# Money in New Keynesian models

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.

• But perfect barter does not deny the existence of prices, nor of changes on them. So in principle, prices does not depend of the existence of a currency (fiat money). Or am I wrong? Maybe I am referring to relative prices, whereas you are referring to an arbitrary index $p$. – luchonacho Sep 18 '17 at 14:00
• By definition a market with perfect barter exists independent of money. A more interesting question is why do people hold money when doing so is costly. Especially given the fact that equally liquid assets yield a positive return. – 123 Sep 18 '17 at 14:12
• @luchonacho; Yes, I am referring to monetary economies. And although you can still have fiat money in the A-D framework, it seems unnecessary to impose additional constraints on the agents that are welfare reducing (when most would argue that money is welfare improving in the real world). My question is similar to the comment posted by @123. – BenBernke Sep 18 '17 at 18:25
• @123, Yes that is also something I've been thinking about. But I am still not sure how we can draw logical conclusions from NK models when the theory they are based on has no role for money. – BenBernke Sep 18 '17 at 18:29
• @123 Which is an equally liquid asset that yield a positive return? My experience with banking tells me that interest on savings accounts are proportionally to withdrawals constraints (for example, a savings account with 6 maximum withdrawals yields less than one with 12 withdrawals per year). – luchonacho Sep 18 '17 at 18:56