Horrible, yes, but easily answered. All the hard work has been done.
You asked us to imagine a global government, Burning Ghost. Given that the governments of most "sovereign" nations wield less power than certain corporations, and that the nations with any residual power are disinclined (to put it mildly) to cede any power to a global authority, the only way a global government will occur is if a corporate entity, being a single monopolising corporation or group of corporations acting together, decide to create it.
Global government will be more powerful than any nation state, and will forbid the collecting of any tax. From this point on the provision of any services to consumers (formerly known as citizens of particular nations) will be made solely according to their ability to pay. The cost of such services will be so calculated that one billion will be unable to afford them.
I know you stipulated something about poverty not being a factor, Burning Ghost, however it really is.