Also important to note that the TRPF is largely about new machinery. Competition involves increasing technology, which raises the mass of commodities and usually the mass of profits, but lowers the rate of profit. This is only fought by further raising the mass of profits via expansion, which is why we get imperialism as capitalism grows.
Capital volume 2 goes over why this can't solve the problem, specifically the sections on departments 1 and 2 (producing means of production and means of consumption).