Q:

Why does low tire pressure increase friction?

I've always thought that it was because the frictional force on the tire was increased due to the bulging of the tires increasing the surface area in contact with the road. However, a colleague of mine reminded me that frictional force is independent of surface area. Why then is fuel economy decreased when tire pressure is low?

A:

Lower pressure increases surface contact and increases static friction, and static friction does not involve heat loss, so that is good. But rolling friction is not good and does involve heat loss.
Rolling friction heating is due to the inelastic deformation the rubber of the tire experiences when it is in contact with the road. See this article on rolling resistance from Wikipedia: https://en.wikipedia.org/wiki/Rolling_resistance
When the rubber is in contact with the road for each revolution, it is compressed, it then expands when it leaves the surface. The compression and expansion is not perfectly elastic, thus there is heat loss in the form of friction. The lower the tire pressure, the more rubber that is in contact with the road for each revolution, and the greater the friction heat loss. These increased heat losses add up to lower fuel economy. 
Hope this helps.

A:

Static friction does not actually reduce your fuel economy. Without it, your wheels would slip, so it is a good thing.
What causes the loss of fuel economy is rolling resistance. This is due to hysteresis; energy lost due to the cyclic deformation of the tyre as it rolls.
It's not a great analogy but imagine the partially inflated tire as a disc with the axel off centre. When rolled the axel will oscillate up and down - i.e. some energy is lost from being able to contribute to the forward motion.
In your case the axel doesn't bob up and down but energy is lost to reshaping the tite from bulging on one side to bulging on the other with each half revolution.

