Pareto optimization of public-private partnership toll road contracts with government guarantees

Government guarantees are frequently used in public-private partnership (PPP) toll road projects to attract private sector partners. In this paper, we propose a multi-objective programming model for Pareto-optimal decision in which the toll, quantity demanded, private firm's profit and social welfare are investigated, and compare the effectiveness of exclusivity guarantees and minimum demand guarantees in PPP contracts. Under certain assumptions, we find that for any government guarantee, the Pareto-optimal toll lies in between the toll set by private firms and socially optimal toll; in addition, the Pareto-optimal toll is higher and monopoly power is stronger under minimum demand guarantee if the relative negotiating power of private firms is sufficiently high. Both the private firm's profit and social welfare depend on relative negotiating power, buyback price, marginal social cost and minimum quantity demanded. In particular, if the minimum quantity demanded and the buyback price are sufficiently high, the government will tend to provide exclusivity guarantee but not minimum demand guarantee. A policy implication of this result is that it is not always the best choice for the government to provide a minimum demand guarantee to private firms.