This is not true. Investment rates of return are much higher when you have smaller amounts of capital to invest, ceteris paribus.
> Fred in this example must pick more conservative investments with his single unit of investable utility - he has only the one to lose!
Must? Clearly not, as lottery "investments" skew heavily towards lower income people, and the lottery is a terrible investment as it has a negative net rate of return.
1. The observation that very wealthy people like Bill Gates and Elon Musk saw their net worth increase at a far faster pace earlier in their career.
2. Basic complexity theory. Managing less assets is less complex than managing more.
3. The range of investments that can absorb one's entire capital without market distortions grows as one has less capital to invest. Say one finds a great opportunity in an ice cream stand on a busy corner that costs $50K. If they only have $50K, they can invest the entire amount and get a great return on investment on their entire net worth. If they have $50 million, that ice cream stand could only efficiently utilize 0.1% of their capital. They would need to find 1,000 similar opportunities to match the return on investment they could have obtained if they were able to invest all of their capital into that one opportunity.
>Also someone with $50 million can still invest into an ice cream stand but someone with $50k cannot be an early investor into a tech company.
That is mostly due to regulatory restrictions on public offerings, and yes, that contributes to greater income inequality.
In a free market however, you'd see low-friction token sales, with thousands of contributors, providing the tech company with its initial capital, not a small cadre of VCs.