From Mises’ Theory of Money and Credit (though it is from the later material, which was written much later than the original 1912 edition):
“There are problems of theory full comprehension of which can be attained only with the aid of the theory of indirect exchange. To seek a solution of these problems, among which, for example, is the problem of crises, with no instruments but those of the theory of direct exchange, is inevitably to go astray.” (p. 462)
I’m not as knee-jerk opposed to “mathematical models” in economics as many Austrians claim to be. I think when we talk about Robinson Crusoe, or a two-country international trade problem, or use a Hayekian triangle, we’re basically doing the same type of thing.
However, Mises’ quote above really struck me, because I had had similar misgivings in our upper-level macro courses at NYU. In the world of the model, people (or should I say, the Representative Agent) had rational expectations, knew all the production functions, demand functions, and vector of equilibrium prices.
In that world, there was no role for money as a medium of exchange. We could arbitrarily pick one of the commodities as the numeraire, define its price as 1, and then price everything else relative to it. But ultimately this was a world of direct exchange, because there was no issue of goods having different degrees of liquidity (which is what drives the demand for money in the Austrian story).
Now of course, the mainstream macro guys want to be able to have a central bank in the model, and to put different monetary policy rules through a windtunnel. So there has to be “money” in the model, and there has to be a reason for people to hold it. So (at least in the standard models we were learning) they would just throw real cash balances directly in the utility function, so that the Representative Agent got utility from holding purchasing power the same way he would get utility from holding a Picasso.
It always seemed fishy to me that we were deriving “optimal” monetary policy in a model in which money really served no purpose, and where we had to make ad hoc tweaks to force people to even want to hold money.