> aggregate market cap will only increase by $50B

If you list 5% of a $1 trillion company on a stock exchange, the aggregate market capitalisation goes up by $1 trillion. (Float goes up by $50bn.)

Market capitalisation is price per share times shares outstanding [1]. Float is price per share times publicly-trading shares [2].

[1] https://www.fool.com/investing/small-cap/2005/04/29/quotouts...

[2] http://www.investopedia.com/terms/f/floating-stock.asp

You sound knowledgable about these matters, and I am not. In my ignorance, "agg. market cap" sounds like an easily gamed number. For example, I could start an exchange and ask every company in the world to list 10^-10 of their shares, and so become the largest exchange in the world by agg. market cap. (Perhaps this doesn't come up in practice because most firms list in only one market, and so agg. market cap becomes a useful measure of how much of the economy a given exchange touches, in some sense.)

It does come up in practice. It's actually a common scam.

When only a small fraction of shares are on the market, it's quite easy to manipulate the price higher... buying pressure goes a relatively long way.

If you can get 1% of your shares to be worth $100k, it now appears as though you are a $10 million company. This makes you appear reputable.

Drive hype about your "valuable" company, and once the stock is sufficiently pumped, dump your shares for profit.