Add to ORKGArrow (1962) showed that a secure monopolist (unconcerned with preemption) has a weaker incentive than would a competitive firm to invest in a patentable process innovation. This paper shows that the ranking can be reversed for product innovations. Only the innovator sells the new product, a differentiated substitute for the old. Under alternative market structures considered, the old product is sold only by that same firm (two-product monopoly), only by a different firm (post-innovation duopoly), or in perfect competition. In an asymmetric Hotelling model, the innovation incentive under monopoly is greater than under duopoly if and only if the new product has the higher quality, and is always greater than under perfect competition.