92 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK 
increase of P P; in return per unit. When the elasticity of X is 
less than unity of .50, then its unit rate of return tends to be 
somewhat above P; and that of Y will be somewhat below. X 
will still have gained but not as much as when its elasticity 
was 0 and that of Y was still 1.0. 
The computations which have been made by Mr. Wilcox indi- 
cate, moreover, that for the productivity surface assumed * X now 
has a slightly larger share of the joint product than before the 
increase in the effectiveness of industry took place. 
If we follow out other illustrations of varying elasticities it will 
be seen that X's gain at zero elasticity will be greater if Y has 
an elasticity of 2.0 than if it has 1.0, for Y in the former case will 
increase twice as rapidly as in the latter, and hence the original 
proportions between X and Y will be more disturbed and the 
marginal productivity of X still further enhanced. Similarly, 
although X will gain less when its elasticity is .5 rather than 0, 
while that of Y is 1.0, it will plainly gain more if Y’s elasticity is 
4.0, than if it is 1.0. 
The conclusion then is clear, that when we are dealing with 
positive elasticities the factor with the least elastic supply gains 
most from an expansion in production, and that it gains the 
more, the more elastic is it rival factor. In the case of the par- 
ticular productivity surface noted above it seems also to be true 
that this holds for relative shares .of the total product as well 
as for payment per unit. 
The problems which arise out of negatively sloping supply 
curves are, however, still more fascinating. Thus, let us assume 
a situation where we have one positive and one negative supply 
curve, but where the elasticities themselves are equal as is repre- 
sented in Figure 11, where unit elasticity characterizes both X 
and Y. The relative supply of both X and Y in the original 
equilibrium is represented by A and the relative price paid 
to each by P. Then an increase in the effectiveness of industry 
would initially raise the return to each above P to, let us say, 
P,. But this, in the sequence now familiar, would cause the 
supply of X (since it is negatively elastic) to contract to B, while 
that of Y would increase by an equal amount. Since the supplies 
of the two factors would thus move in opposite directions, the 
KXitayYl-a 
L 7 = TE where Z is the total product.