The paper addresses the problem of the optimal control of the investment policy with Schumpeterian dynamics of capital stocks with two efficiency levels over infinite time. Pontryagin’s maximum principle was used to find the investment volumes that are optimal for maximizing profit for each level. Qualitative analysis of the dynamical system with a variable structure characterized by optimal control values was carried out. The corresponding equilibrium for each optimal control value was proved to possess global stability. The invariant set for the investigated system with variable structure was identified. The time instant after which the profit will be arbitrarily small was estimated. The viability problem for the economic system with two and an arbitrary number of efficiency levels was formulated. The admissible controls that ensure viability were identified.