Austrian Economics is not about the economics of the country Austria. Austrian Economics is a school of economic thought whose founders were all from Austria. So why am I posting about it? Because I believe in it. Here's why.
The first thing I should do is describe Austrian Economics. Its methodology is much more like geometry than anything else. Whereas most schools such as the German historical school or the Keynesians assume market equilibrium and then immediately begin heavy-duty calculations, the Austrian school makes a few very basic assumptions about human nature and then, by axiomatic-deductive reasoning, attempts to see what the consequences of those assumptions are.
What are its assumptions? There are two major ones: the law of human action, and the law of marginal utility. The law of human action states that, at every moment in time, a human being will evaluate the possible courses of action and their perceived outcomes, and then he will pick the course of action whose outcome is most favorable to himself. This really is inherently obvious. Naturally, wiser men have better developed ideas about outcomes, and are often better at waiting for the longer term for a better outcome. But all men behave in this way. We all want what is best for ourselves. Even sacrifice fits into this picture, because the sacrifice is always for a greater good. The law of marginal utility states that the more we have of a thing, the less valuable each additional unit of the thing is. For example, if I have one gallon of water, an additional gallon might be very valuable. But if I have ten thousand gallons, an additional gallon would be worth considerably less. There is a verse in the Bible that fits this law very well indeed. I believe it's in Proverbs.
From these two assumptions, and essentially modus ponens, the Austrian economists explain an unbelievable number of things. One of their conclusions is that governmental intervention is almost always bad; it is almost always inefficient, and usually produces the opposite of the result desired. In other words, the Austrian school argues for highly limited government and privitization of most things.
Because I believe in the two starting laws, and because I believe in modus ponens as a valid method of arriving at truth from truth, I believe in the results of Austrian economics.
Interestingly, another way of arriving at the advisability of limited government (and thus only serves to reinforce the Austrians' position) is the idea of the inherent sin nature of man. As the saying goes, power corrupts, and absolute power corrupts absolutely. Ergo, government must be severely limited, or it will inevitably oppress its subjects.
I think that Christians should give the Austrian school of economics serious consideration. Where to begin, you might ask? One place is Man, Economy, and State, by Murray Rothbard. Don't be intimidated by the large size: it's quite readable. A tad harder, but absolutely foundational, is Ludwig von Mises' Human Action, which is available for free on the Internet.