A note on Schumpeter’s innovation hypothesis

ABSTRACT

This note reveals that while the monopolist has ideal incentives to innovate, consistent with Schumpeter’s original hypothesis, the oligopolist’s incentive to innovate is non-monotonic in its market share and approaches that of the monopolist in the limit as the number of identical firms grows large. Numerical simulations indicate that the incentive to innovate for the relatively efficient oligopolist exceeds 83% of that of the monopolist. These findings may help explain why the purported relationship between innovation and firm size has defied consistent empirical validation.

KEYWORDS:

• Schumpeter
• innovation
• oligopoly
• monopoly

JEL CLASSIFICATION:

• L11
• L13 L25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ See Scherer (1992) for a review of the literature and McCraw (2007) for historical context.

² The empirical evidence is mixed on Schumpeter’s hypothesis. See AMC (2007), Nicholas (2003) and Cohen and Levin (1989).

³ The sufficient second-order condition for an optimum is satisfied since $-c_{II}\times Q-{\psi }_{II}<0$(strict concavity).

⁴ Arrow (1962) recognizes that the incentive to undertake cost reductions increases with output.

⁵ As$N\to \mathrm{\infty },$industry cost-reducing innovation is fully appropriated through market price adjustments.

⁶ The upper bound is 15% for N= 4 (not reported).