Actually, anarchists do have one thing to thank "anarcho"-capitalists for. Bryan Caplan, professor of economics at George Mason University, wrote an Anarchist Theory FAQ. It had many anarchists heavily criticizing it, particularly its acceptance of "anarcho"-Capitalism... the general idea being "How Anarchistic could it be if it continues Capitalism." One of the best by products of debate with the "anarcho"-capitalists was the refocusing of anarchists on economics, specifically its historical opposition to capitalism and the need to continue to organize against it. Bryan's FAQ also triggered An Anarchist FAQ project, which has become simply the best resource of its kind and spawned itself 6 mirrors and is an UniGuide Featured Site to give you some idea of its academic quality. Fortunately, it doesn't focus simply on "anarcho"-capitalism, or even just capitalism... but is probably the best comprehensive resource.
I'm still anxiously awaiting the completion of the upcoming sections on Platformism, Synthesism, Libertarian Muncipalism and TAZ. Likewise, I look foward to the anarchist critique of State Socialism.
To jump right into economics, a good place to start is Section C - What are the myths of capitalist economics?
C.1 What determines prices within capitalism?
C.1.1 What is wrong with this theory?
C.1.2 So what does determine prices?
C.1.3 What else affects price levels?
C.2 Where do profits come from?
C.2.1 Why does this surplus exist?
C.2.2 Are capitalists justified in appropriating a portion of surplus value for
themselves (i.e. making a profit)?
C.2.3 Why does innovation occur and how does it affect profits?
C.2.4 Wouldn't workers' control stifle innovation?
C.2.5 Aren't executives workers and so create value?
C.2.6 Is interest not the reward for waiting, and so isn't capitalism just?
C.2.7 But wouldn't the "time value" of money justify charging interest in a
more egalitarian capitalism?
C.3 What determines the distribution between profits and wages
C.4 Why does the market become dominated by Big Business?
C.4.1 How extensive is Big Business?
C.4.2 What are the effects of Big Business on society?
C.4.3 What does the existence of Big Business mean for economic theory and
C.5 Why does Big Business get a bigger slice of profits?
C.5.1 Aren't the super-profits of Big Business due to its higher efficiency?
C.6 Can market dominance by Big Business change?
C.7 What causes the capitalist business cycle?
C.7.1 What role does class struggle play in the business cycle?
C.7.2 What role does the market play in the business cycle?
C.7.3 What else affects the business cycle?
C.8 Is state control of money the cause of the business cycle?
C.8.1 Does this mean that Keynesianism works?
C.8.2 What happened to Keynesianism in the 1970s?
C.8.3 How did capitalism adjust to the crisis in Keynesianism?
C.9 Would laissez-faire policies reduce unemployment, as
supporters of "free market" capitalism claim?
C.9.1 Would cutting wages reduce unemployment?
C.9.2 Is unemployment caused by wages being too high?
C.9.3 Are "flexible" labour markets the answer to unemployment?
C.9.4 Is unemployment voluntary?
C.10 Will "free market" capitalism benefit everyone, especially
C.11 Doesn't Chile prove that the free market benefits everyone?
C.11.1 But didn't Pinochet's Chile prove that "economic freedom is an
indispensable means toward the achievement of political freedom"?
C.12 Doesn't Hong Kong show the potentials of "free market"
Section F: Is "anarcho"-capitalism a type of anarchism. Contains an excellent critique.
F.1 Are "anarcho"-capitalists really anarchists?
F.1.1 Why is the failure to renounce hierarchy the Achilles Heel of right-wing
libertarianism and "anarcho"-capitalism?
F.1.2 How libertarian is right-Libertarian theory?
F.1.3 Is right-Libertarian theory scientific in nature?
F.2 What do "anarcho"-capitalists mean by "freedom?"
F.2.1 What are the implications of defining liberty in terms of (property)
F.2.2 How does private property affect freedom?
F.2.3 Can "anarcho"-capitalist theory justify the state?
F.2.4 But surely transactions on the market are voluntary?
F.2.5 But surely circumstances are the result of liberty and so cannot be
F.2.6 Do Libertarian-capitalists support slavery?
F.2.7 But surely abolishing capitalism would restrict liberty?
F.2.8 Why should we reject the "anarcho"-capitalist definitions of freedom
F.3 Why do "anarcho"-capitalists generally place little or no
value on "equality," and what do they mean by that term?
F.3.1 Why is this disregard for equality important?
F.3.2 But what about "anarcho"-capitalist support for charity?
F.4 What is the right-libertarian position on private property?
F.4.1 What is wrong with a "homesteading" theory of property?
F.4.2 Why is the "Lockean Proviso" important?
F.4.3 How does private property affect individualism?
F.4.4 How does private property affect relationships?
F.4.5 Does private property co-ordinate without hierarchy?
F.5 Will privatising "the commons" increase liberty?
F.6 Is "anarcho" capitalism against the state?
F.6.1 What's wrong with this "free market" justice?
F.6.2 What are the social consequences of such a system?
F.6.3 But surely Market Forces will stop abuse by the rich?
F.6.4 Why are these "defence associations" states?
F.6.5 What other effects would "free market" justice have?
F.7 What is the myth of "Natural Law"?
F.7.1 Why "Natural Law" in the first place?
F.7.2 But "Natural Law" provides protection for individual rights from
violation by the State. Those against Natural Law desire total rule by the state.
F.7.3 Why is "Natural Law" authoritarian?
F.7.4 Does "Natural Law" actually provides protection for individual liberty?
F.7.5 But Natural Law was discovered, not invented!
F.7.6 Why is the notion of "discovery" contradictory?
F.8 What role did the state take in the creation of capitalism?
F.8.1 What social forces lay behind the rise of capitalism?
F.8.2 What was the social context of the statement "laissez-faire"?
F.8.3 What other forms did state intervention in creating capitalism take?
F.8.4 Aren't the enclosures a socialist myth?
F.8.5 What about the lack of enclosures in the Americas?
F.8.6 How did working people view the rise of capitalism?
F.8.7 Why is the history of capitalism important?
F.9 Is Medieval Iceland an example of "anarcho"-capitalism
working in practice?
F.10 Would laissez-faire capitalism be stable?
F.10.1 Would privatising banking make capitalism stable?
F.10.2 How does the labour market effect capitalism?
F.10.3 Was laissez-faire capitalism stable?
"Anarcho"-capitalists shouldn't jump straight to this section though... instead they should be sure to read the section on plain old Capitalism first, since many of their criticisms and discussions are already answered there; like Profit vs. Surplus value.
The FAQ, in Section G - Is individualist anarchism capitalic?, questions the claims made by capitalists that their economics are a natural extension of Individualistic ethics.
G.1 Are individualist anarchists anti-capitalist?
G.2 Why does individualist anarchism imply socialism?
G.3 What about "anarcho"-capitalism's support of Tucker's
G.4 Why do social anarchists reject individualist anarchism's
G.5 Benjamin Tucker - capitalist or anarchist?
G.6 What are the ideas of Max Stirner?
G.7 Lysander Spooner - right-Libertarian or libertarian socialist?
The Appendix of the FAQ specifically deals with Anarchism and "anarcho"-capitalism.
Replies to Some Errors and Distortions in Bryan Caplan's
"Anarchist Theory FAQ" version 5.2
1 Individualist Anarchists and the socialist movement.
2 Why is Caplan's definition of socialism wrong?
3 Was Proudhon a socialist or a capitalist?
4 Tucker on Property, Communism and Socialism.
5 Anarchism and "anarcho"-capitalism.
6 Appendix: Defining Anarchism
Replies to Some Errors and Distortions in Bryan Caplan's
"Anarchist Theory FAQ" version 4.1.1.
1 Is anarchism purely negative?
2 Anarchism and Equality
3 Is anarchism the same thing as socialism?
4 Anarchism and dissidents
5 How would anarcho-capitalism work?
I do think that "anarcho"-capitalists grossly over-value their importance in debate in the anarchist movement. Quite frankly, they aren't part of it as they don't choose to work on projects so much as try and "win" their debates on Usenet which only serve to continue to prop up our Oligpolitic system. The most important debates now I believe are interms of how how to organize... what type of libertarian structures to use to improve society. Some of the debates I'm glad that are fading in importance are the Workerist-ZeroWork and Lifestylism-Social Ecoloy. The questions are how best to organize in your community (Libertaian Muncipalism? Anarcho-Communism?), how to organize your job (Syndicalism? Boring from Within? Dual Unionism? The General Strike? Direct Action?).
Finally, there is a book by Ulrike Heider called "Anarchism: Left, Right and Green" folks should check out.