The natural state of affairs when market entry is free is for net
utility gain from profit-orientated investment to tend to zero. This is
not the same thing as average monetary gains because the marginal
utility of money declines as the amount of money an individual or group
has increases. Therefore the utility of money that might be gained in
profit is less than the utility of the same amount of money that might
be lost. An investment would only make sense from a utility point of
view if the potential profit was large enough to cancel out the greater
value of dollars lower on the graph of $ vs. marginal utility. The
difference between the marginal value of higher dollars and lower
dollars tends to zero as the difference in the level decreases, at a
small enough margin the derivative is almost a flat line. The rate of profit in a free market is therefore positive and indeterminable in advance, assuming people have no preference for gaining income by profit compared to wage labor. This however cannot be assumed. People may have a preference for recieving income as profits, as wages or in some other way. Therefore the average rate of profit could be negative if there is a general preference for undertaking entrepreneurial tasks rather than wage tasks. .
Comparetively
rich people would probably be able to make bigger investment will
staying in a comparatively straight area of the graph. The value of
higher dollars would not be significantly greater than lower dollars
until the gap between them was quite large. Therefore rich people would
make larger investments for the same level of profit or make the same
size investment for lower levels of profit than poor people and would
therefore tend to make more smaller profits more often.