An economics professor told me that General Equilibrium models are a sophistication of barter. Does that imply that they don't include money? And if that is the case, are there any attempts to include it?
Moreover, does this have any implications on the way we understand macroeconomics?
Thanks.
While many general equilibrium models do not need to model money to approach the questions that they would like to answer, there are many models that do include money to address questions that need money to be a relevant feature of the model. These models do it in a variety of ways -- some might be more relevant than others. I will try and describe two of the approaches briefly.
When I think of a cash-in-advance (CIA) model, the first models that come to mind are Lucas (1982) and Lucas Stokey (1987). Models that take this approach have agents saving in assets and money, but they must finance any consumption solely through their money holdings (basically assets are less liquid than money which isn't the worst approach). There are many critiques of the CIA of which I find Wallace (1998) to be one of the more thoroughly presented.
More recently there has been a push to use models of money that are less "ad-hoc" about how money works. Some foundational papers of this field are the Kiyotaki Wright papers (1989, 1991, 1993). These papers build a very basic model of money and show what role it plays in economics -- There is a good discussion on Randall Wright's Wikipedia page under the sub-title "Research contribution." While these models confirmed some of the reasons for money to exist in a model, they were quite simplistic and lacked many other features of the real economy. A monetary course I took labeled these types of models as "Generation 1 models of money." There was a group of papers that were known as "Generation 2 models of money, but these shared many of the simplifications made in Generation 1 (so I won't discuss them here).
Since this time Lagos Wright (2004) introduced a more complete framework (we referred to these as "Generation 3 models of money." One of the issues faced by these new monetarist models is that in order to solve the model, one must keep track of the entire distribution of money -- This is computationally infeasible unless the authors introduce a simplification in a different area of the model (in the Lagos Wright model, they simplify the form of utility in order to be able to compute the distribution of money next period). There is on-going research in this area and, in my opinion, is an open area for improvement in the literature.
This might be more of a comment, but hopefully it helps. If you think of the classic Walrasian equilibrium, it can be called a "generalization of barter" in the sense that: In the beginning, everyone starts with some set of goods (and no money). In the end, everyone finishes with a different set of goods (and no money).
Now unlike with barter, in a Walrasian equilibrium you usually tell a nice story that does involve money about what just took place in the middle. Namely, you can suppose that people used money in the process of exchanging these goods, and note that there exist constant prices for each of the goods such that the money exchanged all "adds up" correctly. And often you extend that story by assuming that people start with initial endowments or so on. But it's still a sophistication of barter in that the money has no intrinsic value and is just a means/mechanism/storytelling device for people to exchange goods in order to Pareto-improve.
(Edit/PS, it occurs to me on re-reading the question that you may not have heard of Walrasian equilibrium or general equilibrium models, in which case I definitely recommend reading about them, as it should help clarify the comment.)
