I'm not sure I understand your logic. Let's say 100 men and 100 women move to the Big Apple for their careers. Now let's say 50 of the men and 50 of the women hook up, get married, and move to Scarsdale. Let's say all of the women who have moved to Scarsdale buy a minivan and give up their jobs. Now, during the day, we have 100 men in the city and 50 women, giving a 2:1 ratio of men to women, but there are still 50 single men and 50 single women, giving a 1:1 ratio of single men to single women. And at night there are 50 men, all of whom are single, and 50 women, all of whom are single. Again, a 1:1 ratio.
So where does the demographic skew come from in your model?
Personally, I'm not so convinced that women move to the Big Apple merely search of successful men, though. There's all sorts of stuff going on in NYC that would appeal to women!
And these job vacancies are gender-specific? If the 50 job vacancies must then be filled by 50 single women, then yes we now have a lot more single women in the Big Apple. If they can be filled by 25 single women and 25 single men, then the single men:women ratio is still 1:1.
I guess I might buy the argument that the vacant jobs might go to 30 women and 20 men, which would back up your point.
So where does the demographic skew come from in your model?
Personally, I'm not so convinced that women move to the Big Apple merely search of successful men, though. There's all sorts of stuff going on in NYC that would appeal to women!