The mayor of New York City is Michael Bloomberg, a billionaire. One of his favorite sayings is that a man’s last check should be to his undertaker, and it should bounce.

Bloomberg’s quip is about giving to charity, not selfishness. But many in Bloomberg’s generation are taking the spend-down route — and not necessarily for altruistic motives.

The Los Angeles Times reported on a survey of millionaire baby boomers by the investment firm U.S. Trust. Only 49 percent of the wealthy respondents said it was important to leave money to their children when they die.

The low rate surprised the company, and has led to some speculation about the fate of the baby boomers’ wealth. At one time, many economists had projected that the early decades of this century would see the largest transfer of wealth between generations.

There are 77 million baby-boomers, but some of them are less wealthy than they used to be since the Wall Street crash of 2008. Many older people might worry that they’ll live long enough to strain their retirement accounts, although that is probably less true of the genuinely wealthy.

Some U.S. Trust survey respondents worried about their children getting a sense of entitlement or wasting inherited wealth.

And many families already are seeing cash advances on the bequests, analysts told the Times.

“How can you say no when a child asks for a down payment for a house or money to remodel their house to have a bedroom for a second child?” asked Ken Dychtwald, chief executive of research firm Age Wave. “A lot of boomers are finding that family members are taking cash advances on those inheritances right now.”

There is also the question of inheritance taxes, which continue to be an incentive to leave money to charities. Those bequests are important to society, after all.

Over the next few years, those taxes are unlikely to be repealed, given the federal debt that needs to be paid off — and, of course, much of that revenue will be spent on elderly boomers.

Finally, there’s hope for the boomer progeny.

No one can synchronize his check-writing and his appointment with his Maker as well as Bloomberg’s quip would have it.