I have been doing some reading on general equilibrium theory and it has made me highly confused regarding the logic behind NK models. If I have understood correctly, NK models are based on Walrasian or Arrow-Debreu auctions where there is no role for money, banking or credit (since there is perfect barter in this world).
However, in the NK framework the most commonly used methods for introducing money in to the model, is money-in-utility and cash in advance, but this seems very counter intuitive.
In a world with perfect barter, clearly money provides no utility because it cannot be consumed.
And since CIA imposes an additional restriction on consumers that was not present in the Arrow-Debreu world, are we not imposing a welfare reducing constraint?
I understand that in the real world money has many beneficial functions (store of value, removing double coincidence of wants etc etc). But in the Arrow-Debreu/Walrasian world it has no function. And since modern macro models are built around this, including money does not seem logical.
How can we use models to study the price level/inflation when the underlying theory has no logically consistent way of including money? I mean, I have nothing against the fact that money can provide direct utility or that CIA is a real life constraint. My question is on the theory side rather than the empirical side.