Dear Ms. Sandberg,

Thanks for writing “Lean In,” which I hope we won’t be tired of talking about before it even hits stores on Monday. I’m glad someone as successful as you has reminded young women that, yes, it is good to be confident. And I’m glad, too, that you told those newly minted college grads that crucial secret: if you want to get paid as much as a guy, you must negotiate hard for your salary rather than accepting what is offered. Oh, and by the way, your recommendation to marry an egalitarian-minded man who will support your career — solid stuff there. Your book could kick-start a discussion among ambitious young women about how their personal choices help or hinder women’s ascent up the corporate ladder.

Facebook’s Sheryl Sandberg, author of the new book “Lean In,” which comes out on Monday. (Jean-Christophe Bott — AP)

And last week, when I saw that you were holding closed meetings at some of the most powerful investment banks in our country – Morgan Stanley, Goldman Sachs, and JP Morgan Chase to discuss “Lean In,” I was even more encouraged. Sheryl, those banks could really use your guidance. Maybe you didn’t realize this, but women are only a token presence on their corporate boards. Seriously, you’d be shocked. Morgan Stanley has two female board members out of 14. Goldman Sachs has two female board members out of 13, and JP Morgan Chase has only a single woman – a token! — on their 11-person board. I know. I know. In 2013! I couldn’t believe it either, but you can take a look for yourself right there on their Web sites.

Then I got kind of confused. Maybe you already knew that those big banks were making sure all the money, power and influence stayed with men. I mean, how could you not? I was scrolling around the Web and read that those exact same banks were the lead underwriters on Facebook’s historic initial public offering just last year. As the COO of Facebook, you were involved in the third biggest public offering of all time. You must have looked at who was at the helm. Didn’t you notice that the overwhelming majority of those board members were, um, male? And look here! According to the financial press, Morgan Stanley has generated $1.2 billion in fees from Facebook since 2010.

Now, I don’t want to sound naïve – and I’m not all that well versed in securities law — but money talks, right? I know you don’t control the investment banking industry but it seems to me that if you are the boss at Facebook and Facebook is handing Morgan Stanley $1.2 billion you might have asked a few top dogs there to ‘Lean In’ a little, get over their institutional sexism and name another two or three woman to the board.

If you want to change things for young ambitious women, here’s a little advice from me: forget trying to organize little consciousness raising groups around the country for already stressed out women. Instead, lobby your bosses to get another woman on your Facebook board, then make a public announcement that from now on, Facebook will only do business with companies in which 40 percent — even 30 percent– of their executive team is female. Good lord, Sheryl, you’d set off a quake that would reverberate from Silicon Valley to Wall Street. Forget those nasty book reviewers. It wouldn’t matter if you never sold another copy – you’d change the world for working women overnight.

For now, Sheryl, I’m going to remain open-minded. You already have a big job, and you took on another — becoming an icon for young ambitious women. Now, as my mom used to say, put your money where your mouth is. For the next couple of weeks, I’m going to watch for some big announcement from those investment banks or from Facebook itself. You are the ultimate insider. And if you are willing to use your considerable influence to do what is right for women, I’ll be your biggest fan. And if not, well, not. Because from where I sit, it’s not just the dewy female college graduates who need to think differently about the choices they make so that women can get ahead. You do, too.

Peg Tyre is a journalist and the author of “The Good School” and “The Trouble With Boys.”