Supercharging for economy?

[naturalextraction]

Most all the auto manufactures in their R&D are and have utilized only turbo charging in their Ultra lean burn induction systems and engines. In terms of operating efficiencies (thermal conversion efficiencies; providing an overall higher adiabatic efficiency rate in the ice, negating the typical ice engines mechanical in-efficiencies) in ultra lean burn systems, belt driven supercharges will never be used and are not. Yes, in conventional systems, for power they work well especially picking up for compressor lag in non-lean burn turbo charged systems. However better designed and heat scavenging compressor turbine combinations have virtually no lag. (negligible anyway).

More in line with the OP's question; Utilized in ULB concepts with low fuel to high air ratios, compressing both the fuel and air molecules prior to the combustion chamber also allows for better homogenizing of these hydrocarbon based fuels.
In regards to conventional systems or ULB, under higher compression in the SICE, the stratified charge has a faster flame front travel/combustion speed under this environment providing a higher chemical conversion (now combusted heat energy) to mechanical power transfer (which most of this heat energy is lost to materials/liquids absorption, transference and radiation to atmospheric) thus, without getting into much more complicated details, (gains through variable cam and ignition timing, etc) why higher compression engines or compressed cylinders provide, typically, higher chemical energy conversion efficiencies. Then there are the independent fuel characteristics themself.

Also other considerations/variables are the vehicles CD characteristics, HP/torque to weight ratios, engines overall build efficiencies (parasitic losses, combustion chamber efficiencies), transmission of power to the wheels, etc. Also atmospheric/altitude, driving conditions and many others that will have an effect on the end MPG gain or loss. Quick example; Thus a mechanically geared/standard transmission of power vehicle (lower parasitic losses) will provide a better MPG over an hydraulically controlled/coupled automatics TofP.