Private road networks with uncertain demand

There has been wide interest in private supply of roads as a solution to traffic congestion. We study its efficiency under demand uncertainty: we solve for equilibrium and optimum as benchmarks, and evaluate the efficiency of possible regulatory policies for private road operators. We obtain analytic solutions for simple networks and numerical simulation results for more complex ones. For two serial links and two parallel links, self-financing still holds in expected terms for the first-best case, even though the capacity is higher than the capacity for the deterministic demand equal to the expected value. When forced to apply the second-best optimal pricing, the private supplier makes an expected loss (profit) if there is an untolled substitute (complement) in the network. In contrast to the deterministic counterpart of the problem we study, regulation by competitiv e auction cannot replicate the second-best zero-profit result. For more complex networks, when private firms adds capacity one link at a time, entry by competitive auctions performs better than free entry. For the parameter range considered in the numerical simulation, entry by generalized auction performs better than entry by patronage auction.