inner workings of Mobile-net resolution multiplier - what does it do?
I contacted the authors of the mobile net architecture and papers and they provided me with the following answer:

The multiplier accomplishes what is being articulated in C): it acts as a re-scaling of the original input image to fit the value specified by the parameter. The default image size is 224x244, which corresponds to a resolution multiplier of 1.0. So 112x112 input image resolution corresponds to a 0.5 resolution multiplier which is achieved by simply downscaling the image to 112x112. Technically we scale the smaller side to target and crop the other dimensions. 

I hope this proves as helpful to others as it was to me.