work, the proposed law does not hold for his share of the distributed produce.
This discussion will appear otiose to the economists who are not conversant with the science
of quantity. The proposition that the remuneration of the entrepreneur is equal to the amount of his
work multiplied by its marginal productivity will be interpreted by them as signifying simply that
he will get more, ceteris paribas, the more work he does and the greater the addition to the produce
which he would effect by doing a little more work. For them a product will do duty for a function
of two variables which increases with the increase of either variable. But this easy interpretation is
not open to mathematical economists. They must be aware that the formulae in question affirm some
thing more than the simple truth just stated. If nothing more than that simple truth can be deduced
from the theory of Exchange, it ought not to be a matter of surprise that the “law of marginal
productivity” applied to the entrepreneur should be challenged by those who affect mathematical
precision.
The law of marginal productivity, then, is not fulfilled in the sense that the portion of the
national dividend accruing to entrepreneurs is a sum of terms each of which is the product of an
entrepreneur's work reckoned in hours, or similar doses, and the marginal productivity of a dose
(multiplied by a certain coefficient). Let us see whether the law is fulfilled when we take a larger
dose, the total work of an entrepreneur. The law will then be fulfilled if the net gains of any
entrepreneur tend to be equal to what society would lose if he were removed. Can this be generally
affirmed? Let us look at the typical case of distribution between whites and blacks above instanced.
It may be granted that the white entrepreneur does not normally obtain more than he adds to the
common stock. For otherwise the society would gain through his removal, his black assistants eat
er hunting by themselves or being taken on by other entrepreneurs. And neither of these suppositions
is possible in a state of equilibrium; for, if either were possible, it would have been already brought
about by the free play of self-interest, in a regime of competition. The gain of a white man, then,
cannot be greater, but where is the proof that it cannot be less, than the loss which would be
occasioned to the society by his removal?
Such a proof might be forthcoming if the white men were not, as hitherto supposed, genuine
entrepreneurs, but managers acting under entrepreneurs of our third species, the stockholder. The
income of the managers will fulfil the marginal law of productivity if the new entrepreneurs are
conceived as competing against each other in such wise as to bring about the result that no manager
38. Remark that the correction proposed by Professor Barone for the effect of time is not identical
with Professor Marshall's accumulation of price.