Higher pressure will give you more efficient ride than lower pressure.
For any given pressure, wider tyres have lower rolling resistance than narrow tyres
BUT
narrow tyres are more aerodynamic.
RR is proportional to velocity but aerodynamic drag is proportional to V2.
This means that up to about 12mph, RR is the dominant resistance. At higher speeds, air resistance becomes the limiting factor.

If you ride fast and solo, thin tyres are more of an advantage.