This research mathematically investigates the hypothesis of slow economic growth under capitalism, relative to potential economic growth under a profit-oriented market socialist alternative. The hypothesis is examined within two different economic models: (1) a current-period model that looks at the optimal level of investment in any period from the respective standpoints of the capitalist minority and the general population, and (2) a steady-state equilibrium model that looks at the optimal capital-labor ratio from the respective standpoints of the capitalist minority and the general population. In both cases, two inequalities are derived for the determination of parameter combinations under which growth retardation will hold, the first under the assumption that the aggregate CES production function is linear homogeneous, and the second under the assumption that this function is homogeneous to any degree. The fact that parameter combinations exist under which growth retardation would hold, and also under which growth retardation would not hold, suggests that this issue is essentially an empirical issue rather than a theoretical issue