Welfare-optimal patent royalties when imitation is costly

- Model of invention, imitation, Cournot competition, litigation and royalty payments.
- Welfare-optimal compulsory royalty yields aggregate zero-profit duopoly or no entry.
- Optimal royalty yields higher welfare than prize system for low enough invention cost.
- Fixed or per-unit royalty may be negative, so courts may not enforce using tort law.
- Total royalty payment may be negative, so patentee would not credibly litigate.

We identify welfare-optimal patent royalties in a model of costly imitation, entry and imperfect competition. When the social planner may impose a compulsory license, optimal royalties either blockade imitation, facilitating unregulated monopoly, or yield an aggregate-zero-profit efficient duopoly. When duopoly is optimal, the optimal per-unit royalty pins the equilibrium price at the aggregate average cost and the optimal fixed royalty shifts surplus so the patentee and imitator break even. Efficient duopoly yields higher welfare than monopoly for sufficiently low invention cost, and may also yield higher welfare than a prize system. Interestingly, royalty payments may be negative. Because of this, efficient duopoly may not be feasible if the planner must instead direct the courts to use such royalties.