For an outside innovator with a finite number of buyers of the innovation, this paper compares two licensing schemes: (i) fixed fee, in which a licensee pays a fee to the innovator and (ii) ad valorem profit royalty, in which a licensee leaves a fraction of its profit with the innovator. We show these two schemes are equivalent in that for any number of licenses the innovator puts for sale, these two schemes give the same licensing revenue. We obtain this equivalence result in a general model with minimal structure. It is then applied in a Cournot oligopoly for an outside innovator. Finally, in a Cournot duopoly it is shown that when the innovator is one of the incumbent firms rather than an outsider, the equivalence result does not hold.

中文翻译：

---

固定费用与从价利润特许权使用费的等价性

对于创新购买者数量有限的外部创新者，本文比较了两种许可方案：(i) 固定费用，其中被许可人向创新者支付费用；(ii) 从价利润版税，其中被许可人将利润的一小部分留给创新者。我们证明这两种方案是等价的，因为对于创新者出售的任意数量的许可，这两种方案提供相同的许可收入。我们在具有最小结构的通用模型中获得了这个等效结果。然后将其应用于古诺寡头垄断，以供外部创新者使用。最后，古诺双头垄断表明，当创新者是现有企业之一而不是局外人时，等效结果不成立。