what about the mulitplier effect, see as the rich will most likely save or invest the extra money that they earn from paying less tax, indirectly that will affect aggregate demand through investment spending
however, if this money is redistibuted through the welfare system to the poor (note the automatic stabilizer effect) they will most likely spend the money as they have a higher marginal propensity to consume....the multiplier effect comes into play
the multiplied effect will be much higher than the effect of increased investment expenditure therefore, transfer payments are an injection into the economy (combined with the rest of government expenditure)