Final answer:
The theory that recognizes competition as potentially wasteful but maintains private property within a framework of communal wealth distribution is Socialism.
Step-by-step explanation:
The theory that posits competition may be wasteful but allows for private property is Socialism. Socialism acknowledges the role of private property but emphasizes the public management of resources to ensure equitable distribution. Opposed to the free-market competition of Capitalism, where Adam Smith's concept of the “invisible hand” regulates the market, Socialism advocates for a planned economy where wealth and resources are distributed based on communal needs. In Communism, proposed by Karl Marx, private property is abolished in favor of communal ownership of the means of production.
Mercantilism, largely a historical system, associated with an earlier period, prescribed heavy state regulation and was focused on accumulating wealth through trade surplus and colonial expansion, which is not closely related to the theories of property ownership and competition addressed in the question.