> Let me try and repeat it back. Resource allocation is a zero-sum game within any given year, resource production increases yearly as technology increases, technology increases more as capital increases, so a low capital gains tax will increase resource production more than a high capital gains tax.

Actually, this line of reasoning is tangential to the thrust of my argument. Let’s get to it now:

> If I got that right, here's my best shot at a contradiction. If resource allocation is a zero-sum game, money (liquid assets) determines resource allocation, …

Okay, here’s what I think you’re missing. Money does not determine resource allocation. But spending money does! Only by spending money do you get to consume goods and services. Therefore, by getting wealthy people not to spend but to invest almost all of their wealth, we get them to give up their claim on where today’s resources are allocated. They control wealth but not resource allocations.

> … and low capital gains tax further concentrates money to the wealthy, …

I believe that this claim is more or less true.

> … then the wealthy gain a greater share of resource allocation next year.

But this claim does not follow. Wealthy people gain a greater share of the wealth allocation next year, but they do not spend that wealth, nor the new wealth they gain each year. They spend only a tiny fraction of it – and invest the rest. Thus, most of this “extra” wealth that wealthy people gain is invested, with resource allocations from that wealth to be determined by spending across the population in general, not by the wealthy who invested it.

> I claim that if the wealthy were to put their money in luxuries (things that don't give capital gains), they would control more allocation in a given year, but then they would decrease their share of resource allocation the next year. I also claim that resource production would increase just fine, as technology initially benefiting luxury production expands toward general production.

Let’s say that the wealthiest 1% of people control half of all wealth. If we forced them to spend that wealth, much of the economy’s resources would be redirected to provide goods and services to the top 1% of people. For a very long time, the remaining 99% of people, especially the lower 80%, would find it very hard to purchase goods and services, for their spending would be dwarfed. Resource production would increase, but I doubt it would be “just fine.” Factories producing mega-yachts, doctors providing exotic cosmetic surgeries, and master chefs preparing one-of-a-kind meals with luxury ingredients such as hand-massaged beef fed grasses from the richest soils on Earth… These are not easily adapted to produce things that regular people need.

By getting those wealthy people to invest their wealth instead, we get them to give up their ability to dictate where today’s resources go. In exchange, they (as a group) get the promise of earning more wealth tomorrow from their investments.

I agree, however, that concentration of wealth is a problem for society. When a small number of people can, in effect, buy the government with pocket change, that’s not good. But a low tax rate on capital gains is only one contributing factor to the concentration-of-wealth problem.