Law of Returns: For any factor F, where the quantities of the other factors remain constant, there exists an optimum quantity of F beyond which any additional units will yield a diminishing average return.

 The law of returns can be established by what mathematicians call an indirect proof—that is, by assuming the law to be false, and then showing how that assumption leads to a contradiction or absurdity. Suppose that, contrary to the law, the average return either remains constant or else increases indefinitely after f increases past a certain point f0. Past this point, therefore, repeated increments f in factor F, with no additional input of the other factors, will continue to produce increments c in the production of consumer good C such that c/f is greater than or equal to the average return at f0. Such continuing production from increases in F alone, however, implies that good C is generated by just one scarce factor—a circumstance shown to be impossible at the beginning of this discussion (p. 4.4:42). Q. E. D.

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