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This paper analyzes private and social incentives for levying ad valorem licensing fees in a supply chain under the legal principle of patent exhaustion. With perfect competition at both upstream and downstream stages, the licensing segment choice is irrelevant. However, if one segment is monopolistic, the patent holder prefers licensing at that stage, aligning private and social incentives. Under imperfect competition at both stages, excessive downstream licensing may occur. We show that ”double-dipping” (charging fees at both stages) can be profitable for the patent holder and beneficial for consumers, with implications for applying the patent exhaustion principle.