We present a model which allows for the self-consistent determination of the stationary group III and V concentrations in the droplet and the contact angle versus the group III and V fluxes during the Au-catalyzed vapor-liquid-solid growth of III-V nanowires. The nanowire axial growth rate in the mononuclear regime is taken in the Zeldovich form. Chemical potentials of the group III and V atoms in liquid are considered within the regular solution model. We show how the group III content and the droplet contact angle can be increased be either decreasing group V flux or increasing group III flux. The group V concentration usually decreases for higher contact angles. Overall, these results can be used for modeling and fine tuning of the droplet shapes and compositions influencing the morphology and the preferred crystal structure of Au-catalyzed III-V nanowires in different epitaxy techniques.