It is a widely accepted myth that anarchy is incompatible with capitalism. Even an encyclopedia like Wikipedia states :
There is significant variance between the philosophies of different individualist anarchists. Almost all, following Proudhon, support individual ownership of the particular form of private property he referred to as "possession". (...) However, what these philosophers all have in common is a rejection of both capitalist economics and collectivist notions of society and a pronounced focus on individuality.
Ever since I deconverted to anarchism, I have noticed the widespread existence of this myth. I hope this entry will help dispel it.
First of all, anarchy and capitalism do not pertain to the same thing at all.
Capitalism is a positive ideology - it states what economic system should exist. Strictly defined, capitalism is a system where resources are owned by individuals instead of the government, and where these resources circulate in free markets. Capitalism is based on voluntary action, instead of government coercion or individual force.
Anarchy, on the other hand, is a negative position - no-government. It merely states that government should not exist. This does not indicate what system will indeed exist in an anarchic society, which is why many anarchists label themselves further (such as anarcho-syndicalist or anarcho-capitalist). In an anarchy, people can assemble in any economic system they desire - socialism, capitalism, syndicalism, whatever they desire. But they will also have to face the relative degrees of success of each, something that statist believers definitely do not want.
One property that both capitalism and anarchy share is tolerence for the variety of value systems that exists in any society. In a capitalist system, people are free to express their values, through consumer preference, in any way they want. Anarchy is simply an extension of this principle, because government is the single organization that restricts value-expression the most, by imposing a single value system on the population of an entire territory by force. In an anarchy, the individual not only has consumer preferences, but political preferences as well.
Another related property of both is that they are about individual choice. Government does not enforce values on you (statism/socialism), other people cannot enforce their values on you (democracy/syndicalism), you are truly free to make choices for your own life.
One objection that is raised against this analysis, is that capitalism depends on government to exist. This is usually based on the perennial confusion between corporatism (state capitalism) and capitalism, which are very different concepts. Corporatism - the statist belief that leaders of corporations should exploit political power for their own gain - is definitely incompatible with anarchy. However capitalism, which is based on voluntary action, is not harmonious with government, which is based on coercion, but rather with anarchy, which is based on voluntary action. And we observe in practice that strong governments, with very few exceptions, seek to control more and more of any given economy, eventually completely consuming it.
Certainly it would be difficult for a capitalist system to exist without some form of organizational contractual enforcment (although of course personal enforcment is inherent). Black markets, which are trade systems that evade enforcment (at least of the government kind), are extremely costly and unsafe. However, anarchy is perfectly compatible with private forms of contractual enforcment, so markets in an anarchy would be far safer and have less overhead than black markets.
So it appears that there is in fact no contradiction between anarchy and capitalism. And since capitalism is the natural state of man (insofar as most people are peaceful and desire to cooperate in order to raise their standard of living), an anarchic economy is most likely to evolve into some form of capitalism. Collectivists, who believe that man is too selfish and degraded for freedom, would complain just as loudly as they do today about progress and the expression of individual values, but we would still point and laugh at them. Because there are always people who are just plain stupid.