The Test which Inventions Must Pass: A Correction - Fellner, William (Quarterly Journal of Economics, 1952)
Section II of my article published in the November 1951 issue of this Journal describes an analytical framework for testing inventions, and it contains a statement on the minimum requirement which inventions must satisfy to pass the test in the sense of being promptly adopted as industrial innovations. Criticism expressed by Mr. Alvin Marty has made me realize that the true minimum requirement is more severe than that which I have suggested. I said that the in the marginal cost curve, which occurs at the output where old variable cost becomes equal to new total cost (Figure 3, p. 563), must have shifted to the left sufficiently to make the lower limit of the gap (point D) lie on or below the MR curve. In reality the gap must have shifted to the left sufficiently to put D below MR by at least a distance such that the area bordered by SM, MR, and LM (new) be no smaller than the area PDC. If MR goes through the gap in such a way that the two areas, which on linear assumptions are triangles, are just equal, then the choice between producing at the MR-SM intersection, with the original method, and the MR-LM (new) intersection, with the improved method, will be a matter of indifference to the producer. Expanding from the MR-SM intersection to the output corresponding to the C-D gap causes a loss measured by the area lying between SM and MR in this output range; and further expanding from the C-D output to the MR-LM (new) intersection causes a gain measured by the area lying between MR and LM (new) in this output range. The italicized condition, supra, means that the gain area is no smaller than the loss area.' It remains true of course that any output beyond the C-D gap will be produced by the new method, if it is produced at all. But the output corresponding to the C-D gap and the outputs lying in a definite zone around the gap, will never be produced. This buffer zone extends from the MR-SM intersection to the MR-LM (new) intersection at the time when the test becomes satisfied.2 A producer who maximizes his profits, subject to the inequality here in question, wvill always jump over this zone.