It is an important condition for long-term harmony of human interests that labor is much more scarce relative to land. It's a great big world out there, and that's very good.
The reason is that land cannot be produced. We can erect tall buildings, but in their case, the taller the building is, the higher the cost per each floor. Physical limits do not permits skyscrapers in most locations. Unless we learn to raise islands from the bottom of oceans or travel to distant Earth-like planets, the supply curve for land is vertical.
If land begins to become scarcer, then society will change in mood. In particular, it will tend toward a status society, in which one's relative "rank" in relation to other people will matter more. One may prefer to be a big fish in a small pond to being even a bigger fish but in a much bigger pond, because it is one's relative bigness that will determine who will live in the best locations. This is because competition among consumers will not cause any additional supply of land to come into existence.
This is similar to how we assumed, following Frank, in the previous posts that the quality and price of schooling are fixed forever.
This may skew economic logic toward strange avenues, like, as Frank theorizes, voluntary contractually entered into "progressive taxation" in which people trade off their absolute positions for relative positions and vice versa.
Fortunately, however, land is and will remain for the near future almost a super-abundant good. Therefore, Frank's conclusion that high-ranked positions cannot be occupied "free of charge" and are privileges does not follow. There are too few genuinely positional goods for anyone to worry about. And under laissez-faire, a "high-ranked position" can only be obtained via superior service to the consumers which by definition consists in the production of nonpositional goods. If the result of Bill Gates' genius is that he also claims some few and far between positional goods, then I say, so be it.
For notice that the existence in a free society of a positional good whose supply is extremely inelastic even in the long-term only means that no resources will be spent on producing this good. If there are only so many habitable tropical islands out there, it may well be that a private island will always remain a luxury, never becoming a necessity. Unfortunate though this is, one result is that there is no economic problem associated with islands other than the problem of distribution. All the economic laws hold true for the rest of the nonpositional economy. And even in regard to distribution of islands, the market will still produce the best results as compared with potential rivals.
Here is my own thought experiment: suppose that all goods are positional. They are scarce and cannot be produced. It is obvious that everyone will have an incentive to kill all of his rivals, becoming a single human being in the world or at least on a territory he can successfully defend. What can we expect but a savage battle for resources followed by mutual autarky? There can be, or we can expect there to be, only one. The last men standing will enjoy the few berries and nuts and mushrooms they will be able to gather and die either quickly if those mushrooms turn out to be poisonous or eventually. Then the world's economic problem will be solved for good.
So, Frank proves too much, namely, that economics as it has been developed by its ablest practitioners is mostly false. But we see that this claim is empirically and self-evidently false, and if it were true, then there would be no need for economics at all.
Finally, let me suggest that the idea that the world's tax systems have been set up (as if themselves by an invisible hand, in an unplanned manner but still promoting economic efficiency) to get the top achievers pay a price for their high rank is not only false but a bit naïve.