In theory higher pressures yield, lower rolling resistance, which equals higher fuel economy. It also creates a stiffer sidewall, that prevents the tire from "leaning" when turning. This improves handling.
There is a point of diminishing returns though. At some pressure, the tire becomes so stiff that imperfections in the road are no longer absorbed by the tire, but instead transferred into the suspension. Harmonics sets up in the suspension and actually causes higher rolling resistance.
Then you also get other negatives of higher pressure. The ride quality suffers, as does straight line traction.
This is definitely not for everyone. Like I said, I understand the theory behind higher pressures and also the consequences of running them. There is definitely a point north of the vehicle manufacturers recommended tire pressure that will give better mileage and handling and a point south of their recommendation that will improve ride quality and straight line traction. It is up to the individual to find what compromises they want to make to get what they want from the car; higher fuel mileage or softer ride.
I have left my tires at the tire manufacturers maximum limits for 85,000 miles and haven't had any complaints. I haven't done any side-by-side mileage tests at lower pressures to verify that I am running the optimum pressure for economy though, so your mileage may vary...
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