My initial reaction is that (1) is preposterous, because there is no economics of the brain, as it is not made up of rational actors who trade or manage resources as individuals. Therefore it must be (2).
Also, I happen to know from experience that there is much said and written about (2) and less about (1).
Here is some evidence supporting this:
- Duke University's Center for Neuroeconomic Studies states that they apply "the techniques of cognitive and systems neuroscience – along with computational modeling – to understand economic decision making and related behavior".
- The IISDM at NYU (who have a program in neuroeconomics) says their goal is to "better understand the mechanisms, predict the impacts, and shape the policies that will define the study of decision-making tomorrow (...) by developing novel research infrastructures to support the propagation of neurobiological insights about the human animal into the policy domain"..
- The Society for Neuroeconomics says their mission is to "foster research on the foundations of economic behavior by promoting collaboration and discussion among scholars from the psychological, economic, and neural sciences".
- The most highly cited result on Google Scholar for "neuroeconomics" is titled "Neuroeconomics: How Neuroscience
Can Inform Economics". The third hit's abstract says "Economics, psychology, and neuroscience are [aiming to provide] a single, general theory of human behavior. This is the emerging field of neuroeconomics (...) The goal of this discipline is thus to understand the processes that connect sensation and action by revealing the neurobiological mechanisms by which decisions are made."
So I would conclude from this that neuroeconomics is the study of human decision making, by application of neuroscience.
Granted, at this point I feel compelled to admit that perhaps I was too quick in my initial reaction: Is it really possible to isolate the study of the human brain from the study of human decision making? There is just so much overlap that even a "pure" neuroscientist will inevitably generate research which bears much relevance to economics. And with economics, the only way to "escape" neuroscience is to assume that all actors are perfectly rational, which is almost certainly at least a little bit untrue (although a staple of classical economics). It's probably a bit of loop, and I'd favor NYU's emphasis on it being interdisciplinary field rather than "field X applied to field Y". That said, indeed, most neuroeconomics studies appear to be interested in solving economics problems, and not neuroscience problems.