>I am assuming that we hold M2 velocity of money constant for the purpose of this analysis
Poor people have to spend money on essentials as soon as it comes in. Rich people don't. That's pretty much the simplest possible definition of being poor. So that is not a valid assumption.
>If this assumption is true, both will create the same total 'demand', but for different goods.
This can't possibly be true either. Rich people spend money on essentials and on luxury goods and on investments and keep some spare cash on hand, because why not?
Poor people spend money on essentials, and perhaps a little distraction and entertainment.
Why would the total demand from both somehow be the same?
> The primary (economic) difference between these goods is their impact on long-term productivity.
Which is the crux of the problem - speculative casino "investment", which is based on gaming markets, isn't economically productive. Neither is an economy that leans heavily on usury.
Productive investment in R&D, small business development, and wage growth stimulates economic capacity and increases confidence.
Speculative investment - including speculative gambling, systems of forced debt like student loans and payday lending, and asset inflation which drives up rents and property prices - destroys demand and economic capacity.
The fact that we're even discussing negative interest rates while in the middle of severe commodity deflation proves the core problem hasn't been addressed.