The facts are these a bit different than your assumptions:
Federal Circuit Bar Journal
2000
DeFranco, Denise W.
Article
Authored by Denise W. DeFranco
Introduction
The patent statute provides that the damage award in a patent infringement action must be "adequate to compensate for the infringement, but in no event less than a reasonable royalty for the use made of the invention by the infringer, together with interest and costs as fixed by the court."1 Courts have construed this statutory phrase as requiring an award of lost profits, or other compensatory damages, where the patentee can prove, and elects to prove, such damages. However, where the patentee cannot prove, or elects not to prove, such damages, the statute provides for an award of a reasonable royalty.2 Therefore, even where the patentee has not shown any harm caused by the infringement, the patentee is still entitled to the award of a reasonable royalty.
Sections I and II of this paper review the case law regarding the award of lost profits and reasonable royalties, respectively. Section III addresses two statutory limitations imposed on damages. Finally, Sections IV and V briefly address enhancement of damages and other awards.