Distance traveled, transit design and optimal pricing

Should transit prices vary with distance? And if so, how? Two arguments that point in opposing directions have been presented in the literature: long distance users induce larger operators' costs while short distance users induce larger in-vehicle times. Here we formulate a stylized model of a corridor where these and other elements are taken into account to approach the optimal strategic design (frequency, vehicle size, and route length) and its associated optimal pricing problem considering identical users that travel different distances. A crucial element is the consideration of the crowding caused by passengers entering the system at different points along the corridor, affecting the value of in-vehicle time which increases with the load factor through a crowding factor that, ultimately, is the single element that triggers optimal prices that increase with distance at a decreasing rate.