Proposition 2 When the number of licensees is determined endogenously, a license
holder can achieve monopoly profit with a unit royalty scheme that satisfies equation
(13) despite the level of fixed fee being regulated.
This proposition asserts that a policymaker’s decision never affects the equilibrium
outcome. This result contrasts with the case where the number of licensees is exoge-
nously determined. If n is determined as a fixed number n, then the profit of a license
holder is πi = nf + nqw, and each licensee may obtain positive profit. Therefore,
the zero-profit condition does not hold and the license holder cannot extract the entire
profit from the market.12
Kamien and Tauman (1986) study the case of a unit royalty scheme as well; however,
they assume that the number of licensees is exogenously given. In the discussion here,
a unit royalty scheme is considered under endogenous entry of licensees. We show that
if any fixed cost other than the fixed fee, e.g., a set-up cost, does not exist, then the
license holder earns the monopoly profit.
Sen and Tauman (2007) examine the two-part tariff scheme, and show that it is
optimal for a license holder to offer a fixed fee that is equal to monopoly profit and to
make only one licensee accept this offer. In this discussion, even if the level of fixed
fee is regulated to make it lower than monopoly profit, the license holder can achieve
monopoly profit by offering an appropriate unit royalty. We can easily understand that
a lower fixed fee increases the number of licensees from one. However, the equilibrium
output and equilibrium market price remain unchanged and are determined as the
monopoly level. A license holder obtains the monopoly profit, irrespective of the level
of competition in the downstream market.
5 Concluding Remarks
We considered the licensing scheme of cost-reducing innovation where the number of
licensees is endogenously determined. First, it was shown that as long as the marginal
cost is constant, a fixed fee scheme is sufficient for a license holder to earn monopoly
profit. Thus, with a constant marginal cost, the result of Kamien and Tauman (1986)
was found to be robust. Second, we analyzed a case with a regulated fixed fee. Even if
the license holders cannot choose their fixed fees, they can obtain monopoly profit with
the optimal unit royalty wherein the number of licensees is endogenously determined.
This result implies that license holders do not have to determine the number of
licensees that they sell to when a sufficient number of potential licensees exist. License
holders are only required to determine the price of their license, and to take open access
policy for their technologies. Any discrimination in the license schemes among licensees
12 Note that the zero-profit conditions of licensees are also satisfied in the fixed fee case of Kamien
and Tauman (1986). A license holder can impose the zero-profit condition on licensees by setting /
equal to monopoly profit.