Licensing Schemes in Endogenous Entry

technology when the unit production cost is constant. Thus, as in our model above, the
levels of w and f do not affect the equilibrium market price and total output. Therefore,
the license holder can extract the entire industrial surplus with any combination of w
and f that ensures that the equilibrium market price is equal to the unit production
cost of the alternative technology.

4 Discussion

Proposition 1 implies that when a unit royalty and a fixed fee are both available, the
license holder always earns monopoly profit. In what follows, we demonstrate that
monopoly profit is achieved even if the level of fixed fee is regulated.

Consider a licensing scheme (w, f ) where w denote the unit royalty, and f denote
the regulated fixed fee.¹⁰ From the perspective of the competition policy, excessively
high prices of licenses are occasionally regulated in several countries e.g., Korea. The
policymaker establishes a particular level for f. Subsequently, given f, the equilibrium
conditions in the second and third stages are derived as in Section 3. Since the fixed
fee is determined by the policy, the equilibrium output level and the equilibrium num-
ber of licensees are functions of w rather than functions of (w,f ). Let q**, Q**, n**,
and w** denote the equilibrium output level of each licensee, equilibrium total output,
equilibrium number of licensees, and equilibrium unit royalty, respectively.

In the first stage, the license holder chooses w in order to maximize its profit P' =
n(qw + f). Substituting the zero-profit condition, π ^l can be rewritten as follows:

P' = nq(P (nq) — c).                               (12)

This implies that despite the fixed fee being determined by regulation, the license
holder’s profit is equal to the total industrial profit as in the case of the two-part tariff
scheme. Then, the license holder maximizes π ^l with a unit royalty w. Using equations
(6) and (7), the first-order condition is:

d-p _   (P — c + n**P'q**)(P — c — w** — P'q**)

dw    P '(P — c — w** — P 'q**) + P '' q**(P — c — w**)    '

Thus, we have the equilibrium condition as follows:

P (Q**) — c + Q**P ' = 0.                           (13)

The equation (13) yields the following proposition.¹¹

¹⁰We assume f > 0.

¹¹The second-order condition with respect to w is as follows:

^(2P. _{+ qp}''⁾⁽g_{)2 +} (P ^— _{c + qp}ɔ< ⁰>,

where Q = nq. Since the first-order condition implies that P — c + QP' = 0, and (dQ∕dw) > 0, it can
be rewritten as 2P' + QP'' < 0. Since we assume that P' + QP'' < 0 and P' < 0, the second-order
condition is satisfied.

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