combination, and the vertical or Y distances, the corresponding total physical output of the group. In graphic terms the point where diminishing returns begin is the point (3) where this curve becomes tangent to a straight line through the origin. Less than this proportion of the variable agent cannot intelligently be employed even if it is free, for the output could be increased by discarding a portion of the other factors, if no more of the variable one could be obtained at a uniform price. It is true, necessarily and a priori, that there is such a point on the curve, that for less amounts the product increases in greater ratio than the factor. That is, for any point on the curve between this point (3) and the intersection of the curve with the X axis the tangent must cut the X axis positively. Now, if below this point (3) the tangent to the curve cuts the positive X axis, if at this point it passes through the origin and beyond this point it cuts the positive Y axis, then manifestly the curve is concave downward at the point in question. And this is the graphic condition representing decreasing increments of product. It seems reasonable to assume that the same condition (concavity downward) holds from point 3 to the maximum point (4), but this is not demonstrable a priori. If it is untrue for a certain stage in this interval between points 3 and 4 over the whole field of industry, as represented by the dotted line in the figure, there is indeterminateness in the competitive situation in that interval and to that extent, but this is a rather incredible supposition.
It is immaterial what shape the curve has below point 3 so long as its tangent always cuts the X axis. No doubt in any one industry the curve will show stages of increasing returns interspersed with stages of decreasing returns, and various proportions of combination of the factors are wise and stable.[1]
- ↑ It is to be noted that we must assume the size of individual establish- ments to be nearly a matter of indifference. The above reasoning proves also that the curve itself cuts the X axis
