
doi: 10.1086/260762
In a recent paper, Franklin Fisher and Peter Temin (hereafter F-T) attempt to disprove the logic of the Schumpeterian proposition that industrial concentration would increase industry's R & D output given the existence of increasing returns to scale to R & D activities with respect to research input and firm size. They also intend to show that past tests of the Schumpeterian hypothesis have been inappropriate. In order to do so they develop a model of a profit-maximizing firm engaged in both R & D and other productive activities. After determining what they believe are necessary and sufficient conditions for profit maximization they show that those conditions do not necessarily imply the required relation between the firm's size and its R & D output. Unfortunately, F-T only looked at local profit-maximization conditions and did not realize that their assumptions require that the firm earns negative profits from its R & D activities. While F-T are careful in stipulating and using the second-order conditions for profit maximization (to the extent that the last sentence in their paper reads: "One cannot do comparative statics without second derivatives" [1973, p. 70]), they overlook that local profit maximization does not imply positive profits and that no profit-maximizing firm would engage in an activity that yields negative profits. It follows that no profit-maximizing firm will choose to be at the equilibrium described by F-T and therefore that all of their results in the paper, based on comparative static analysis around that equilibrium, are invalid.
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