[Schroedingersat]

d/dt(wealth) = a * wealth - constant

This is the definition of an exponential and the definition of profit. If under your system you can profit in terms of proportion of a real, finite commodity which is essential for life (ie. control more land in proportion to how much land you control on average with a known strategy available to anyone) then your system definitionally has runaway wealth inequality and will necessarily end in violent collapse or totalitarianism.

The inclusion of the constant prevents entry to the system by people with less than a threshold level of wealth and skews the benefits towards wealth levels where the constant is small. The result also holds as long as the term on the right is polynomial or larger.