Competition In or For the Field: Which is Better

of Lemma 2.

3.4 The social planner

Next, we consider the case of a social planner who wants to contract for the provision of a service. As an
example, consider highway franchises. In many developing countries roads are being franchised to private
firms. In exchange for toll revenue, the franchise holder finances, builds, operates and maintains the road.¹⁹
In some cases roads are natural monopolies, and are awarded to the firm offering to charge the lowest toll.
Nevertheless, when there is more than one way to get from one point to another, as is often the case in
large cities, different roads could be awarded to different franchise holders.²⁰ Should the regulator award all
franchises to the same firm or award several highway franchises and let them compete? Another example is
the auction of the rights to provide local telephony in rural areas, where the auction is based on the price of a
standard local call. Is it better to have a single company provide the service or would it be better to allocate
two companies to the area?

In this case the principal cares about social surplus (i.e. consumer and producer surplus) so that S(p) =
R∞ D ( 5 ) ds + pD (p ) — 2 c Ç D^p ´ ; and π( p ) = 1 pD (p ) — c h D^p ]. Then

S⁰ = (p-c⁰)D⁰,

S⁰⁰ = ( p — c⁰ ) D⁰ + D  1 ( D⁰ )² c⁰,

and π⁰, π⁰⁰ are the same as in the case of dealerships (with t = 0). Condition (1) now leads to

( p — c ) D⁰⁰ + D⁰ — 1 ( D⁰ )² c⁰⁰   ( p — c' ) D⁰⁰ + 2 D⁰ — 1 ( D⁰ )² c⁰⁰

( p — c⁰ ) D⁰         >       D + ( p — c⁰ ) D^{0       ,}

which, after some algebra yields

(7)                          (p — c) £DD⁰⁰ — 2(D⁰)²] < — 2π⁰D⁰ + 1 (D⁰)²Dc⁰⁰,

which is the same condition as in the case of procurement. Hence, again decreasing marginal revenue is
sufficient for WJ > WS .

Finally, we present a concrete example which suggests that welfare gains may be important when using
a Demsetz auction instead of separate auctions.

Example We use the notation and definitions from the preceding subsection and assume D(p) = 1 —p,

¹⁹See Engel, Fischer and Galetovic (2001b) for a discussion of highway franchising.

²⁰One example is the La Dormida project in Chile, which would compete with Route 68, the highway that currently joins Chile’s
capital, Santiago, with the port of valpara´so. The Ministry of Public Works weighed the benefits of joint and separate auctions.

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