I found a review in a relatively obscure journal, but it seems a reasonable summary of the existing research, except for the fact that income and wealth aren't necessarily the same:
A review of literature regarding income and altruism revealed mixed evidence. Chen, Zhu, and
Chen (2013) showed that, under a dictator game setting, pre-school children from higherincome
families give fewer stickers (endowment of the game) to others compared to kids from
lower-income families. Miller, Kahle, and Hastings (2015) altered the game so that the tokens
(endowment of the game) had to be earned via work and the kids were told that the recipients of
their donation would be other sick kids who were not able to make it to the venue on that day.
They still found that kids from richer families are less likely to donate their tokens compared to
kids from poorer families. Piff, Kraus, Côté, Cheng, and Keltner (2010) conducted experiments
on adults using economic games and scenarios and found that individuals of lower socioeconomic
status appeared to be more generous, more trusting, and more compassionate.
On the other hand, Hoffman (2011) investigated historical data during the World War II
on people’s decision to rescue the Jews. He found that the higher the income of the people, the
more likely they were to rescue the Jews. Holland, Silva, and Mace (2012) used a lost-letter
experiment. They dropped letters on pavements in different neighborhoods in the United
Kingdom and found that letters dropped in the richer neighborhoods were more likely to be
returned to the address listed on the letters. Looking into this issue more thoroughly,
Andreoni, Nikiforakis, and Stoop (2017) designed a more complicated version of the lostletter
experiment. Under their setting, the envelopes used were thin enough so that contents of
items in the envelopes (cash, or bank transfer cards) could be seen from the outside. The
letters were mis-delivered to rich and poor households in the Netherlands. Their initial results
revealed that the rich were more likely to return the envelopes compared to the poor.
However, with further investigations, the authors found that the rich were not more altruistic
than the poor. The fact that the rich were more likely to return the envelopes was because they
faced lower financial constraint and had lower marginal utility for the found money.
The above evidence showed that the relationship between income and altruism may be
ambiguous. Thus, it cannot yet be concluded whether the degree of altruism [...] should be higher for the rich or for the poor.
Unfortunately, that may not be as relevant as I had hoped because
It is unfortunate that a false dialectic between narcissism and altruism is in common usage. The two entities regularly co-exist. Vaillant, in his longitudinal study of healthy males, found that altruism increases significantly in the second half of life – not simply because we become more selfless as we age, but rather because helping others becomes more rewarding to us. A neuroimaging study demonstrated that those who are altruistic directly benefit from their altruism. Participants had to choose to endorse or oppose societal causes by anonymous decisions to donate or refrain from donating to real charitable organizations. The mesolimbic reward system was engaged when one donated money in the same way as it was when one received monetary awards. In other words, altruism activates brain centers that are associated with selfish pleasures like sex or eating.
Unfortunately the narcissism-wealth link alone has received less attention, perhaps because most researchers were interested in outward behavior (like altruism). Or in more prosaic terms, most people don't care how long you look at yourself in the mirror as long as you give them money :P