Patent strength and optimal two-part tariff licensing with a potential rival incorporating ad valorem royalties

•We show that the patentee may prefer ad valorem royalties to per-unit royalties.•The optimal contract depends on the degree of the substitutability between goods.•In the high cost scenario the contract sets a pure ad valorem royalty.

We show that an internal patentee may prefer to use ad valorem royalties instead of per-unit royalties in the licensing contract of a new product to a potential rival who may develop a substitute good.