Patent Licensing and Capacity in a Cournot Model

We consider the problem of patent licensing in a Cournot duopoly in which the innovator (patentee) is one of the firms and it is capacity constrained. We show that when the patentee can produce a relatively small (relatively large) quantity, it prefers licensing by means of a fixed fee (unit royalty). When the patentee can set two-part tariffs in the form of combinations of fixed fees and unit royalties, it charges a positive fixed fee if and only if it is limited to producing a relatively small quantity. We also show that with combinations of fixed fees and royalties, the royalty rate is lower than is true for the standard case.