This is a bit misleading; correct to " reserve army of labor." In the past, for example, the main reserve army was the rural population.
But the main error is seeing this reserve army as the "problem," when in fact the elimination of that reserve army would be the death knell of capitalism. Economic crises are NOT "crises of capitalism" but, rather, the _health_ of capitalism.
Carrol
P.S. Marx's Critique of Political Economy is of course incomplete*. But no part of his theory is as rock-solid as this principle of the reserve army.
*If humanity escapes more or less whole from the barbarism of capitalism (which is looking doubtful) historians a few centuries from now, looking back on capitalism, can perhaps complete the Critique (as an interesting historical curiosity).