c(q) = c0. We also assume that the separate and joint auction of both franchises dissipate all rents.21 Since
S0(P) = -D(P) = P — 1 and ∏(P) = P(1 — P) — c0, we have that ∏00 /∏0 < S00/S0 if and only if —2/ (1 — 2P) <
-1/(1 -p) for allp < pm = 1/2, which indeed holds. It follows that the sufficient condition for Proposition
2 is satisfied.
Assume that the ex-ante distribution of market structure outcomes in the case of separate franchises F
is a point distribution with weights of 1/2 on collusion at the bid price and 1/2 on price competition with
price equal to marginal cost (zero). Then PJ is the smallest solution to P(1 - P) = c0 while PS is the smallest
solution to 2p(1 — p) = c0. The existence of a solution in both cases requires c0 < 1 /8. Then:
WJ - Ws = 2(1 -Pj)2 - 4 ©(1 -Ps)2 + 1} = 8 ∣2pT- 4c0 - 1 - p 1 - 8c0] > 0, ∀c0 > 0,
Furthermore, in this example a joint auction can lead to a welfare increase of as much as 17%. ∣
4 Conclusion
We have shown a simple condition for a principal to prefer to contract the provision of a good from a single
agent via a Demsetz auction, rather than by having multiple agents provide the good under (imperfectly)
competitive conditions. In the canonical cases of procurement, royalty contracts and dealerships, decreasing
marginal revenue ensures that a Demsetz auction (ex ante competition) is better for the principal than ex
Post competition. This result is surprising, because it is independent of the expected intensity of ex post
competition.
The results in this paper do not necessarily imply an endorsement of monopolies, since many relevant
factors were left out of our analysis. First, we assumed a single service quality, which can be verified at no
cost, even though in most cases quality will be worse in the absence of competition. Second, we ignored
political economy and asymmetric information considerations, which may be worse when a regulator deals
with a monopoly. Third, we rule out incomplete contracting and the hold-up problem. For example, a
manufacturer might prefer to have competing dealers in order to avoid a bilateral monopoly. Finally, we
have not considered the possibility of technical change in the delivery of franchise services, a factor that if
present makes competition more desirable if it accelerates the introduction of new technologies.
On the other hand, there are some aspects we left out which strengthen the case for a joint auction. First,
if agents are risk averse, the preference for joint auctions increases. More importantly, we have assumed
that a joint contract does not lead to any cost savings; or, conversely, that ex post competition, which
implies more than one agent, does not lead to (fixed) cost duplication. A common concern when formerly
monopolistic markets are liberalized is that competition may lead to inefficient cost duplication through
“excessive” entry.22 With a Demsetz auction, however, cost duplication is no longer an issue. Our result
21Thus the common value of both expressions in Condition 1 is zero.
22See, for example, Armstrong (2000).
13