Because n*q* = Q*, we can rewrite the condition (10) as follows:
P(Q*) - C + Q*P' = 0. (11)
Equation (11) implies that the license holder obtains monopoly profit given Wj. Monopoly
profit is the maximum profit for the license holder to obtain under the consumer de-
mand function P. Since monopoly profit is achieved when Wj is given, even if the license
holder chooses w in addition to f, the license holder cannot increase its profit more
than monopoly profit. In other words, the following equation holds in this case:
max nq(P(nq) — c) = max nq(P(nq) — c).
f {w,f }
Therefore, two problems, (LP) and (LP,), yield the same profit. Moreover, since we
take W arbitrarily, a pair of w and f which satisfies equation (11) must be a solution
to (LP). Now, we have the following proposition.
Proposition 1 When the number of licensees is determined endogenously, a license
holder can earn monopoly profit by offering any combination of a unit royalty and a
positive fixed fee that satisfies equation (11). Moreover, even if the license holder uses
only a fixed fee, it can earn monopoly profit.
Proposition 1 implies that the result of Kamien and Tauman (1986) is robust when
the demand function is general. They show that if the demand function is linear, then
a license holder can earn monopoly profit by setting the fixed fee, f, equal to the
monopoly profit, and only one licensee buys the license. Here, we show that even if
we consider general forms of the demand function, the license holder obtains monopoly
profit. In particular, there is an equilibrium wherein the license holder only employs
a fixed fee as in the case in Kamien and Tauman (1986). (Note that this is the case
where the license holder chooses w = 0.)
de Meza (1986) considers a two-part tariff scheme and incorporates the endogenous
entry of licensees. He shows that the license holder cannot achieve monopoly profit using
a fixed fee scheme if the demand function is linear and the marginal cost is increasing.
He argues that if the number of licensees is endogenously determined, a positive unit
royalty must be combined with a fixed fee to earn monopoly profit. However, our result
implies that when the marginal cost for production is constant, a fixed fee is sufficient
for monopoly profit even if the demand function is in general form.9
Note that when alternative inferior technology is freely available, especially when
the unit production cost with this inferior technology is lower than monopoly price, i.e.,
the non-drastic innovation case in Kamien and Tauman (1986) and in other standard
literature, a similar result may be derived. In the non-drastic innovation case, the
equilibrium market price is determined by the unit production cost of the alternative
9Note that in the analysis of de Meza (1986), the equilibrium number of licensees is implicitly
assumed to be greater than one. This may be another reason why a positive unit royalty is necessary.