Competition In or For the Field: Which is Better

off the monopoly for a fixed fee and charge no royalty.¹⁶ In that case, the principal does not want competition
downstream. When fixed lump-sum fees are not feasible, the patent holder must make her income through
royalties. But then the double marginalization problem bites, and controlling market power downstream
becomes an issue. Our result implies that decreasing marginal revenue is sufficient for a Demsetz auction
(ex ante competition) to be better than ex post competition when ex post market structure is uncertain.

One could argue that an exclusive contract with a two part tariff is enough to prevent the double marginal-
ization problem. Note, however, that to choose the right fixed fee the principal must know the demand curve.
Our analysis implies that when marginal revenue is decreasing in quantities a joint franchise solves the prob-
lem.

3.3 Dealerships

Dealerships are similar to licensing, except for the fact that the principal’s cost increases with the number
of units sold. For example, consider the case of car dealerships. Cars are provided by the manufacturer at
a fixed price and the dealers are free (within limits set by list price of the manufacturer) to bargain their
markup with clients. The question for the manufacturer then is whether to have dealerships that are, say,
spatially close and thus compete with each other, or to have one dealer with a cap on the resale price.¹⁷

Assume that c(q) is the principal’s cost function, with c⁰, c⁰⁰ > 0. Then S(p) = tD(p) — c(D(p)), and, as
withlicensing, π(p) = 2(p — t)D(p) — c(D(p)/2). Then:¹⁸

S⁰ = (t — c⁰ ) D',
S⁰⁰ = (t — c⁰)D⁰ — (D)²c⁰⁰;

and

^{π 0} = 2 [D+ ( ^p—t^—c ) D⁰ ]^,
π⁰⁰ = 1 [ D + (1 — ^c2D⁰') D⁰ + ( p — t — c ) D⁰ ].

We now show that 2P⁰ + qP⁰ < 0 is again sufficient for WJ > W_s. As before, since π⁰ > 0 for all p ∈ [p, pm ),
it follows, after some straightforward but tedious algebra, that S⁰⁰π⁰ < S⁰π⁰⁰ for all p ∈ [p, pm ) is equivalent
^to                                                                                  0 2 00

(6)                          DD⁰⁰ — 2(D⁰)² < 2π⁰ (D-c- — ¹ (D)³c",

(t —c )   2

which holds because the right hand side is (obviously) positive, while the left hand side is negative because

¹⁶See Gallini (1984) and Katz and Shapiro (1985).

¹⁷We abstract from other important considerations in these contracts, such as service quality.

¹⁸Note that royalties corresponds to the case where c ≡ 0.

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