E-hailing companies offer classic rides as a fast mode of transportation and shared ride as an economy option. Unlike private riders, shared riders may experience a match and share their ride with someone else. A match makes the trip longer as this typically generates a detour to pickup and/or drop off the second passenger. Since the companies pay their driver by time and distance regardless of the number of riders in the vehicle, it is possible to reduce the cost of serving a shared ride by matching it. As shared demand increases, more matches can be made and the variable cost of serving shared rides decreases. The goal of this research is to provide a quantitative insight on the conditions for the existence of a profitable equilibrium with both shared and classic rides in a given region.