Road Pricing and Capacity Decision under a Self-Financing Constraint

Every morning commuters have to travel from a residential area to a workplace by using their private cars on a bottleneck-constrained highway. Consider the maintenance cost and infrastructure investment, we model road pricing and capacity decision under a self-financing constraint then derive how a planner chooses pricing and capacity chooses to maximize the social welfare. The optimal fine toll is sequentially given, and then the property is derived as the positive solution to the model, if existing, is unique. Numerical illustrations are presented to help better understanding the theoretical analyses.