‘Autonomous cars’ are cars that can drive themselves without human control. Autonomous cars can safely drive closer together than cars driven by humans, thereby possibly increasing road capacity. By allowing drivers to perform other activities in the vehicle, they may reduce the value of travel time losses (VOT). We investigate the effects of autonomous cars using a dynamic equilibrium model of congestion that captures three main elements: the resulting increase in capacity, the decrease in the VOT for those who acquire one and the implications of the resulting changes in the heterogeneity of VOTs. We do so for three market organizations: private monopoly, perfect competition and public supply. Even though an increased share of autonomous cars raises average capacity, it may hurt existing autonomous car users as those who switch to an autonomous car will impose increased congestion externalities due to their altered departure time behaviour. Depending on which effect dominates, switching to an autonomous vehicle may impose a net negative or positive externality. Often public supply leads to 100% autonomous cars, but it may be optimal to have a mix of car types, especially when there is a net negative externality. With a positive (negative) externality, perfect competition leads to an undersupply (oversupply) of autonomous cars, and a public supplier needs to subsidise (tax) autonomous cars to maximise welfare. A monopolist supplier ignores the capacity effect and adds a mark-up to its price.