How to license a downstream technology when upstream firms are constrained?

In this paper, we study the relationship between capacity constraints and licensing strategies. To do so, we focus on the licensing strategy of an outside innovator who licenses a process innovation to the downstream sector of a vertical Cournot oligopoly. Downstream firms source an essential production factor from a capacity constrained upstream sector. In this setting, we show that the innovator optimally licenses large innovations via per-unit royalty contracts and small innovations via fixed fee contracts. Moreover, an increase in the strength of the capacity constraints makes it more likely that the optimal licensing contract includes a strictly positive per-unit royalty rate. As a final point, we discuss the relationship between capacity constraints and the social optimality of the innovator's licensing strategy as measured by aggregate welfare or the diffusion of the innovation on the downstream market.