Capitalism is the fullest expression of anarchism, and anarchism is the fullest expression of capitalism. Not only are they compatible, but you can't really have one without the other. True anarchism will be capitalism, and true capitalism will be anarchism
Murray RothbardI define anarchist society as one where there is no legal possibility for coercive aggression against the person or property of any individual. Anarchists oppose the State because it has its very being in such aggression, namely, the expropriation of private property through taxation, the coercive exclusion of other providers of defense service from its territory, and all of the other depredations and coercions that are built upon these twin foci of invasions of individual rights.
Murray RothbardPlacing the state in charge of moral principles is equivalent to putting the proverbial fox in charge of the chicken coop.
Murray RothbardIn fact, the libertarian would reason that the fact that human nature is a mixture of both good and evil provides its own particular argument in his favor. For if man is such a mixture, then the best societal framework is surely one in which evil is discouraged and the good encouraged. The libertarian maintains that the existence of the State apparatus provides a ready, swift channel for the exercise of evil, since the rulers of the State are thereby legitimated and can wield compulsion in ways that no one else is permitted to do.
Murray RothbardThe essence and the glory of the free market is that individual firms and businesses, competing on the market, provide an ever-changing orchestration of efficient and progressive goods and services: continually improving products and markets, advancing technology, cutting costs, and meeting changing consumer demands as swiftly and as efficiently as possible.
Murray Rothbard