Rent extraction with securities plus cash

Auctions employing steeper securities generate greater revenues when bidders have equal opportunity costs. However, when opportunity costs rise sufficiently quickly with valuations, security bids decrease in NPV and steeper securities reduce seller revenues. We show that when such adverse selection obtains, using combinations of securities with differing steepness can generate higher revenues than using securities of the same steepness. We determine the optimal combination of cash plus equity; identify a novel way of implementing the optimal mechanism via decreasing royalty rates ; establish the robustness of the mechanism; and identify when auction designs combining cash with steeper-than-equity securities increase seller revenues.