106 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK

of X to expand while the fall in the price of Y would, since its
supply curve is negative, cause the quantity of Y to expand also.
But since Y’s negative elasticity is unity while X's positive
elasticity is now .9, this would mean that the quantity of Y
would tend to increase more rapidly than that of X, and hence its
marginal productivity would continue to fall and that of X
would continue to rise, so that the supply of Y would be continuously
 increasing faster than X, and there would tend to be a
cumulative increase in the remuneration of X and a corresponding
 fall in that of Y. Under these elasticities it might be thought
that there would not be stable equilibrium. But the outcome
depends on the type of productivity equation which is assumed,
for its partial derivatives furnish the demand curves for the
factors whose intersections with the supply curves determine the
point of equilibrium.
If, however, the negative elasticity of the one were equal to
the ultimate positive elasticity of the other, after the initial
alteration in productivities developed, there would be no further
alteration of the equilibrium
 since the increase in
quantity would be the
same for both.
If the final positive elasticity
 were to be higher
than the negative elasticity,
 then there would
be a counteracting force
tending to bring the relative
 returns nearer even
to the original level than
that which would result
from equal elasticities.
Where both supply
curves are negatively inclined
 (Figure 21) there are further possibilities of unstable equilibrium.
 Thus, if the supply curve of one factor X is to shift
to the left, so that less will be offered at the same price as before,
then the increase in payment to X will cause its supply to contract
 while that of Y will expand. This will in turn mean a still
oreater increase in the marginal productivity of X and a further