This is a question that I enjoy asking and I’m curious in the answers you get as well. I attended Mises University this past summer and I had the chance to ask the question in the panel on micro-economics. Here’s the answers I got:
DiLorenzo: economics of taxation and public finance. Labor economics.
Block: “pick something you enjoy”
Klein: theory and practice of entreprenuership (currently a poor understanding in applied entrepeneurship in the economy). Theory of rent (see Fetter).
Herbner: interational trade.
Murphy: need to look at disequilibrium yet with predictible change.
I also attended the FEE Austrian Economics seminar this past summer and here are the answers I got when I asked Garrison, Horwitz, and White the question, plus some suggestions brought out during the lectures from other lecturers.:
Horwitz: look @ eHarmony, see why it is successful in terms of human capital. Regulatory and fiscal policy in relation to capital based macro.
Butos: what prevents scientific discovery from being commercialized? Is it possible How to assign property rights?
White: need to story out which cycles were caused by central banking and which were a result of technical shocks. Essentially, more work in ABCT.
There’s also Mises’ Suggested Research Topics which is available for download on the site and has some great stuff.
The parallels between cognitive science and the Austrian method and a praxeological account of the philosophy of science, broadly based on neo-Aristotelianism.
Anything involving global warming. An enormous amount of public money is funneled into AGW research. If you linked anything Austrian, like studies of business cycles during periods global warming, you could probably get a ton of grant money.
You could increase knowledge, deprive the state of resources, and at the same time profit.
Third. Especially the work by Hayek regarding Spontaneous Order. This is used in everything from physics to neurology to explain or illustrate specific kinds of behaviors that were once considered random ‘noise’ in systems.