Given the internal and logical consistency apparent in this life, it stands to reason the Boltzmann brain would have to be simulating the entire thing -- the thought processes of other people, countries, wildlife, the movement of the stars, and so on.
Absent some calculation cost, which Boltzmann brains don't seem to provide, there's no reason everything wouldn't be fully rendered inside the Boltzmann brain.
At some point you just have a God, and are right back at old-timey religion, not that there's anything wrong with that.
Right, GP is leaving out A. necessary skills, and B. the size of the labor pool (multiplied by the labor force participation rate).
For any given skill there is a labor pool with some participation rate, of people who currently have that skill, such that it is accurate to say that the market has a shortage.
Answers to the shortage must solve for either the size of the labor pool, the rate of participation, or the amount of people who have that skill.
Those answers vacillate between importing labor to solve the problem now, or forcing the market to educate people by blocking imported labor.
The problem with importing labor is that it reduces market incentives to educate people. The problem with not importing people is that it means you'll have a labor shortage until the market adjusts and people re-educate.
Profits aren't automatically inflated margins. There are healthy margins, and there are inflated margins. There are even margins that are so thin that it's unhealthy, as in the airline industry.
Now, to loop back around to your point about investment; either party having additional capital will allow that party to further invest.
That is true in the case of formalized businesses, like the ones your thinking about, who can further invest in capital goods.
However, it's also true of more informal businesses that you're ignoring, specifically, the employed individuals themselves.
Employees are in the business of services -- they perform some labor, be it mental or physical, and are paid for that labor. Formalized businesses are their customer.
Profits that those employees obtain are also capital which can be invested -- whether that investment is in their health, their happiness, their residences, their educations, buying tools, the stock market, creating new businesses, affording time to raise and educate their children, and so on.
Theories of economics which ignore that the employed are also themselves informal businesses are disjointed, and fail to explain the totality of economic growth and investment.
Competition only increases efficiency if the price of a good is currently inflated.
Labor is likely under-priced as a good relative to other expenditures, like property and the means to production, so an increase in competition for jobs does not necessarily equate to a more highly functioning society.
Absent some calculation cost, which Boltzmann brains don't seem to provide, there's no reason everything wouldn't be fully rendered inside the Boltzmann brain.
At some point you just have a God, and are right back at old-timey religion, not that there's anything wrong with that.