The monopolist’s incentives towards product proliferation are evaluated in an optimal con- trol model considering three alternative regimes: profit-seeking; social planning; and a hybrid case with monopoly pricing and a regulator setting product innovation to maximise welfare. In equilibtium, the profit-seeking firm supplies a socially suboptimal number of varieties to reduce cannibalisation while the social planner exploits the same effect to sat- isfy consumers’ love for variety and decrease the market price of all products. In terms of the Schumpeter vs Arrow debate on the relationship between market structure and innova- tion incentives, the results obtained in this model have a definite Arrovian flavour.