In the US, there is great disparity but little hunger and thirst.  Yet in many, e.g., Communist regimes, there is little disparity and much hunger and thirst.  Part of the reason for that is incentive: the promise of prosperity drives the wealthy to increase wealth, which creates jobs, and helps others achieve in the system of the meritocratic workplace.

I think the trajectory of economic disparity points to more wealth for the rich and more wealth for the not-so-rich.  That is not to say that there should not be some redistribution at the upper end, since as in the game of Monopoly, if there is no control at the top, there is one winner in the end.

I think the Gospels pretty much ignore the role of government relative to the poor (whom we will always have); it addresses individuals.  The focus of the Gospels is the Kingdom of Heaven: give up what you have not to help the poor, per se, but to achieve the Kingdom, for it is easier for a poor man to enter the Kingdom.