This post is really about maths, dark ages, and understanding macro.
There are two ways of putting monetary exchange into a macroeconomic model: the proper way; and the quick and dirty way. Keynesians generally use the quick and dirty way. That's OK. But there may be problems if people don't understand what you are doing.
There's a lot to be said for the quick and dirty way. It's quick, even if it is dirty. It's a perfectly defensible short-cut that does the job quickly and simply, even if it's not perfect. The biggest problem is not that it's not perfect; it's that people may not realise you have introduced monetary exchange. Precisely because it's so quick and easy, they might not realise you've done it. Sometimes even the model-builders themselves might not realise they've done it. The biggest danger is that people will think it's a model of a barter economy, when it isn't.
Suppose you start with a non-monetary real business cycle model, and you want to introduce money into the model.
The proper way is to introduce trading frictions or transactions costs explicitly into the model. Then show that people in the model will find it cheaper or easier to do monetary exchange than barter exchange.
The quick and dirty way is simply to assume that barter is prohibitively costly, while monetary exchange has zero transactions costs. You ban barter. You ban all markets except monetary markets.
In a barter economy with n goods, there are n(n-1)/2 markets, where each of the n goods can be swapped directly for each of the n-1 other goods. (You divide by 2 because if there's a market where you can swap apples for bananas, that is also a market where you can swap bananas for apples.) In a monetary exchange economy, with n goods (including the good that is used as the medium of exchange), there are only n-1 markets, where money can be swapped for each of the n-1 other goods.
The quick and dirty way of introducing monetary exchange into a macro model simply amounts to "banning" a whole slew of those n(n-1)/2 markets. The only markets that are allowed to exist are the markets where one good ("money") is traded against each of the other goods. You write down the supply and demand functions, or equilibrium conditions, for the n-1 monetary markets, and you don't write down the equilibrium conditions for the other "banned" markets, because those markets don't exist.
The trouble is, anyone looking at the model may not realise what you've done. They don't see what isn't there. They don't see what's missing. They don't see that you have implicitly assumed a monetary exchange economy. Because you didn't say you were doing it. In fact, you may not even realise yourself that you have done it. Because we live in a monetary exchange economy, where each good (except money) has one market, and one price, it's natural for us to think this way. We didn't see the rabbit go into the hat. We might even think it's still a model of a barter economy, because nobody ever said explicitly that the barter markets were banned.
Let's take an example.
There are two goods: apples and bananas. And two time periods: today and tomorrow. That means there are really 4 goods: apples today; apples tomorrow; bananas today; and bananas tomorrow. With n=4, there are n(n-1)/2=6 markets. Apples today can be traded for: bananas today; apples tomorow; and bananas tomorrow. That's 3. Bananas today can be traded for: apples today (already counted that one); bananas tomorrow; and apples tomorrow. That's 2 more. And apples tomorrow can be traded for bananas tomorrow. That's 1 more, making 6 markets in total.
With 4 goods it's tempting to say there are 4 prices, but we can make one good the numeraire, and measure all prices in terms of that numeraire good, and say there are 3 relative prices. That's conventional wisdom. But it's wrong.
There are 6 markets, so there are 6 relative prices, one for each pair of goods traded in each of the 6 markets.
How do we get from 6 down to 3 relative prices? How do we make conventional wisdom correct again? We introduce arbitrage. If the 6 relative prices were out of line, there would be an infinite excess demand or supply in some of the markets, which would bring the 6 relative prices back in line.
But arbitrage only works if you can buy and sell as much as you want. If the relative price in one market is sticky, and is away from the market-clearing price, there will be excess supply of one good and excess demand for the other. So some traders won't be able to trade as much as they want to at that price, because they won't be able to find someone to take the other side of the trade. Arbitrage only works if prices are allowed to adjust to market-clearing levels.
But in a barter economy there are more markets than are needed. If people want to swap apples today for bananas today, but can't, because the price in that market is stuck at the wrong level, they just work around it, by trading apples today for apples or bananas tomorrow, then trading those for bananas today.
Now let's introduce money into this economy using the quick and dirty method. There is money today and money tomorrow. That's now 8 goods, and 32 markets. Now let's ban trade in all but 5 of those markets. You can trade money today for: apples today; bananas today; and money tomorrow. And tomorrow, when the markets re-open, you can trade money tomorrow for apples tomorrow and bananas tomorrow. We have banned all markets which don't trade money; and we have also banned the futures markets where you can trade money today for apples and bananas tomorrow. If you want to swap apples today for bananas tomorrow, there is only one way to do it. You have to sell apples today for money today, sell money today for money tomorrow, wait till tomorrow, collect your money, and buy bananas tomorrow.
The markets that exist in the model economy I have described above are exactly the same as in the standard New Keynesian model. The only difference is that the New Keynesian model has many different varieties of fruit, while I have only two.
What's the difference between the original barter model, with 6 markets open today, and the monetary exchange model, with 5 markets, but only 3 of which are open today?
If people know the future with certainty, and if all prices are at equilibrium, it makes absolutely no difference whatsoever. Any trade you want to do in the original barter economy you can still do in the monetary exchange economy, just in a more roundabout fashion. Exactly the same equations that define the equilibrium in the original barter economy will still define the equilibrium conditions in the monetary exchange economy.
Anyone looking at the equations describing the equilibrium conditions for the New Keynesian model could very easily be fooled into thinking that the New Keynesian macroeconomic model is just a Real Business Cycle model in disguise. Because the equations are identical.
Introducing uncertainty will make a bit of a difference, but only because I have banned the futures markets where money today can be traded for apples or bananas tomorrow. People might want to use those markets, to buy and sell insurance against future bad harvests. But let's ignore uncertainty.
It's when prices are not at market-clearing equilibrium levels that banning those barter markets will make a big difference. Let me explain why.
Suppose all prices are initially in equilibrium. There are 5 markets and 5 prices in this economy: money is the numeraire, so there's the money prices of apples and bananas today and tomorrow, and there's the nominal rate of interest which is the price of money today relative to money tomorrow. The price of a loan of money from the central bank, in other words.
Now suppose we hold 4 of those prices fixed, but assume the central bank makes a mistake and raises the rate of interest above the equilibrium level. What happens?
In a barter economy, where all markets were open, very little would happen. And if all agents had the same rate of time preference, and if tomorrow's preferences and productivity for apples and bananas were the same as today's, so there wouldn't be any loans in equilibrium anyway, absolutely nothing would happen.
Just to keep it simple, assume apples and bananas perish at the end of the day. With the real rate of interest set too high, everyone will want to save. There will be an excess supply of apples for money, and an excess supply of bananas for money. Apple producers will be unable to sell apples for money, and banana producers will be unable to sell bananas for money. So what. The only reason the apple producers wanted to sell apples for money was so they could use that money to buy bananas. And the only reason the banana producers wanted to sell bananas for money was so they could use that money to buy apples. Why don't they just swap apples for bananas? If it's not prohibited by very high transactions costs, or theorist's fiat, they will. And because the relative price of apples for bananas is at the right level, by assumption, we will get the right level of production and consumption of apples and bananas.
If producers can directly barter apples for bananas, bad monetary policy (or anything else) that sets the rate of interest above the equilibrium natural rate cannot prevent the efficient production and trade of apples and bananas. Bad monetary policy cannot cause a recession.
But if producers cannot directly barter apples for bananas, because the theorist has banned direct barter, bad monetary policy that sets the rate of interest above the equilibrium natural rate will prevent the efficient production and trade of apples and bananas. Bad monetary policy will cause a recession. If everybody wants to save, and forego current consumption for future consumption, producers will be unable to sell apples and bananas for money. So they will stop producing apples and bananas, because there's only so many apples that apple producers will want to eat themselves, and likewise with bananas.
Paul Krugman is right, unfortunately. It is too easy to be blinded by the maths. You can stare at the equations defining the equilibrium conditions all you want, but you won't see what's not there. You will see the consumption-Euler equation, which defines the equilibrium condition for present vs future consumption. But you won't see the equation which defines the equilibrium condition in the barter market for apples and bananas. Because that equation doesn't exist; because that market doesn't exist, in a monetary exchange economy. And that equation doesn't exist, because it is redundant, because that market is redundant, in a real business cycle model where all prices are at equilibrium. And because you don't see what's not there, you won't be able to see the difference between a real business cycle equilibrium model of a barter economy and a New Keynesian disequilibrium model of a monetary exchange economy.
Stop looking at the damned equations, because you can't see the equation that's not there. Think about the model. In particular, think about what markets exist and what markets are implicitly assumed not to exist.
And Paul Krugman is also right that there's a Dark Age. There's nothing original in this post that is not somewhere in Clower, Barro-Grossman, or Malinvaud. I've just applied some old 60's and 70's stuff to talk about New Keynesian macro, and New Monetarists' misunderstanding of it. But then I don't think New Keynesians are blameless either. How many New Keynesians make explicit that they are introducing monetary exchange into their models by the quick and dirty method — by banning all except monetary markets? And how many of them really understand what it is they are doing when they introduce monetary exchange, and why it matters? (Update: and as Andy says, in the first comment, some of those "Dark Age" economists have indeed been introducing money the "proper way", which is good).
Worthwhile Canadian Initiative 
Scott: I think I am agreeing with you. But since it’s the real interest rate that matters (in this NK model), it wouldn’t matter what units we measured the nominal interest rate and prices in. What actually gets lent by the central bank is the medium of exchange. But it’s the real interest rate measured in apples and bananas that matters.
Gizzard: ” As long as I could keep my press running, for as long term as I wished, I could maintain production at that level.”
No. The 1970’s told us we can’t. Theory tells us we can’t. Zimbabwe tells us we can’t. You can only do it as long as actual inflation exceeds expected. If you keep on trying, you destroy the currency altogether.
“Trading and selling are two completely different things. Selling is what modern economies depend on barter economies are simply trades. Not until money is introduced are we selling something.”
No. That’s just semantics. When I sell apples for money, I am buying money with apples, and trading money and apples.
When I first came to Canada I walked into a bank, put some pounds Sterling on the counter, and said I wanted to buy some Canadian dollars. The teller gave me a strange look, but it made perfect sense to me!
Money is really weird.
Consider: suppose that tomorrow everyone woke up and forgot about money. People discover pieces of paper and metal discs in their wallets, and notice numbers on something called a “bank account”, but just see pieces of paper, metal discs, and numbers on a screen with only non-monetary uses. It occurs to nobody to accept these things as a medium of exchange, and all trade is reduced to barter.
How does an economist describe this transition? Did M fall to zero, or did V fall to zero? While the pieces of paper, metal discs, and bank account records all remain the same as the day before, is there any sense in claiming that M was constant? If something isn’t used as a medium of exchange, then in what sense should it still be counted as part of the money supply?
This is an extreme example, but what if the change was gradual, occurring over a year or more. How can one tell the difference between a fall in V and a fall in M? Aren’t they kind of the same thing? I don’t know … this is getting confusing.
JP:
but the first piece of paper will never be accepted by C
This line of reasoning reflects regrettable decline in morals running so deep that it is not even possible to imagine a group of people who would recognize mutual obligations without outside coercion. The operative word in the imaginary scenario with pieces of paper was “trust”.
Gold scarcity is an imperfect substitute for lack of trust in accounting for labour (broadly understood), as is partial trust of the populace in the modern banking system, in combination with the legal system coercive power to make up for deficit of such trust. Either make possible use of the respective medium as a store of value, without need to appeal to some intrinsic value.
None of what was said above is of course original or not well known.
Nick
Youre telling me that if I went to every business in my area and purchased $1000 gift certificates(which I then gave away to people) with my printed cash, and I did this regularly and I paid someone to do that all around the country until I had spent my hundreds of billions of undetectable counterfeit currency, that this would only cause price rises and not bring forth new and untapped production.? Why would they simply raise prices because some guy comes in regularly and pays a thousand dollars cash for gift certificate every week or so.?
Your reference to Zimbabwe is specious. That was not simple printing money. It was an extreme fall in productive capacity that severely caused real prices to rise.
When you sell apples for money its the presence of money that allows that to happen. It introduces something new and NON NEUTRAL to the transaction. Prior to the introduction of money If you wanted my lemons there was not a fixed “market” price of the number of apples needed for a lemon. The banana guy might want three of my lemons for his banana and you might want two for your apple. In addition you guys might trade your apple and banana one for one. The economy changes completely once someone introduces a money price into the equation. I dont think its simply semantics at all. They are different beasts all together.
Gizzard: Have a read of my old post: http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/05/units.html
Lee: “Consider: suppose that tomorrow everyone woke up and forgot about money. People discover pieces of paper and metal discs in their wallets, and notice numbers on something called a “bank account”, but just see pieces of paper, metal discs, and numbers on a screen with only non-monetary uses. It occurs to nobody to accept these things as a medium of exchange, and all trade is reduced to barter.”
That’s a lovely thought-experiment. It’s one I have used myself. It shows that history matters. Here’s a similar one: suppose everyone woke up and forgot who owned what.
Economists have a saying “Bygones are bygones”. In cases like these, that saying is totally false.
I would describe your case as M fell to zero. The physical stuff remains, in the same quantity as before, but it’s no longer seen as a medium of exchange, and so is not used as such, and so is not money.
But Nick, instead of everyone waking up tomorrow and forgetting about money, suppose it occurred gradually over a decade.
After a month economists begin noticing falling NGDP and deflation. The same quantity of money exists as before, so they conclude money demand has increased. The central bank increases the supply of money to offset the decrease in money velocity and NGDP is stimulated. But people just keep holding more and more money and spending less and less, for whatever reason, and the increasing money supply can’t keep up. It seems like velocity is falling while the money supply is growing. Eventually, after ten years we are in the same situation as before, and all trade is reduced to barter.
Why is this a fall in the money supply and not a fall in velocity? Did the falling velocity cause the fall in the money supply? But then how are we to separate the concepts of supply and demand for money? Is a fall in velocity in some sense equivalent to a fall in supply? But it would be nonsense to say something like this for any other goods.