1 Introduction
The optimal licensing scheme has been a matter of great concern for economic re-
searchers. A pioneering work in this regard is Kamien and Tanman (1986), who com-
pare a nnit royalty scheme and a fixed fee scheme. They conclnde that a fixed fee
scheme is optimal for license holders with Conrnot competition of licensees. Fnrther-
more, nnder a fixed fee scheme, a license holder earns monopoly profit, with only one
licensee. The literatnre that extends Kamien and Tanman (1986) primarily focnses on
the case wherein the nnmber of licensees is given exogenonsly.
This paper considers a licensing scheme wherein the nnmber of licensees is endoge-
nonsly determined. A two-part tariff scheme, i.e., a combination of fixed fee and nnit
royalty schemes and a general demand fnnction is considered. We show that if the mar-
ginal cost of prodnction is constant, then a fixed fee continnes to be snfficient for license
holders to earn monopoly profit. More precisely, nnder free entry of licensees, a license
holder can obtain monopoly profit with any combination of a positive fixed fee and a
nnit royalty that satisfies a certain condition. Onr resnlt shows that even if the demand
fnnction is in a general form and the nnmber of licensees is endogenonsly determined,
Kamien and Tanman’s main theorem is robnst, i.e., a fixed fee scheme is snfficient for
a license holder to earn monopoly profit. This is in a sharp contrast with the resnlt of
de Meza (1986), who shows that a combination of fixed fee and positive nnit royalty
schemes is necessary for earning monopoly profit if the marginal cost of prodnction is
increasing, not constant.1 Fnrthermore, as an extension of onr basic model, we consider
the case where the fixed fee is regnlated to be a certain level; we show that the optimal
nnit royalty with a regnlated fixed fee enables license holders to obtain monopoly profit
even in this case.
In this paper, we extend a standard patent licensing model to the endogenons entry
environment. In the model, a license holder offers a licensing scheme for downstream
firms (e.g., prodncers). If downstream firms bny licenses, then they employ the tech-
nology in their prodnction processes. Downstream firms engage in qnantity-setting
competition. The license holder’s technology is essential for the operation of each of
the downstream firm’s bnsinesses in the indnstry. Onr model generalizes Kamien and
Tanman (1986) in the following two aspects.2 Kamien and Tanman (1986) assnme that
the demand fnnction is linear and that the license scheme is a fixed fee or a nnit royalty.
We consider a model with a general demand fnnction and a general license scheme that
combines the fixed fee as well as nnit royalty.
1de Meza (1986) considers endogenous entry of licensees. See Table 1 for main assumptions made
in de Meza (1986).
2The sitnation wherein it is essential for all downstream firms to possess a license holder’s tech-
nology is considered. These downstream firms do not possess any alternative (or old) technology for
mannfactnring prodncts. This represents a simplified sitnation, which is termed as “drastic innova-
tion” by Arrow (1962). He defines that an innovation is drastic if the monopoly price nnder the new
technology does not exceed the price in perfect competition nnder the alternative technology. Even if
alternative technology with a modestly higher nnit prodnction cost is incorporated in onr model for
replicating the non-drastic innovation model, onr qnalitative analysis remains nnchanged.