Libertarianism is about freedom, this includes the freedom to buy and sell things, which is capitalism. Not only are they compatible but they are part of each other, for capitalism, you need freedom, and freedom implies capitalism. They are quite close, only that capitalism focuses on economic freedom while libertarianism focuses on personal freedom.
The free market is a system where no person or corporation has unlimited power. It breaks up concentrated power and offers a choice to consumers. Consumers also have some kind of say in the market through "dollar voting." Competition will foster diversity and innovation, as well as generally making cheaper prices. It also means that the most inefficient companies go bankrupt and the most efficient ones remain (and new companies are started). Agreements and exchanges are voluntary and mutually beneficial. The market allocates resources most efficiently. This fits in with libertarian values of freedom and economic power. It is also generally not in the interest of the market to fight wars, which is also a libertarian policy. The market also takes the place of the government in many economic areas and the libertarians are very much in favor of small government. Economic freedom plays a large part in all freedom and Libertarians endorse this. Overall, a true free market, not a "crony" or corporate state, may well be better for the economy and people as a whole.
Libertarian values and free market capitalism go hand-in-hand. Libertarians usually stand on the side of small government, which is unequivocally important in the argument for free market capitalism. The Libertarian belief that government should stay out of people's lives should translate easily into laissez-faire policies that would encourage a government devoid of mettling in the economy.
I don't have a ton of knowledge on this subject but I feel I should say that... Yes. I don't exactly know why but I know that free market capitalism is what has set the United States apart from other countries and allowed us to be successful. I mean it is great isn't it?
Free Market Capitalism is merely the idea that government has no business in telling a man what he can do with his own business, body, and property.
Even so, the definition of free market capitalism is quite narrow and simple. Therefore as a system it does not require extreme arguments to refute. For example:
Buying a car to roll with is all good for the dealer and the customer, but even that has effects for everyone such as global warming. The buyer has used financially legitimated power on others. Whether or not the legitimation is correct is subject to petition in a democratically arranged society.
In a true free market individuals don't always have a say in how financially legitimated power is used upon them. But in a libertarian society, no power should be used in a manner that violates of the rights of others. That calls for democratic arrangements that are incompatible with a truly free market.
In fact they would work better than our current values as they'd allow the free market to thrive and be much healthier than it is now. If we stopped allowing the big businesses to control the market, the free market would be in a much better place, as everyone would be on a level playing field. As it is now, it is severely uneven, and the little guys have hardly a chance to succeed against the big boys. If we instilled Libertarian values, I believe this would change. So yes I think Libertarian values are very much compatible with free market capitalism and in fact may be much better for the free market system.
Libertarian values are not only compatible with free market capitalism, they are the values most compatible with a truly free market. Libertarians believe in a minimal amount of government intervention, generally allowing the free market and the private sector to sort things out for itself. Provided there is limited government intervention to keep big monopolies from destroying the free market, this will allow a free market to thrive.
One of the basic principles of a free market economy is that both buyers and sellers have perfect knowledge. Well, big businesses like Monsanto, tobacco companies, and the Koch family have repeatedly demonstrated that they will go to the ends of the Earth to prevent consumers from gaining full knowledge about their products and the effects thereof. Time after time, government regulation has become a necessity to force companies into full disclosure. Unless you adopt the precautionary principle as a mandatory criteria for consumer goods (and provide a means of enforcement - not very libertarian), a libertarian government would be incompatible with a free market economy because corporations would work to subvert the need for perfect information in the market place, hurting consumers and violating the principles of a free market economy.