Sure. If you want to look up economic research about this, the main thing you would want to to look for is what they call the MPC, the "marginal propensity to consume"; that is, if you add 1 more dollar to someone's income, how much will their consumption increase. It's generally somewhere between 1 and 0, 1 being "you give someone another dollar in income and they spend all of it" and 0 being "the spend none of it". Generally speaking, MPC tends to decline the more income someone has.

Here was one study, done in Italy in 2012 on the subject.

http://www.stanford.edu/~pista/MPC.pdf

We find that households with low cash-on-hand exhibit a much higher MPC than affluent households, which is in agreement with models with precautionary savings where income risk plays an important role. The results have important implications for the evaluation of fiscal policy, and for predicting household responses to tax reforms and redistributive policies. In particular, we find that a debt-financed increase in transfers of 1 percent of national disposable income targeted to the bottom decile of the cash-on-hand distribution would increase aggregate consumption by 0.82 percent. Furthermore, we find that redistributing 1% of national disposable from the top to the bottom decile of the income distribution would boost aggregate consumption by 0.1%.

It's worth mentioning that while the "marginal propensity to consume declines with income" idea is something that was assumed by Keynes and is part of Keynesian economic, it is something that others have contested. There is a lot of debate, for example, on the difference between "windfall income" and "permanent income" and how each affects MPC. But in general, if you look in most economic textbooks, the model you usually see is a sloping curve, where as income goes up MPC drops; it never goes quite to zero, there is usually some increase in consumption as you increase income, but it falls quite close to zero as income rises. The consumption function usually looks something like this:

http://en.wikipedia.org/wiki/File:MPC.png