rich people with more money have a super low propensity to spend - they will save OR invest. Most economists would say that is good too as that provides the long term capital needed by corporate America ... and cash at banks to loan. But it does not help the economy in the short term one bit
As to poor people spend more when they have more - that is not what keeps them poor
a person at 125% of the poverty level - needs about 20? 40? percent more money just to pay the bills .... that is not keeping them poor
but yes - give a person with income at say 100-300% of poverty level and they will not save it --- but I would argue they have BILLS to pay and that spending it is not on booze and gambling and waste
we all - at any income level - have some propensity to waste new money - but frankly the poor have too many bill collectors chasing them and so many old appliances and bare thread clothes they likely will do less waste of the EARLY ADDED money
and - fact shown over and over again -- those who right or wrong do not expect to have a lot for a long time --- have a super hard time ever saving .... and that is a shame
and - fact shown over and over again .... those with 25,000 in the bank saved are 5 or 10 times more likely to save "extra" new money than those with zero (who simply can not see that savings lasting and growing)