Verhoef, E. (2007). Second-best Road Pricing through Highway Franchising Journal of Urban Economics, 62(2):337--361.

This paper considers the welfare impacts of a range of franchising regimes for congestible highways. For a single road in isolation, it is shown that a competitive auction with the level of road use as the decision criterion produces the socially optimal road (in terms of capacity and toll level), provided neutral scale economies characterize highway operations. The auction outperforms various alternatives, in which the bidders are asked to minimize the toll level or toll revenues, or to maximize capacity or the bid for the franchise. When second-best network aspects are taken into account, the patronage-maximizing auction is no longer optimal. With unpriced congestion on parallel capacity, the second-best highway would generate losses and the auction produces a below-optimal capacity. With unpriced congestion on serial capacity, the auction produces an above-optimal capacity. However, the patronage-maximizing auction does replicate the second-best optimum under a zero-profit constraint in both cases. An inquiry into the degree of generality of this result shows that the first-order conditions suggest that this similarity would carry over to generalized networks, of undetermined size and shape. But second-order conditions are not fulfilled in general, and also corner solutions may occur. A numerical example is used to illustrate that the patronage-maximizing auction may then achieve the least efficient among the possible zero-profit roads. {\textcopyright} 2006 Elsevier Inc. All rights reserved.