He says

The easiest way to see why this argument is wrong is with a concrete example. Suppose we’re in an economy with a 0% annual growth rate. Its stock market has just one stock, ACME, which always costs $100/share. Every year, ACME pays dividends of $10 per share to its shareholders. If you have a portfolio consisting entirely of ACME stock, and you always re-invest your dividends in buying more ACME stock, then you’ll consistently get a return of 10 percent a year.

Now, Smith is right in a trivial sense. Obviously, everyone holding ACME stock can’t simultaneously grow their portfolios by 10 percent per year, because they’d have no one to buy stock from. But that fact doesn’t tell us anything about individual investors. At any given time, some investors will be looking to cash out, while others will be looking to buy in.

This is precisely my point.

So eventually if there is only one investor who keeps re-investing his dividends then eventually he will own all of ACME. At that point the growth rate of his portfolio will fall to zero.

He can still earn a positive yield on his portfolio but he can’t keep growing it because there is nothing left to buy.

Now, of course this will take a long time with one person starting with say $1000. However, if – as the financial industry did – you attempt to sell this concept to millions of people all at the same time you are going hit the “nothing left to buy” constraint faster.

At that point attempts to buy the more stock can only bid down the yield. No more real growth is possible.