There is considerable controversy about the relative merits of the apportionment rule (which results in per-unit royalties) and the entire market value rule (which results in ad-valorem royalties) as ways to determine the scope of the royalty base in licensing negotiations and disputes. This paper analyzes the welfare implication of the two rules abstracting from implementation and practicability considerations. We show that ad-valorem royalties tend to lead to lower prices, particularly in the context of successive monopolies. They benefit upstream producers but not necessarily hurt downstream producers. When we endogenize the investment decisions, we show that ad-valorem royalties improve social welfare when enticing upstream investment is optimal or when multiple innovators contribute complementary technologies. Our findings contribute to explain why most licensing contracts include royalties based on the value of sales.

We analyze the welfare effects of patent licensing at different stages of the production chain and the level at which a patent holder would choose to license. We consider the incentive to invest in enhancing the value of the final product at the different stages of production. We study the effects of allowing a patent holder to discriminate among different products downstream and/or accounting for differences in information that potential licensees at different stages might have about the validity of the patent. We show that in those circumstances, a conflict arises between the stage at which patent holders prefer to license their technology and the stage at which it is optimal from a social standpoint that licensing takes place. Whereas the patent holder usually prefers to target downstream firms, society is often better off if upstream firms take the license.

The energy transition will imply a change in the competitive paradigm of electricity markets. Competition-wise, one distinguishing feature of renewables versus fossil-fuels is that their marginal costs are known but their available capacities are uncertain. Accordingly, in order to understand competition among renewables, we analyze a uniform-price auction in which bidders are privately informed about their random capacities. Renewable plants partially mitigate market power as compared to conventional technologies, but producers are still able to charge positive markups. In particular, firms exercise market power by either withholding output when realized capacities are large, or by raising their bids above marginal costs when realized capacities are small. Since markups are decreasing in realized capacities, a positive capacity shock implies that firms offer to supply more at reduced prices, giving rise to lower but also more volatile market prices. An increase in capacity investment depresses market prices, which converge towards marginal cost when total installed capacity is sufficiently large, or when the market structure is sufficiently fragmented.

It has been commonly argued that the decision of a large number of inventors to license complementary patents necessary for the development of a product leads to excessively large royalties. This well-known Cournot-complements or royalty-stacking effect would hurt efficiency and downstream competition. In this paper we show that when we consider patent litigation and introduce heterogeneity in the portfolio of different firms these results change substantially due to what we denote the Inverse Cournot effect. We show that the lower the total royalty that a downstream producer pays, the lower the royalty that patent holders restricted by the threat of litigation of downstream producers will charge. This effect generates a moderation force in the royalty that unconstrained large patent holders will charge that may overturn some of the standard predictions in the literature. Interestingly, though, this effect can be less relevant when all patent portfolios are weak making royalty stacking more important.

We analyze the optimal licensing contract that a patentee provides for a cost reducing innovation to a set of firms competing in a downstream market. We study two alternative licensing regimes: (i) a combination of royalties on sales and flat fees and (ii) fixed fees only. The first contract depends on the degree of competition in the final good market: when competition is stronger, the patentee demands a higher royalty. We also show that, contrary to the literature, using fixed fees only is not optimal for the patentee when firms are heterogeneous or when there is product differentiation. The reason is that royalties allow the patent holder to soften competition in the final good market. Finally we show that even though a combination of royalties and fees allows for improved access to the technology, social welfare is lower compared with using fixed fees only.