Engel E., Fischer R., Galetovic A. (2001).

Least Present Value of Revenue Auctions and Highway Franchising. Journal of Political Economy, Volume 109, pp. 993-1020.

Abstract:

In this paper we show that fixed-term contracts, which are commonly used to franchise highways, do not allocate demand risk optimally. We characterize the optimal risk-sharing contract and show that it can be implemented with a fairly straightforward mechanism—a least-present-value-of-revenue auction. Instead of bidding on tolls (or franchise
lengths), as in the case of fixed-term franchises, in an LPVR auction the bidding variable is the present value of toll revenues. The lowest bid wins and the franchise ends when that amount has been collected. We also show that the welfare gains that can be attained by replacing fixed-term auctions with LPVR auctions are substantial.