I have noticed that on several (all?) highways in the Bay Area in California, US, carpool lanes are being replaced by paid fast lane (typically payable via FasTrak). This made me wonder: Does the introduction of paid fast lane as replacement of the carpool lane increase or decrease the traffic speed?
These Express Lanes (generally known as High-Occupancy Toll lanes, or HOT lanes) don't replace carpool lanes; they enhance them: carpools and other eligible vehicles get in for free (in some locations, carpools with only two people in the car have to pay half price and 3+ are free), and others can pay a toll to use them.
The intent is to manage the occupancy of the lane to maintain free-flowing traffic. Carpool lanes are inefficient if the volume of carpool traffic happens to be less than the lane's capacity; that's extra capacity someone could be using. As such, express lanes use dynamic tolling based on speed sensors to maintain speeds greater than 45mph by adjusting tolls. If the lane has extra capacity, the tolls are lowered (or turned off entirely at night), attracting more drivers (and freeing up space in the general traffic lanes). If traffic in the lane slows down, the tolls are raised, eventually reaching the point when only 3+ carpools are permitted and the situation is no different than the old carpool-only lanes. Other policy levers, such as adjusting the rules at particular locations for carpools and clean air vehicles, can help balance traffic as well based on long-term trends.
More generally, express lanes are at least an attempt to wiggle out of the trap that is induced demand, the theory that highway expansions end up just producing more traffic as congestion quickly returns to previous levels. Express lanes, at least in theory, try to mitigate that problem somewhat by providing greater incentives for transit use and carpooling than a normal highway widening project. They don't always produce those results in practice, though there's a lot of ongoing research into these projects. More prosaically, the lanes can generate revenue, which can be used to obtain low-cost financing from the federal government to help fund construction or to pay for maintenance and other transportation projects.