Optimal welfare price in a highway competing with an untolled alternative: the influence of income distribution

In some countries it is fairly common to see two roads with the same origin and destination competing in the same corridor. One of them is usually a toll highway that offers a better quality to the users compared to its alternative: a free parallel single road. The users thus have to decide whether it is worth paying the toll for the advantages offered. This problem, known as the “untolled alternative”, has been largely studied in the academic literature. Particular attention has been paid to calculate the optimal welfare toll that maximizes economic efficiency. However, there is a gap in the academic literature regarding how income distribution affects the optimal toll. The main objective of the paper is to add knowledge on the topic by analyzing the influence of the distribution of the values of travel time (VTT) of the users of this corridor —which is closely related to their income distribution— on the optimal toll price. To solve this problem, we define a mathematical model aimed at obtaining the optimal welfare price for this kind of corridor under the hypothesis that drivers decide over the expectation of free flow conditions. The results show that the higher the average VTT the higher the optimal price, and the higher the dispersion (variance) of this VTT the lower the optimal price