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Once in a while I see a blog post that I really need to print, carry to a comfortable chair, and think about for a while. This is one of those. Thanks.

1 - What's the point of the nominal interest rate in a barter economy? Nobody has any nonzero balance of credits to have interest on.

2 - Isn't the standard Keynesian and New Keynesian approach to presume the goods (K)/labor (NK) market equilibriates, then invoke Walras's law to link unemployment (K)/excess supply (NK) and excess demand for money? So if we remove the money market, and we assert the goods market still clears, then of course unemployment/excess supply vanishes... we have, however, only allowed the goods market to clear despite sticky wages/prices by presuming that relative prices are market-clearing, and of course there are no nominal prices to talk about in a non-money economy. The relative prices are the prices; there's no absolute price to talk about - everything is denoted in weighted baskets of goods.

I may be reading your analysis wrong, but in the absence of identical firms and hence identical markups, inflexible and noncompetitive barter prices may well be the non-market-clearing relative prices, and thus the result collapses and we have excess demands and supplies of assorted whatever. It is possible to read the K/NK point as focusing about excess money, but I think reading it as "the relative price of money and whatever is wrong" may be more appropriate. Conveniently, money plays such a massive role in the economy and has the peculiar behavior of having derived demand that it has obvious macroeconomic impact, but wrong relative prices of any prominent nonmoney good can already create excess supplies all on their own, even in a barter economy.

Nick, this isn't a New Keynsian model so I really wish you wouldn't call it that. Lots of readers might believe you.

NK models have sticky prices.

I must be very impressionable, because when you first posted about this, I thought you were right. In fact, I thought you were necessarily right. But like all impressionable people, I am flighty; upon reflection, I changed my mind.

The key stickyness requirement is not money, but credit. And, while you can't have money without credit, you can definitely have credit without money; money is a credit derivative. Your axiom "... he enforces Say's Law, at the individual level. No individual can carry a positive or negative balance of credits" is necessary to make your meta-model work; but it is wrong.

Adam: "Nick, this isn't a New Keynesian model so I really wish you wouldn't call it that. Lots of readers might believe you. NK models have sticky prices."

This model most certainly does have sticky prices. In the standard Calvo Phillips Curve, a fraction theta of all firms are allowed to change prices each period, and the rest have to keep their prices fixed. The only difference I have made is to assume that that fraction of firms theta have to set a new price *before* observing the central bank set the rate of interest. So my model has slightly stickier prices than in the standard Calvo model.

David: "1 - What's the point of the nominal interest rate in a barter economy? Nobody has any nonzero balance of credits to have interest on."

Both monetary and barter exchange is allowed. Each individual *may* carry either positive or negative credit balances into the next period. But in equilibrium, the aggregate change in the stock of credit balances will be zero. And, if all individuals are identical, and if we only consider symmetric equilibria, where all firms set the same price, it will be zero for each individual too in equilibrium. But the fact that each individual may choose to accumulate of decumulate credit balances does affect the sort of equilibrium we get. And on this point my model is exactly like the standard NK model.

David: "1 - What's the point of the nominal interest rate in a barter economy? Nobody has any nonzero balance of credits to have interest on."

Both monetary and barter exchange is allowed. Each individual *may* carry either positive or negative credit balances into the next period. But in equilibrium, the aggregate change in the stock of credit balances will be zero. And, if all individuals are identical, and if we only consider symmetric equilibria, where all firms set the same price, it will be zero for each individual too in equilibrium. But the fact that each individual may choose to accumulate of decumulate credit balances does affect the sort of equilibrium we get. And on this point my model is exactly like the standard NK model.

No Nick, this model doesn't have sticky prices. It doesn't have monopolistic competition either.

David point 2:

Yes. the model is symmetric, and I have only considered an equilibrium in which all firms have set the same prices, so all the relative prices are right. Away from that symmetric equilibrium, the sticky prices would cause the economy to move away from the flexible price competitive equilibrium. But those would be distortions at the micro-level, rather than macroeconomic.

Phil: In monetary exchanges, if we buy something off someone, in exchange for money, the seller can use the money to buy other goods, or to buy bonds (i.e. save until next period). But, if the transactions costs were small enough, we could also do barter exchanges in addition to monetary exchanges, where you have to exchange goods for goods of equal value, with no saving. And in the second part of my model, I show that people would want to do those additional barter exchanges, because some mutually advantageous exchanges cannot be conducted with monetary exchange.

@Adam P, would you prefer to say it has *fixed* prices?

@1 - Oh, I see. My next question would be whether the symmetric model is so robust that it is a reliable guide to intuition for non-symmetric circumstances - if nobody borrows, who cares whether the interest rate is wrong? Are there no macroeconomic effects here?

@2 - No, that's not true, the distortion can act at the macroeconomic level as well; the Akerlof-Yellen argument of individually small (second-order) effects of wrong relative prices but macroeconomically significant (first-order) losses works just fine here. Isn't that the NK narrative here - monopolistic competition, menu costs? Money so happens to be one good which everyone uses, but everyone uses oil and water, too. An oil shock would generate macroeconomic effects. Money only comes into play at the part where central banks set the relative price of money, and are thus in a position to alleviate the macroeconomic distortion, but a distortion from wrong relative prices occurs all the same, regardless of use of barter in lieu of money; an oil-price-setting authority in the NK barter framework here would be the 'monetary' policy authority.

@2 (cont.) - to make the hypothetical oil-price mechanic explicit - in monetary NK, the central bank nudges the relative value of money, creating the microeconomic side-effect of taxing holders of nominal assets and rewarding holders nominal liabilities. The nudge is costly but small relative to the gain from reducing the degree of error in relative prices. But this works for any good, with some price-setting authority of the relevant shock good, and thus works for barter NK - the authority sets relative prices by taxing net consuming the good and subsidizing net selling the good, or vice versa.

Nick: "... Each firm announces a price, to maximise expected profits/utility. The auctioneer then announces all those prices, and asks if any firm wishes to change its price (recontract), now that it has seen all the prices set by the other firms. When no firm wishes to recontract, the auctioneer then closes the auction, and those prices are then fixed for the period."

I gather you mean that some fraction of firms get to set prices?

Adam: Is this why you saying that it doesn't have sticky prices?

david: "My next question would be whether the symmetric model is so robust that it is a reliable guide to intuition for non-symmetric circumstances - if nobody borrows, who cares whether the interest rate is wrong? Are there no macroeconomic effects here?"

It's reasonably robust, unless there are some big non-linearities somewhere.

Nobody borrows or lends in equilibrium, but it is their *attempts* to lend, rather than spend, that causes a recession if the interest rate is too high. Because each wants to consume less than his income, income must fall until they stop wanting to lend. Again, this part of the model is almost standard New Keynesian. It is only when I introduce the second auctioneer that the model departs from the standard NK one.

Patrick: "I gather you mean that some fraction of firms get to set prices?"

Yes. Some firms cannot change price this period. The remaining firms can change price, but must change price before the central bank announces the interest rate. But how big that fraction is makes no difference to my analysis, since I assume that firms expect the central bank to set the "right" rate of interest, at which those firms that can change price choose to set the same price as the firms that cannot. In other words, all firms expect the central bank to keep monetary policy at what's required to maintain the 0% inflation target. Then, after all prices are fixed, the central bank surprises them. And they cannot change prices in response. *All* prices are now fixed for the period. They cannot adjust prices in response to the monetary policy shock.

I'm travelling so no long comments (posting on my blackberry). Patrick, it's fine that they can recontract on price before seeing the interest rate or quantities, that's not the problem.

Hint: I know Nick has violated the sticky price assumption and the monopolistic competition assumption entirely from C* < C^.

He's also violated ratex but that I think is no big deal.

Adam: C* is the natural rate of output under monopolistic competition (Bertrand Model, monetary exchange). C^ is what the natural rate of output would be under perfect competition. It is entirely unsurprising that output would be lower under monopolistic competition than perfect competition.

But the result that the economy goes to perfect competition if you allow barter *is* surprising. It surprised me. And before posting I was trying to "rig" the model so it didn't give this result (by switching from Bertrand to Cournot, for example). My prior, before cranking through the model, was that with barter, the equilibrium would go from Ci to C*. (I.e. the effects of bad monetary policy would be cancelled, but the effects of monopolistic competition would remain.) But the model really didn't want to be rigged. So I let that result stand.

In the limit, as e approaches infinity, C* approaches C^, and my model approaches Barro and Grossman 1971. I.e., if you allow barter, the economy jumps to the natural rate, despite bad monetary policy.

As for contradicting Ratex: it is true that, if firms could predict the second auctioneer would open up, they would set different prices in anticipation of this. But that doesn't affect my conclusion. All I need to show is that the standard NK equilibrium falls apart if you introduce barter. Therefore the NK model must assume barter is ruled out.

Yes, but you haven't shown anything of the sort. Really why is this not clear to you?

In the barter market you're letting the prices change, ignoring the interest rate and ignoring the monopolistic competition. Of course you get the competitive equilibrium outcome, you've made it a competitive flex price market.

If the prices in the barter maket have to be the same as they were in the first market, and the real rate is the same then your proof falls apart. An actual NK model would have the prices stay stuck in the barter case, the real rate stay the same and keep the monopolistic competition.

And we know that in the barter market you've removed the monopolistic competition because otherwise you'd get C*, not C^.

C* is what you get with monopolistic competition and flex prices. Money or not, the *only* way to get to C^ is to remove the monopolistic competition.

Why does the barter market not have monopolistic competition?

Nick, let's take this a step at a time.

Suppose it's fully flex price so the central bank and rate of interest changes nothing. In the monetary exchange market we get C*. We also get a price of the consumption basket C in terms of say apples (call the price of apples p). So C/p is the price of the consumption basket in terms of apples.

Now, the structure of the demand curves is the same in both the barter market and monetery market right?

The demand curves, and demand curves alone, imply that in order to sell more apples C/p must rise (that is p must fall) and this is equally true in both markets. So, in the barter market if the apple producer is able to trade apples for more of the basket he must be doing it on worse terms then he did in the cash market.

Now, we've said we're doing flex price so that sounds ok but it's not. You've let him price discriminate! For the monopolistic competition assumption to have meaning whatever ratio C/p obtains in the monetary market must carry over unchanged into the barter market.

But if you do that you force him to sell all his production, even what he sold in the monetary market, at a lower price and he chooses not to do that. He chooses not to do that because he chose p to be his total reveune (and utility) maximizing point.

So, getting from C* to C^ required violating the monopolistic competition assumption.

OK, next step. The real issue is whether or not we can have an outcome C < C* in the barter market.

(I just realized that above I misused Nick's notation, above I used C as the price of the consumption basket. Now I'm using as the number of units of the basket, as it's used in the original post.)

So, back to the sticky price situation and suppose the central bank sets the real rate too high so that in the monetary market we get the outcome C < C* as agents attempt to save. Now go to the barter market.

I imagine Nick will say that in the barter market there is no money, thus no saving medium and thus effectively no real rate so markets will clear to C* (he actually said C^ but we already know that was wrong). People can't save so do the next best thing or whatever.

Again though, Nick is changing the model. All you need is to allow a savings medium in the barter market and to assume the central bank sets its real interest rate. Well, that's easy, just let agents issue private bonds that are bought for units of the conumption basket and promise to redeem for units of the consumption basket.

Now, if in the barter market the apple guy wants to save he trades apples for the consumption basket and then trades the consumption basket for one of these "barter bonds". If the real rate is too high then everyone tries to save and we again have too little demand.

Of course how does the central bank peg the real interest rate on these "barter bonds"? It issues them and uses the monetary market tomrrow to buy the consumption basket with which to redeem the bonds.

BTW, if you're wondering how the CB could lower the real rate on the "barter bonds", it would buy them for newly created money just like always.

Why do agents accept the money if it is useless for the barter market? Because they can keep it for tomorrow and use it in the monetary market tomorrow.

I don't understand the models. But Keynesian business cycle theory only started making sense when I realised it was all dependent on monetary exchange. In a barter economy, there cannot be an general glut of the same kind that emerges from an excess demand for money. The paradox of thrift is a good example of a completely monetary phenomena, in my opinion -- it really has nothing to do with real factors like saving. Monetary exchange is like independent suspension, because it allows the two wheels of supply and demand to move independently in bumpy conditions. The job of a monetary central planner, like the Fed, is to prevent those bumpy conditions and help the economy behave like it has a non-independent suspension.

I cannot agree strongly enough with Adam. This is just not a New Keynesian model.

The most obvious way to see this is that basic Woodford-style NK models are total barter economies - there is NO money and all exchange occurs in goods. Interest rates and prices are there, but it's all in terms of consumption units, not money.

A lot of people get tricked into thinking NK models are about money because a) you can still do monetary policy in a barter economy by adjusting nominal interest rates (how? swept under the rug) and b) Woodford was good about getting people to use their old Keynesian intuition to think about NK models, even if that connection is weak. Williamson has made point (b) a few times quite well.

I also agree with Adam about the monopolistic competition points.

And, to beat the old drum, more math needed!

Set up two models, from the basic elements in math, and let's see what the equilibria look like. Stating one equilibrium in math and then talking through everything else in words is very confusing and leads to a lot of needless confusion, IMO.

I usually really like reading the articles here and I thought form the title that I would like this one but the opening two sentences;

"Keynesian macroeconomics in general, including New Keynesian macroeconomics in particular, makes absolutely no sense whatsoever in a barter economy. If people could trade goods and labour directly at zero transactions costs, without having to use monetary exchange, all Keynesian macroeconomics would be total rubbish."

Just makes me say SO WHAT!!??

I'm not entirely sure the statements are correct but I really dont care if they are, because they describe a condition I will never exist in.

Your absolutely correct about monetarism being incorrect too (even worse) since it was Friedman (I believe) who said that money is a neutral veil. Which implies (to me) that he believes the distribution of money in our society would be the exact same as the distribution of real goods if their werent any money................ so obviously false I cant believe he could say that with a straight face.

The truth is no moneyed system will behave anywhere close to a barter system.

Andy: was it you I was arguing with, on the same subject, on Steve Williamson's blog? I think so. Welcome!

So, I'm definitely not attacking a straw man. Steve, Adam, and Andy think I'm totally wrong. My guess is that many others do too.

On the other side, my guess is that Post Keynesians would say I'm obviously right, and everyone knows this, since Say's Law applies in a barter economy, so any form of Keynesian economics that's really Keynesian would only work in a monetary exchange economy. And if New Keynesian macro doesn't have that property, so much the worse for New Keynesian macro!

Now, there are two ways you could disagree with me:

1. The NK model is really barter, and bad monetary policy doesn't cause macro fluctuations in that model, it only causes micro misallocations because of relative price distortions due to staggered Calvo price setting. I think this is Steve's view. Maybe Andy's too?

2. The NK model is really barter, but bad monetary policy does nevertheless cause macro fluctuations (if you tighten monetary policy you get too little fruit in total), on top of any micro misallocations caused by staggered price changes and relative price distortions. I think this is Adam's view. Correct?

Maybe I should join the Post Keynesians ;-) (But I don't think they would accept me).

More later.

"Maybe I should join the Post Keynesians ;-) (But I don't think they would accept me)." as a post-keynesian i say please don't join us! not because i don't think you're smart or insightful but because it sometimes lifts me out of my depression that a few people see reason even in the mainstream! losing you from the "mainstream economists i respect" group would be a huge blow.

Every single previous comment on this post argues about the theoretical implications of a barter economy with no attention paid at all to the object of barter or the actual conditions under which barter takes place. Why?

May I suggest a more down-to-earth problem? Your barter example: Fruit.

Firms don't produce fruit. Fruit is not manufactured. It is grown. Nature plays a predominant role. As a result of weather, annual fruit yields vary enormously, far more even than grain yields. The result is unpredictable fluctuations of supply. You don't stop and start production of fruit; it takes years for fruit trees to produce. Supply constraints dominate demand. In any real barter economy it is feast or famine -- and people glut or starve.

Do you want to change the example to "woolen fabric" in order to continue the theoretical discussion with a manufactured product? Then you might explain how woolen fabric could be produced in any quantities without paying wages. Better to call them "theoretically conformable widgets" with no real-world qualities at all except their utility for pursuing theoretical abstractions.

I don't think this is a quibble. It illustrates the totally ahistorical, abstracted-from-the-real-world character of much contemporary economic debate. Keynes, his predecessors, and his successors notwithstanding.

OK. The result that, under barter, the equilibrium is the same as perfect competition, is really surprising. I didn't believe it at first either. Let me give a partial equilibrium model to explain why it works.

There are 3 goods: Apples, Bananas, and Carrots.

It takes labour to produce Carrots, and there are hundreds of carrot producers, so Carrots are perfectly competitive.

There's a single monopoly producer of apples. Zero costs to produce apples. Same with Bananas.

Every agent has a utility function U=A-A^2 + B-B^2 + C (linear in carrots, quadratic in Apples and Bananas).

Take carrots as the unit of account. The apple monopolist faces a linear demand curve from each agent Ad=1-Pa. With zero costs, he maximises profits by setting Pa=0.5.

Same for the banana monopolist, who sets Pb=0.5.

So, we get an equilibrium in which Pa=0.5, Pb=0.5, Pc=1, and every person consumes 0.5 apples and 0.5 bananas, plus as many carrots as he can afford.

Now, suppose the apple producer approaches the banana producer, and makes the following offer: "I will give you one half extra apple, *which you cannot re-sell*, and you give me one half extra banana, which I cannot re-sell". Note that this offer is at exactly the same prices as everyone else pays. There's no price discrimination here. Note also that both monopolists would be better off if they accept this deal. (They both go to satiation in apples and bananas, which is efficient fro them, since by assumption there's zero costs of producing apples and bananas.) They each consume the competitive equilibrium quantity of apples and bananas, even though each has a monopoly.

It's the *bilateral* monopoly which drives this result.

My macro model is just an n-person version of bilateral monopoly.

I'm not sure I've ever posted on Steve's blog, but I have certainly posted here before. :)

I certainly agree with your point (1). Prices can be 'incorrectly' set in an NK model so we get misallocations. I do not understand the difference between micro misallocations and macro misallocations. Misallocated resources are misallocated resources. Misallocations should always lead to a smaller pie - that's what inefficiency means.

I don't follow the PK logic you state either. Standard Woodford NK models are barter economics and monetary policy has bite and Say's law doesn't hold. What am I missing?

"The result that, under barter, the equilibrium is the same as perfect competition, is really surprising."

It's not surprising it's wrong, your proof in the post is nonesense and you're not doing better here. I'm mystified as to why you can't just admit you're wrong and move on.

Andy: sorry. I was arguing with someone on Steve's blog, whose name was also Andy, IIRC, and I thought you might be the same person.

Here's what I mean by the micro vs macro misallocation:

With Calvo price-setting, different firms change prices at different times, so if the central bank causes steady inflation, relative prices are distorted. One period you get too many apples, relative to bananas, and next period the reverse. That's the micro distortion. Sure, it means total utility is lower. But, if all demand curves were approximately linear, total output would be approximately the same.

If we changed from the Calvo assumption, to assume that all firms change prices at the same time, and hold them fixed for a number of periods, we don't get those relative price distortions. But, if the central bank suddenly tightened monetary policy, after prices had been set, we should still get a decline in output of all goods. That's the macro distortion.

Adam: come on. I could ask you the same question. But I don't. I wouldn't. You think you are right; I think I'm right. That's OK. People disagree at times.

Nathan: Thanks! I'm feeling a bit at bay here, having failed to convince Andy and Adam at all.

Let me try another tack.

The optimal allocation of resources is the competitive equilibrium C^, The monopolistic competition natural rate, C* is worse for everyone. And the equilibrium in a recession, Ci, is worse still. Ci is less than C*, which is less than C^. But all firms have a real (relative) price of 1 in all three equilibria.

If we found ourselves in Ci, what would Coase say? Coase would say "OK, if we all increase output by 1%, and all increase consumption by 1%, we would all be better off; so why don't we all agree to this deal?" (Notice, by the way, that this Coasian deal respects the assumption that all relative prices are 1.)

Under monetary exchange, each individual would want to accept the deal, but would cheat on it. If everyone else followed the deal, and increased their consumption by 1%, his income would rise by 1%, but he gets that income in the form of money, and would save part of that income (he keeps some of the money, then buys bonds with it), and increases his consumption by less than 1%. So under monetary exchange, where each swaps goods for credits, the Coasian deal is unenforceable. So accepting the Coasian deal is not a Nash Equilibrium.

But in a barter exchange, the Coasian deal is enforceable. You don't get income in the form of money; you get it in fruit. So accepting the Coasian deal is a Nash Equilibrium.

@Adam P

There are sticky prices in Rowe's model; it's just that the sticky prices happen to be exactly the same prices that would exist in a flexible competitive framework, by virtue of presuming identical firms. In the absence of money, the only prices that matter are relative prices, and with identical markups, the markups cancel each other out and relative prices remain exactly the same.

My dispute here is as my point (2) above - once we remove the assumption of identical firms, it is not true that the resulting distortions in relative prices are only microeconomically significant; there will be macroeconomic impacts as well from any short-run shock and the impacts will be the NK model we all know and (possibly) love.

David: Yep on your first paragraph.

On your second paragraph: if we drop the assumption of identical firms, (or drop the assumption that we are starting in an equilibrium where all firms just happen to have set the same price), then there will be micro distortions, and those micro distortions will be very unlikely to exactly cancel out at the macro level. Though they might. But, to my mind, keynesian macro is not about those micro distortions. It treats them as a second-order complication. "It takes a lot of Harberger triangles to fill an Okun gap", as they say.

And Arnold Kling thinks that what I'm saying is obvious, and the model is totally unnecessary to prove it! http://econlog.econlib.org/archives/2010/12/morning_comment_26.html

Adam: "Again though, Nick is changing the model. All you need is to allow a savings medium in the barter market and to assume the central bank sets its real interest rate. Well, that's easy, just let agents issue private bonds that are bought for units of the conumption basket and promise to redeem for units of the consumption basket."

But the whole point of the barter market is precisely because it doesn't allow a savings medium.

The apple producer says: "swap you one apple for one banana?" He doesn't say "swap you one apple for a promise to pay one banana next period?" Well, he might try suggesting the second deal, but the banana producer, who also wants to swap one banana for one apple next period, would refuse the deal. But the banana producer would accept the first deal. It makes both better off.

While I suppose it's good for my soul to try to get my head around Nick's model, this from Arnold:

"If barter were possible, then firms would pay their workers in goods. If you can pay your workers in the goods and services they produce, then you eliminate any wedge between the real wage and the marginal product. So there is full employment."

was a whole lot easier.

"On your second paragraph: if we drop the assumption of identical firms, (or drop the assumption that we are starting in an equilibrium where all firms just happen to have set the same price), then there will be micro distortions, and those micro distortions will be very unlikely to exactly cancel out at the macro level. Though they might. But, to my mind, keynesian macro is not about those micro distortions. It treats them as a second-order complication. "It takes a lot of Harberger triangles to fill an Okun gap", as they say."

Sadly, no. The NK narrative that monopolies only have second-order losses from not adjusting to nominal shocks (due to menu costs) and that this has large, macroeconomically significant, first-order effects works just fine here.

Think about it this way: by valuing everything by relative prices, you've denominated everything in units of GDP, weighted by share of consumption. That is the new numéraire, taking the place of money. Any distortion to individual components of the numéraire will have small second-order effects, but even a small change in the weighted sum - caused by, say, a slight imbalance in one direction from a distorting shock - will have 'large' first-order impacts, via the same mechanism as a small alteration on the money supply. The shares of consumption has changed, but everything is priced in pre-shock shares of consumption, and as per sticky relative prices will remain so.

On Mr. Kling's summary - I should note two things. It is true that if people are paid in exactly what they produce, then the wedge between "what people are paid in" and marginal product vanishes. But then "what people are paid in" won't be real wages, unless all firms produce units of GDP exactly weighted by consumption shares and all people identically consume those units of GDP; a firm that makes only apples and pays its workers in apples can continue to pay apples, but the ability of a fixed sum of apples to buy a basket of consumption will have changed. So the real wage is not fixed in the face of shocks. This violates the presumption of sticky relative prices (of labor vs goods), furthermore.

The second point is this: no involuntary unemployment obtains, of course, in Kling's summary (where W=MPL). But there is no involuntary unemployment in New Keynesian models, either, so that is unsurprising. Wages in both are flexible. What we have instead is excess supply.

If instead Kling's workers are paid in fixed sums of GDP units, then the real wage is no longer identical to marginal productivity. This gives us unemployment. There's no way to salvage this. Your barter economy exhibits Keynesian behavior under shocks.

(for more rigorous elaboration on the first-order/second-order distinction - since this seems to be the important point here - I point you to Akerlof and Yellen 1985. And again (why do they even have two papers on the same subject anyway? And which one are New Keynesians referring to when they point to their 1985 paper?)).

I don't have ungated access to the first one, but from reading the second one, it is apparent that their model doesn't require money. Sticky relative prices will suffice for the result.

I should add that a "monetary policy" authority in the barter economy - an authority that sets the real price of exactly one prominent good, by taxing/subsidizing its possession/nonpossession - can resolve shocks by shocking relative prices so much that monopolistic firms adjust prices despite the menu costs.

Indeed, this is a way monetary authorities in New Keynesian monetary economies can derive power to deal with real shocks to the economy...

"But the whole point of the barter market is precisely because it doesn't allow a savings medium."

while that may be true in the model you're constructing it's *false* in the NK models. Which is my point here, your not taking this seriously, your just answering arguments with irrelevant counter examples.

If you want to say that recessions are impossible with no possiblity of a savings medium, say all loans are outlawed (even ones that pay zero interest) that is fine. We could argue that if you want.

You wanted to claim that NK models need money to make sense but you're not even trying to make that argument.

And Nick, think about the logic here. If youu want to claim that NK models only make sense with monetary exchange then examples of non-NK models that can't generate recessions without money are irrelevant. You're not saying anything about models that are NK.

NK models have bonds, no money, none of the goods cost nothing to produce.

Furthermore, if the real argument you want to make is that only monetary exchange economies can have recessions then you need to also addresss RBC models, most of which don't have money but all of which generate recessions.

David: Over 20 years ago, I used to be good on the small menu cost stuff. Here's my 1989 paper (gated, sorry): http://www.sciencedirect.com/science/article/B6X4M-4D5NR5G-149/2/77ed81445a7531d7250c2f98ac987c04

IIRC (it's a long time ago) the Akerlof and Yellen papers were really partial equilibrium (but my memory could be wrong).

What you say about small menu costs is correct. Second order of smalls menu costs under monopolistic competition can explain why firms don't cut prices when the money supply falls, and the loss in welfare from the drop in *aggregate* output will be first order.

But I am arguing something different, about the "micro distortions". If the average price level is correct, relative to the stock of money, but *relative* prices are incorrect, the resulting first order of small distortions of relative outputs (aggregate output will be roughly unchanged) will cause only a second order of smalls drop in welfare.

Intuitively, all firms have output too low at the natural rate, due to monopolistic competition. If relative prices are wrong, then half the firms will have output lower than the natural rate, which causes a first order loss in welfare, and the other half will have output higher than the natural rate, which causes a first order gain in welfare. The net effect, when we subtract the losses from the gains, will be a second order loss in welfare. The trapezoid loss from one half the firms, minus the trapezoid gain from the other half the firms, equals a triangular net loss.

To explain further what I mean by "trapezoids", draw a picture of a monopolist. MC, MR, and D curves. Standard ECON1000. Start in profit-maximising equilibrium. Now shade in the Net Welfare Loss triangle between the MC and D curves. Do that for two monopolists.

Now force one monopolist to raise its relative price and cut output. The NWL triangle is increased, by a trapezoid.

Now force the other monopolist to lower its relative price and raise output. The NWL triangle is reduced, by a trapezoid.

Now take the difference between the first and second trapezoids. It's a triangle.

And, trapezoids are first order of smalls. Triangles are second order of smalls.

Adam: "Which is my point here, your not taking this seriously, your just answering arguments with irrelevant counter examples."

I take exception to that comment.

I am doing my best to explain to you why I think what I do. In fact, This whole post, and most of the comments following, are me trying bloody hard to explain to you (and anyone else) why I think what I do. (And to think it through more clearly for myself). Obviously I am failing to explain to you why I think what I do. My fault, your fault, whatever. But don't accuse me of arguing in bad faith.

Nick, I'm sorry I offended you. I wasn't trying to make this personal.

Nonetheless, you said: "But the whole point of the barter market is precisely because it doesn't allow a savings medium."

I respond: "NK models have bonds, no money, none of the goods cost nothing to produce."

Your barter market admits no savings medium, NK barter markets do. So how does a result from you barter market that depends entirely on there being no saving medium say anything about the NK barter market where there are bonds?

Your other example had the two monopolisticaly produced goods having zero production costs, of course people will always want more of them. In NK models everything has a cost of production so again, how is this relevant?

You may be taking the argument seriously but the counter examples are irrelevant to the central assertion.

Nick: "But the whole point of the barter market is precisely because it doesn't allow a savings medium."

Ha! Now I get what you're saying. But, I don't think 'barter' means what think it means. Barter does not imply no wealth. For your model to hold there would have to be no stores of value what so ever, and capital goods. Is that what economist's mean typically when they talk about 'barter economies?' Is doesn't seems so.

Here's Robert Waldman from a year ago or so talking about John Cochrane, but that also seems to anticipate your model:

Cochrane has to assume that people have no wealth of any kind. Anything durable, not just money invalidates his argument.

Let's say we all plan to sell our shares (commmon stock) to buy goods and services. That way planned consumption plus taxes plus investment plus net exports can be greater than GNP. The distinction between money and other financial assets is very important in many ways, but it is not relevant to Say's law which would be invalid even if we bought and sold stock with non-durable consumption goods (apples) and not with money.

Cochrane is right in a Walrasian model with one period or in a Walrasian model in which nothing nothing at all lasts from period to period. So a model where we trade apples for oranges is a model in which my yearly planned consumption must be roughtly equal to my yearly income. However, if the model also includes apple trees and orange trees, then this is no longer true....

If I own apple trees then my demand can be greater than my income. I have wealth (the trees). I can buy apples and oranges by selling my trees. If everyone wan't to sell trees (not made this period) to buy fruit (made this period) then planned consumption of goods produced this period will be greater than production of goods produced this period.

The value of trees does not appear in GNP unless they just matured (the value of pruning trees does). The budget constraint includes, at least, current income plus wealth (with perfect financial markets it also includes the expected present value of future labor income).

Cochrane is assuming that income = wealth. This is a much stronger assumption than that there is no money or no financial instruments.

http://rjwaldmann.blogspot.com/search?q=SAY%27S+LAW+APPLES+ORANGES+TREES

Oh, I should have proof read that, multiple typo's. Sorry. Anyway, the Waldman quote is clear enough.

I have been trying to make the same point as Adam. NK models are 100% barter, have savings, have monetary policy, and have misallocations. Your baseline model is NOT NK.

While I may not be quite as aggressive as Adam :P, I do wish you would stop saying that this post and the comments have said anything at all about NK models. Instead, it's been about two alternative models, which may be informative in general, but is not proving or disproving anything about NK.

And, to repeat myself, the best way to discuss NK models is to actually use NK models, by which I mean, USE MATH! All this confusion would be immediately resolved if you wrote up your original model in conventional macro math where it would be clear how different your set-up is from a Woodford-style set-up (it's a lot).

Adam: OK.

This is what I *think* is going on:

Suppose I start with the same underlying structure, preferences etc. as in the standard NK model, but said that the *only* trades allowed were barter trades, *with no savings medium*. Then it is definitely unsurprising that I don't get NK results. Then you would be right to say it's not really a NK model, and that I haven't proved my point.

Is that maybe what you think I'm doing? If so, I understand your critique.

But I think I'm doing something different. This is what I think I'm doing:

I start out with the same underlying structure, preferences etc. as in the standard NK model. I then add in a trading mechanism, *with a savings medium*, that I think is the same trading mechanism as in the standard NK model. And I get what (I think) is the standard NK equilibrium.

Starting in that standard NK equilibrium, I add in an *additional* trading mechanism (I call it "barter"), *on top of* the existing trading mechanism, which does have a savings medium. And I get different results.

I am not taking away a savings medium. It's still there.

I want to compare two equilibria:

The first with only the "Monetary" auctioneer.

The second with two auctioneers: the "Monetary" auctioneer (with savings), plus the "Barter" (without savings) auctioneer.

I have no idea if that will clarify anything.

@Nick Rowe,

Yes, that is all true provided the average price level remains the same but there is no guarantee that this will be the case; in fact it would be extraordinarily unlikely. Think about what that means, in the context of your relative-price economy; a shock alteration in the quantity of any product has only small impacts on relative prices but a direct impact on (real) GDP. National income has changed but real wages (or the price of a representative consumption basket) are denominated in those old units.

You can't just say "oh that's okay, I am paid in apples so I only need to consider the second-order change in relative prices of apples to the shocked good" - there will be more or less total stuff for you to buy, aggregated together.

Yes, David. Nick let the barter market transact at different prices. He dropped the sticky price assumption.

Barter had nothing to do with anything. Flex prices neant no recession.

Andy: Yep. Maths might help some readers, but:

1. I am cr@p at math, and even worse when trying to write it in TypePad.

2. Sometimes, and I think this might be one of those times, the math may actually hide things. It's the implicit assumptions about the trading structure that need to be clarified, and you can't always see that in the math. And my auctioneers are my attempt to make explicit exactly what I am assuming about the trading structure. For example, the standard Walrasian auctioneer story clarifies for me the implicit assumption about the trading structure of Walrasian/Arrow-Debreu GE theory, in a way that the mathematical existence proofs and equilibrium conditions can never do. That's why the Walrasian auctioneer was invented in the first place.

OGT: "Here's Robert Waldman from a year ago or so talking about John Cochrane, but that also seems to anticipate your model:

'Cochrane has to assume that people have no wealth of any kind. Anything durable, not just money invalidates his argument.' "

I actually disagree with Robert Waldman here. I think it is money (the medium of exchange), and only money, that invalidates Say's Law. An excess demand for other non-produced storeable goods, like land, or antique furniture, cannot cause a general glut. An excess demand for money will cause a general glut.

This is a moderately radical position. Many think I am wrong. I am denying Walras' Law. I did some old posts on this. Here's one of them:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/10/the-paradox-of-thrift-vs-the-paradox-of-hoarding.html

Andy P is starting to make a little bit of sense to me now. I can sorta see where he's coming from.

That said, I have a general question: does the term 'sticky prices' make sense in a barter economy with N(N-1)/2 markets and prices? The concept of sticky prices in a monetary economy is clear to me, but the concept of sticky prices in a barter economy is not. Can someone elaborate?

@Nick: Now would be a good time to get better at math! I always think of math as a language we use so that everyone agrees on what each sentence means. A lot of confusion arose here because of semantical distractions, IMO.

@jsalvatier: Prices are just exchange rates and don't have meaningful units in a barter economy or a monetary economy. Economists will often just choose one good and call it the numeraire and denote everything in units of that good. For instance, if we choose oranges as the numeraire, then the price of an orange is 1, the price of apples is apples per orange, and so forth. It is a straightforward result that this denomination is contentless; any good could have been chosen as a price unit. Money is totally irrelevant for the concept.

What are sticky prices? Just fixed exchange rates - say 2 apples for one orange - regardless of demand or supply conditions.

Nick at 1:09pm.

I understood perfectly that you were doing the second thing you describe. However, I assume that you wanted the second, barter, market to have all the same structure as the first one with the one exception of no money used in trade. Only then do you make your point, yet you didn't do that.

Question from someone a lap behind. What is it about having a non monetary savings medium that creates the sticky price induced output gap in the nk model? I am used to thinking about price distortions as frustrated deflation caused by an excess demand for the medium of exchange. I don't understand how the price stickiness (calvo or whatever) comes to matter in a woodford cashless economy.

Can there be recessions in barter economies? Sure. A bad crop due to weather can do that. Can there be a general glut? No, there would always have to be something in excess demand. That excess demand, or more appropriately short supply, which historically has been for food, can lead to excess supply in all other goods. Says law, production equal consumption, holds even if production and consumption includes investment goods, it just doesn't mean production must equal consumption excluding investment. One can't really save in a barter economy; the closest one can 'save' is invest in inventory, a speculation at best. While one can try to construct a numeraire of a consumption basket, it's value in terms of other goods or of other goods in terms of it would be subject to fluctuation. While a consumption basket may include storables, it cannot be totally storable or it wouldn't be a consumption basket. While a bank might set a consumption basket interest rate, this would mean foregoing setting a money interest rate. While a barter economy could have bonds, there is no assurance those bonds could be met; they would at best remain hopes.

jsalvatier: There's the "numeraire", which is the good the economic modeler measures prices in. And there's the "medium of account", which is the good agents in the model (or real world) measure prices in.

As Andy says, the numeraire doesn't matter at all. (Except, maybe, what's most convenient for the modeller).

And in a world of perfectly flexible prices, it doesn't matter what the medium of account is either, except for people's convenience. In a monetary exchange economy, people nearly always use the medium of exchange as the medium of account, simply because it's more convenient. (If we paid in dollars, but talked about prices measured in peanuts, we would have to divide by the price of dollars in terms of peanuts to figure out how many dollars to hand over, which is a hassle.)

In a barter economy, since we can pay in anything, it's not obvious which good would be most convenient to use as medium of account.

But, convenience aside, all the exchange ratios (relative prices) can still adjust whichever good is used as medium of account.

But if some prices are sticky, it matters which good is the medium of account. If there are 3 goods, A,B, and C, and if the price of A is sticky, then the relative price of A to B is sticky if B is the medium of account. If C is the medium of account, then it's the relative price of A to C that is sticky.

For example, if the relative price that is sticky is a relative price whose equilibrium never changes anyway, then sticky prices are not a problem for the economy. All prices stay in equilibrium, because the one that cannot change never needs to change anyway. But if the relative price that is sticky is an important relative price, whose equilibrium value does change, then it matters. It means a relative price that needs to change cannot change. So the economy is forced away from equilibrium.

Lord: Yes, a bad harvest will cause a drop in GDP, even if all prices are flexible, or even if the economy is responding to that real shock in a perfectly efficient manner. Some economists (Real Business Cycle theorists) would call that a recessions. I wouldn't. It doesn't have the (to me) key feature of a recession -- that it gets harder to sell stuff (goods and labour) in a recession -- which is what we call a general glut.

When we say "harder to sell stuff", we mean "harder to sell stuff *for money*". (It's easy to sell *money* and get stuff in return in a recession). Barter is like selling stuff and buying stuff in the very same act. So, to me, recessions look like essentially monetary phenomenon, because it's the exchange of stuff for money that gets harder for the person on one side of the transaction (the one who has the stuff and wants money), and easier for the person on the other side of the transaction (the one who has money and wants stuff).

But Nick,

A bad harvest in barter economy does make it harder to sell stuff, all stuff! Thus, even in your terminology Lord's example *is* a recession.

Well, I should say it gets harder to sell all stuff that isn't agricultural.

Dlr; "I don't understand how the price stickiness (calvo or whatever) comes to matter in a woodford cashless economy."

good question! Normally, in an economy with cash, sticky prices cause a recession because they prevent the real stock of cash adjusting to the equilibrium value. If prices fell, the real stock of cash would increase, and increase aggregate demand, and get the economy out of the recession. And that can't be what's going on in a cashless economy.

Instead, a recession happens because the central bank sets the interest rate too high. The only role of the degree of price stickiness is to help determine how quickly prices will adjust in future, and how quickly they will be expected to adjust in future, and that determines the real interest rate for any given nominal interest rate set by the central bank.

But, as Andy said (somewhere above in the comments, IIRC) it is less than clear how exactly the central bank can set the rate of interest in a Woodfordian cashless economy. Normally, a central bank can set the rate of interest by changing the nominal supply of cash which, if prices are sticky, also changes the real supply of cash. But it can't do that if there is no cash.

One way to resolve this puzzle is to think of the cashless economy as just the limiting case of an economy with cash. That's how Woodford does it, IIRC.

In my model above, I made the central bank the monopoly supplier (and monopsonist demander) of all inter-period loans in the form of trading credits. I assumed that agents cannot borrow or lend trading credits between themselves, but can only borrow from or lend to the central bank. So the central bank can set whatever (nominal) rate of interest it wants.

Nick,

Take a barter economy and divide output into A for agricultural and C for all other consumption. Now, hit the economy with a poor harvest so A has fallen.

Now it has gotten harder to sell C! A unit of C used to trarde for x units of A, now it trades for less than x units of A. Doesn't that mean it's gotten harder to sell C?

Futhermore, if this is RBC world thereal wage accruing to the producers of C is lower (they can't buy as much A as they could before so the real value of their output is less). Thus the producers of C supply less labour and output of C falls!

The fall in C means it's now harder to sell A! So, there is no money, it is pure barter and yet the recession looks exactly like a situation where it's gotten harder to sell stuff. Just as you asked. Someone living in this world would say it's gotten harder to sell stuff just as he does in the monetary exchange world, he would not be able to tell the differenc.

Monetary exchange is not needed.

Adam: honestly, I am doing my best to understand your criticisms, but I still don't get it.

"Yes, David. Nick let the barter market transact at different prices. He dropped the sticky price assumption."

I don't think I did. I started in equilibrium with all prices the same, and so all relative prices were 1. I held all prices fixed, so all relative prices stayed at 1. In my barter auction, all relative prices stay at 1. Why do you think they are not 1?

"However, I assume that you wanted the second, barter, market to have all the same structure as the first one with the one exception of no money used in trade. Only then do you make your point, yet you didn't do that."

I thought I did. What do you see as the difference?

Adam:

1. Suppose I noticed that when GDP dropped it was easier to sell food, and harder to sell non-food. I would suspect that the drop in GDP had something to do with an excess demand for food.

2. Suppose I noticed that when GDP dropped it was easier to sell money, and harder to sell non-money. I would suspect that the drop in GDP had something to do with an excess demand for money.

2 seems to fit the facts much better than 1.

"2 seems to fit the facts much better than 1."

Not in a barter economy.

Nick,

Lord's first sentance was: "Can there be recessions in barter economies? Sure."

We're talking about barter economies here. You respond by claiming that a recession, IN A BARTER ECONOMY, that was caused by a bad harvest would not look or feel like it got "harder to sell stuff".

I then respond that, IN A BARTER ECONOMY, a recession caused by a bad harvest would look and feel like it got "harder to sell stuff".

You then respond by going back to a money economy. Are you even reading the comments?

Since this is mostly about NK models I'm going to sit on the sidelines, but I do see a problem with this from Nick: "Suppose I noticed that when GDP dropped it was easier to sell money, and harder to sell non-money. I would suspect that the drop in GDP had something to do with an excess demand for money."

What if it’s easier to sell bearer bonds, foreign currency, gold, forged passports and tickets on the next plane out of the country? You would surely then suspect that the drop in demand for locally-produced goods had something to do with fears for the future of that particular locality. It seems to be that this argument revolves around the question of whether an increased demand for money necessarily has to do with money’s role as a medium of exchange, rather than its role as a store of value when other assets look too risky. At the moment it’s quite easy to sell US and German government debt. That suggests to me that the demand is not for the medium of exchange as such, but for safe assets of any kind.

I don’t think Nick should look for a home among the Post-Keynesians. Paul Davidson is awfully insistent on the significance of the fact that “money is a one-way time vehicle or time machine for store of value purposes” (his emphasis). I don’t think money’s role as a medium of exchange is especially important to him. Joan Robinson was also very insistent that the crucial differences between her views and those of “the bastard Keynesians” related to uncertainty and time. I seem to remember that she and John Eatwell actually used a Keynesian barter model in their ill-fated textbook, but it’s a long time since I read it.

Kevin: suppose we used cows as money. Suppose there were an increased demand for milk. That would increase the demand for cows, not because people want more money, but because people want more milk. But it would still cause a recession.

Cows, the medium of exchange in that example, also give milk. Money, the medium of exchange, is also a store of value. If there's an increased demand for a store of value that happens to be a medium of exchange, that could cause a recession.

But yes. Perhaps I shouldn't join the post-keynesians quite yet. They are a disparate lot, though.

I don't think the fall in C means it's now harder to sell A; the fall in A has made it harder to sell A, not due to diminished demand but diminished supply. Someone with stores of A or unaffected by a fall in A would do well. It is just A would be in short supply so most would be worse off, even producers of A. I don't think it would be more difficult for the barleyman to barter with the cornman, assuming they were similarly affected, or the tailor with the weaver other than weakness due to starvation, but more difficult for the other trades due to the change in relative price between A and C, and would make selling A easier if it existed and selling C harder. Real output would be lower due to nature.

So what would inflation look like in a barter economy? Hyperinflation?

Greg: in a pure barter economy, with no money, it would depend on what good prices were measured in. For example, we might all quote prices in apples, even if we exchanged bananas and carrots directly.

I've got a sort of impure barter economy. People start out using monetary exchange, with prices quoted in money, then a barter market opens up afterward, for any trades that people can't carry out in the monetary exchange system. The idea is that people sell as much as they can for money, and buy goods with money. Then, if they still want to sell more (they will) they do swaps on the barter exchange. But they still use the same money prices to determine the relative prices in the barter exchange. So if apples and bananas each are priced at (say) $5 in terms of money, one apple will swap for one banana in the barter exchange.

"Yes, David. Nick let the barter market transact at different prices. He dropped the sticky price assumption."

I don't think I did. I started in equilibrium with all prices the same, and so all relative prices were 1. I held all prices fixed, so all relative prices stayed at 1. In my barter auction, all relative prices stay at 1. Why do you think they are not 1?

Yes, your barter-economy no-excess-supplies result obtains when there is one firm, one good, or one consumer (or identical duplications thereof). It's a bit tricky once those assumptions are dropped, though... your barter market in your reply to my question does, indeed, have flexible prices*, since you asserted that you could drop the assumption of identical firms.

* to be precise, depending how you formulate it (since you left this undefined in your model), prices are fixed at full employment or at goods-market-clearing levels, but not both.

You didn't reply to my latest reply but Adam P covered the point I was trying to make (I think).

Hm, no, wait, I think I see where you're coming from. You're taking a monetary economy, then removing money and imposing a barter structure, which shunts any excess demand (for money) that exists into whatever there was excess supply of. Conclusion: no excess demands remain.

But that's only true if the shock was a monetary shock (and, strictly speaking, if there is only one good - however, the excess demands from wrong relative prices of multiple goods in this case would be second-order small). Unsurprisingly, monetary shocks have no effect on a barter economy (no demand for money), and little-to-no effect on a monetary-then-barter economy, and so I presume that this wasn't the point you were intending to make! If the shock was a real shock, then any real shock large enough to generate first-order losses in a monetary economy will also generate first-order losses in a barter economy, unless you relax the presumption of stickiness among enough real (relative) prices so much so that excess demands can be shunted into them.

The reason we disagree (I think) is this: if all real relative prices are fixed, then no adjustment can take place and we have unemployment or excess supply at first-order levels; if none are fixed, then total adjustment takes place and no excess supply or unemployment exists. In between (with some prices sticky and others flexible), we add or remove Harberger triangles to fill the Okun gap. Intuitively, you started thinking from the latter and applied Tobin's dictum; I started from the former and applied the dictum. But formally I think you are wrong, too :P - you buried flexible wages in your model, in a non-obvious manner, and since your model only has labor and fruit, all relative real prices are flexible.

You're not grokking my earlier attempts to convince you of the first-order losses, so let me try to convince you instead that your barter model does have changing prices. Your model only has fruit as a good, so wages are paid in fruit (or, identically, the price of fruit is labor). There is hence only one possible relative set of prices. A real shock must affect prices, and there is only one price to affect here, so how do labor wages, or the price of fruit, remain sticky?

*"A real shock must affect real prices"

David: "Hm, no, wait, I think I see where you're coming from. You're taking a monetary economy, then removing money and imposing a barter structure, which shunts any excess demand (for money) that exists into whatever there was excess supply of. Conclusion: no excess demands remain."

Almost. I'm taking a monetary economy, then I'm not *removing money* but I am *adding* the possibility of barter trades. And then yes, that does shunt any excess demand (for money) that exists into whatever there is excess supply of.

"But that's only true if the shock was a monetary shock (and, strictly speaking, if there is only one good - however, the excess demands from wrong relative prices of multiple goods in this case would be second-order small). Unsurprisingly, monetary shocks have no effect on a barter economy (no demand for money), and little-to-no effect on a monetary-then-barter economy, and so I presume that this wasn't the point you were intending to make!"

The shock was a monetary shock.

Is it unsurprising that monetary shocks have no effect when barter is allowed?

I get two different reactions:

1. "It's unsurprising. It's totally obvious"

2. "It's totally wrong"

Take your pick!

I'm still not following the rest of your comment.

"A real shock must affect prices, and there is only one price to affect here, so how do labor wages, or the price of fruit, remain sticky?"

There are n different kinds of fruit. They are not identical. They are imperfect substitutes. But the equilibrium is perfectly symmetric, so all fruits will have the same prices in equilibrium.

The price of each fruit is fixed in terms of money.

The labour market is suppressed in my model. Each firm is owned by the one person who works there. If I made the labour market explicit, the money and real wage would be perfectly flexible.

No, you're removing money. You are requiring that everybody have a zero balance of credits at the end of the barter auction. There's no reason for anyone who desires to save to have a zero balance of credits, so they won't do this on their own. You can impose this on a monetary economy, too, and achieve the same result of no excess demand for money and no excess supply of anything else.

There are n different kinds of fruit. They are not identical. They are imperfect substitutes. But the equilibrium is perfectly symmetric, so all fruits will have the same prices in equilibrium.

The price of each fruit is fixed in terms of money.

The labour market is suppressed in my model. Each firm is owned by the one person who works there. If I made the labour market explicit, the money and real wage would be perfectly flexible.

All right, so there are multiple fruit with identical prices. People are endowed with assorted fruit, which they use to buy other fruit, at a sticky price that is the same among all fruit. So there's still only one relative price: one to one. Either a real shock is impossible, or some prices are flexible.

You need at least three goods with three different prices to have two different relative prices, one of which can be sticky and the other not. Even then, the degree to which excess demand can be moved to and fro depends on elasticities. Modeling money here as a tradable good with independent real value is an obvious next step.

Nick, in the interest of re-engaging with you, I do feel a bit bad about how rude I've been getting in this thread, let me go back to this comment of yours:
Let me try another tack.

The optimal allocation of resources is the competitive equilibrium C^, The monopolistic competition natural rate, C* is worse for everyone. And the equilibrium in a recession, Ci, is worse still. Ci is less than C*, which is less than C^. But all firms have a real (relative) price of 1 in all three equilibria.

If we found ourselves in Ci, what would Coase say? Coase would say "OK, if we all increase output by 1%, and all increase consumption by 1%, we would all be better off; so why don't we all agree to this deal?" (Notice, by the way, that this Coasian deal respects the assumption that all relative prices are 1.)

Under monetary exchange, each individual would want to accept the deal, but would cheat on it. If everyone else followed the deal, and increased their consumption by 1%, his income would rise by 1%, but he gets that income in the form of money, and would save part of that income (he keeps some of the money, then buys bonds with it), and increases his consumption by less than 1%. So under monetary exchange, where each swaps goods for credits, the Coasian deal is unenforceable. So accepting the Coasian deal is not a Nash Equilibrium.

But in a barter exchange, the Coasian deal is enforceable. You don't get income in the form of money; you get it in fruit. So accepting the Coasian deal is a Nash Equilibrium.

I have two points.

Point 1) In the NK model you can buy bonds for fruit. It's an economy that does not have money but does have bonds, ergo whoever buys bonds does so in exchange for goods.

This seems to be where we've been talking past each other. You say, the possibility of saving is still there but you can only buy your bonds out of the monetary market. I say that even in the barter market people will attempt to save and you have the same problem. Effectively what will happen in the barter market is the apple producer shows up saying "I'll give you apples today in exchange for bananas tomorrow" and the banana producer repsonds "No, I want apples tomorrow, not today, and I'm willing to give extra bananas today for it. However, I'm not willing to give extra bananas tomorrow for it." (People want bonds, not futures trades).

Point 2) Even if I agreed with what you said here you'd have already lost the argument in a certain sense. Even in your argument money's *medium of exchange* properties are *not* the cause of the recession. It is an excess demand for saving that is the problem, money only enters because you've mysteriously made money the only way to get a bond.

PS: in point 1 above the reason people in the barter market prefer to save is the same as in the cash market. The real rate of interest on the bonds are the same in both markets.

If you allow the real rate to be flexible in the barter market then you've departed from your central assumption.

Adam: you have definitely succeeded in re-engaging me in those last two comments.

I agree a lot with what you say here. You very definitely have a point. It's a valid criticism. I see (OK, I'm pretty sure I see) where you are coming from.

You have now put your finger on the point where my argument is most vulnerable, and where I am least sure that I am right, and least clear in my own mind.

I am going to argue against you on this point. But I will fully understand if you find my counter-argument less than 100% clear, and less than 100% convincing. It's because my own head is not 100% clear on it either.

Give me some time to try to marshall my counter as best I can.

Some minor preliminaries:

"Point 1) In the NK model you can buy bonds for fruit. It's an economy that does not have money but does have bonds, ergo whoever buys bonds does so in exchange for goods."

Yes, it does have bonds, and the "barter" market doesn't. We acn interpret the "trading credits" that people may hold between periods as "bonds". Whether it does or does not have money is the point I need to argue about. Because it is definitely "cashless" in some sense.

"It is an excess demand for saving that is the problem, money only enters because you've mysteriously made money the only way to get a bond."

I need to be clearer on the "mysteriously" bit. I can understand why it appears mysterious.

"PS: in point 1 above the reason people in the barter market prefer to save is the same as in the cash market. The real rate of interest on the bonds are the same in both markets.

If you allow the real rate to be flexible in the barter market then you've departed from your central assumption."

Agreed.

Will be back later, to do my best.

Oh, and yes, if there's a real shock, after prices have been set, even barter (at those fixed relative prices) won't get the economy to the competitive equilibrium. Agreed.

Adam:

To summarise your critique (as I understand it)

I have two trading systems (auctioneers). The two trading systems are identical, except: in the first one you can buy bonds; in the second one buying bonds is prohibited. And that is what is driving the results. That's why adding the second trading system gets the economy out of the recession.

(Agreed with all of the above).

Which raises the question: why do I call the first one "monetary" and the second one "barter"; and what's that got to do with the prohibition on buying bonds?

Here's my best shot at the answer:

I'm the apple producer. If I buy bananas for money, I can't control what the banana producer spends that money on. I can't prohibit him from spending some or all of it on bonds. If I buy bananas in barter for my apples, I can prohibit him from buying bonds with the proceeds from his sale of bananas. I prohibit him from buying anything with the proceeds, except my apples. It is as if I gave him $100 for his bananas at the posted price, but added a rider in the contract that says he must immediately spend the whole of that $100 on buying my apples at my posted price.

My prohibition on buying bonds in the second trading system was my attempt to model that difference between monetary and barter exchange.

Given the setup in my model, people will accept those riders against buying bonds with the proceeds, even though they would prefer to break those riders if they could get away with it.

I don't know if this is clear, or convincing, or if it even misses your criticisms completely. It's about the best i can do.

(But what I may have failed to model correctly, and what I can't quite get my head around, is the difference between bilateral barter of 2 fruits vs multilateral barter of n fruits. I can't get my head clear on whether this matters.)

For some reason, this reminds me of Joan Robinson noting that the Walrasian analysis applies pretty well in only one case, that of a prisoner of war camp (a pure, closed barter system), mainly because two characteristics of industrial capitalism are missing in the POW case (and from the Walrasian model): 1) the distinction between income from work and income from property and 2) investments made with uncertain expectations from a long future. Both seem key features of Keynes' model. Perhaps I read through this too quickly and missed them. If I'm right and they are not there, then can this be a truly Keynesian model, I wonder? Maybe someone has already raised this and I missed it. If so, I apologize for appearing to belabor a point already made.

Maxine: There's a good reason it reminds you of that. It's because it shares the belief that trading systems matter.

But I think Joan Robinson was wrong. As in Frances' Nov 11th post, on the POW camp, they did use money, both as medium of account and medium of exchange. Prices were measured in cigarettes, and people, even non-smokers, traded other goods for cigs. Cigs were money. And you can build uncertain investment into the Walrasian model (OK, Arrow-Debreu). And there is one difference between income from work and income from renting out other property in the Walrasian system: the first gives disutility at the margin. (Of course, Joan Robinson had some beliefs that income from property was different from wages in more ways than that.)

Adam: (Yes, I'm beginning to think that there is an important difference between pairwise and multilateral barter. When I swap you my apples for your bananas, I not only prohibit you from buying bonds with the proceeds, I prohibit you from buying dates with the proceeds. And I wouldn't buy your bananas if I thought you were going to spend the money on dates, or bonds. I think I should have built this in explicitly in my "barter" market(s).)

Well I think we're comunicating now! But I think we're drifting away from the original argument.

We've agreed that what's driving the results is whether or not agents can buy bonds, it's not a money/no money distinction. So then, going back to the first parargraph of the post where you say:

All Keynesian macroeconomics, either explicitly or implicitly, assumes monetary exchange. It's not just sticky prices that generate Keynesian results. It's sticky prices plus monetary exchange.

Basically then, taking away bonds prevents the intertemporal Euler condition from having any effect on behaviour and so goods markets clear. So I agree, no bonds or money (no savings medium of any kind) means no recession.

On the market structure question, I'd have just had the auctioneer in the barter market also auction off the bonds. His job would be to clear all the goods markets and the bond market with the additional proviso that the bond market clear at the interest rate that the central bank wants. That's what I've always understood the NK model to mean.

This would imply that to clear the bond market the Euler condition would have to be satisfied and so if the central bank sets too high a rate then we'd get a recession.

Can we now agree that, at least in principle, an NK model that has no money but does have bonds makes sense, that you can get a recession if the central bank sets the real rate too high? (And perhaps you want to change the second paragraph in the original post?)

Now, as for what your starting to think about in these last few comments I have to think you're on track for a good point. Notice my understanding of the NK model was multi-lateral barter including bonds. If you restrict to bi-lateral barter then you may well be right, even if I what I want is for someone to sell me a bond, if there's none to be found I may well settle for utility improving trades that are still second best.

Even this is not obvious though, seems to me there might be search friction that gets in the way of market clearing. If I want a bond but you won't issue me one perhaps I don't trade with you, I go on to the next meeting and try to get the next person I meet to issue me a bond.

Thinking more on pairwise vs multilateral barter:

1, In the second market, n(n-1)/2 pairwise barters could get the economy out of the recession. The apple-seller trades some apples for bananas, some apples for carrots....and the banana seller sells some bananas for carrots...etc. That's a Nash equilibrium to accept.

2. In the second market, one big n-person barter, that all have to sign off on simultaneously, could also get the economy out of the recession. The apple seller produces n more apples, and gets 1 banana, 1 carrot,...etc in return. That's also a Nash equilibrium to accept.

3. What will NOT work is the mere prohibition on buying bonds with the proceeds of a sale. The apple seller will not spend $n on bananas, because he knows that only $1 will be spent on apples, and the remaining $(n-1) will be spent on other fruit. Escaping the recession that way is not a Nash equilibrium.

Barter is normally 1. Barter can be 2. (though it's rare). But 3 isn't barter. It's more like monetary exchange, rather that barter, with just one restrictive covenant attached about what you can't spend the proceeds on.

Pure monetary exchange is totally unrestricted on what you can do with the proceeds of sale. Pure barter is totally restricted on what you can do with the proceeds of sale.

"This would imply that to clear the bond market the Euler condition would have to be satisfied and so if the central bank sets too high a rate then we'd get a recession."

Agreed.

"Can we now agree that, at least in principle, an NK model that has no money but does have bonds makes sense, that you can get a recession if the central bank sets the real rate too high? (And perhaps you want to change the second paragraph in the original post?)"

Not really. The question is not whether it has (a stock of) "money", but whether it has "monetary exchange", and what precisely that means. If there are no restrictions on what the seller of goods can do with the proceeds of the sale, then I would want to call it "monetary exchange". And if there's monetary exchange in that sense, and the central bank sets the real rate too high, you get a recession. And I would say that "Barter exchange" means that there are total restrictions (no freedom) on what the seller can do with the proceeds of the sale. And with barter exchange, in that sense, there would be no recession even if the central bank set the interest rate too high. There would just be an excess demand for bonds.

One of these days I'm going to re-write my post from scratch. Because I really do think it makes a valid point, but it's not as clear as it should have been (because I wasn't as clear in my head as I should have been).

So a NK model that has money regularly exchanged for goods and services, but no bonds or savings, doesn't have monetary exchange? Mr. Rowe, with all due respect, I think redefining terms that way is potentially misleading (to say the least). How did "monetary exchange" become "restrictions on what your trading partners can do"? If you wanted to remove bonds from the economy, just say a "no-bond economy".

david. Think about the real world.

When you buy something with money, do you tell the seller what he is allowed to spend his money on? Of course not.

When you buy something with barter, do you tell the seller what he has to buy with the proceeds? Of course you do, by definition. He has to buy your apples if he wants you to buy his bananas.

Considering money is just a bond with a zero maturity, redeemable on demand, whatever redeemable means, I don't think bonds can be separated from money unless one is willing to impose a redeemable when due or expiry condition on the forward contract. Separating money from bonds is more possible by banning lending and forward contracts, though reciprocal gifting would soon circumvent this, wink wink, nod nod. An investment or speculation in inventory is possible whenever one deems exchange unfavorable, but that would be in a specific good by a specific person. A bubble may form in it if enough do then change their mind, but as with all speculations, prices fluctuate.

No. There's no restriction on what the seller must buy. You mentioned multilateral barter yourself already.

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