[Update 4 December: after long arguments with Adam P., which finally started to bear fruit in the comments of December 4th, I'm now clearer on what's essential in this model about the difference between "monetary exchange" and "barter exchange". It's this: In monetary exchange, there is no restriction on what the seller can do with the proceeds of a sale. He can spend the proceeds on anything, or save them. In barter exchange, there is a restriction on what the seller can do with the proceeds of a sale; he must spend all the proceeds on the buyer's goods. That is what is driving the results in this model. I think that is one important distinction between monetary and barter exchange. I have left the rest of the post as is.]
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. 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.
I used to think that the above paragraph was totally uncontroversial. I thought everybody understood this. I have learned they don't. So I'm going to do my best to explain why it's true.
I show that if we introduce barter into an otherwise nearly standard New Keynesian model, the solution immediately reverts to the perfectly competitive equilibrium, regardless of the degree of imperfect competition in the original model, regardless of any mistake made by the central bank in setting the nominal rate of interest, and regardless of sticky prices.
Just to be clear, this is in not a criticism of Keynesian macroeconomics. Barter is costly, and people do use monetary exchange. It's entirely reasonable that a model should assume people always use monetary exchange and cannot barter. And Monetarism would also be total rubbish if people could easily use barter instead of monetary exchange.
And just to be clear again, I am not saying that the particular way in which Keynesian models incorporate monetary exchange is unproblematic. I think it is problematic. But that's not the (main) point of this post. It's just an aside.
What I am going to build is a model of a model. Just as a model is an interpretation of the world, my model is an interpretation of a model. It's a model of the canonical New Keynesian model.
Here's my model.
There are n people, where n is a large enough number that each individual ignores the effect of his choices on the aggregate. Each person is a worker/firm, who produces one type of fruit. Each person produces a different fruit. The apple producer gets disutility from working L hours to produce A apples, with a production function A=F(L), and utility from consuming a Dixit-Stiglitz basket of fruit C with elasticity of substitution e (different fruits are imperfect substitutes). Each person maximises an infinite horizon subjectively discounted sum of present and expected future utilities U(C,L) etc.
In other words, exactly the same set-up as in the standard New Keynesian model, except I have suppressed the labour market for simplicity. Each firm is a worker. (If the labour market were perfectly competitive, and money wages were perfectly flexible, it would be exactly like my model.)
I will make one other small simplifying change to the standard New Keynesian model. I will assume that all firms must set prices before the central bank announces the nominal rate of interest. The firms that can change prices in a given period can only do so before observing the nominal rate of interest. This allows me to consider a symmetric equilibrium, where all firms have set the same price, and this makes everything much simpler when the central bank sets the "wrong" rate of interest. (Under the standard Calvo assumption, some firms would change their prices immediately when the central bank sets the wrong interest rate.)
I want to take this same underlying model, and impose two different trading structures. First I will impose "monetary exchange"; then I will add "barter". I want to show that adding barter makes a difference.
In what follows, remember that the Walrasian auctioneer is a great fiction. The auctioneer imposes a trading structure, and also solves the equations. I will introduce auctioneers. Like the Walrasian/Edgeworthian auctioneer, they will use "tatonnement with recontracting" to solve the equations. (Groping towards the solution, and all deals are re-negotiable until the auctioneer finds the solution). Unlike the Walrasian auctioneer, first there will be a tatonnement over prices, prices are then fixed, and only then will there be a tatonnement over quantities.
"Monetary exchange".
There is a central bank that also acts as auctioneer.
First, the central bank holds a tatonnement with recontracting on prices. 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.
Second, the central bank announces a nominal rate of interest.
Third, the auctioneer asks each firm how much fruit it would like to produce and sell.
Fourth, the auctioneer conducts a tatonnement on quantities. The auctioneer announces a tentative initial vector of quantities of fruit sold. That initial vector can be arbitrary (quantities, not prices, criee au hazard). Each firm is assigned monetary credits equal to the quantity of fruit sold times the price it set. The firm then decides how to spend those credits. It can spend them on fruit, or save them. Any unspent credits earn interest and can be spent next period, or saved again. (And any negative credit balance must pay interest, then be deducted from next period's balance.) The auctioneer checks to see if the amount of apples demanded equals the initial guess at the amount of apples sold, then checks bananas, and each fruit in turn. If the initial guess is wrong, all the initial demands are nullified, and the auctioneer guesses again, and repeats the auction. Only when the auctioneer guesses right are the contracts to buy fruit binding.
Fifth, all people then buy what they have contracted to buy, and work to produce and sell the quantity that others demand.
(In principle, the quantity of apples demanded might be larger than the quantity of apples supplied, and the auctioneer might have to ration buyers of apples. But this could only happen in equilibrium if the central bank set a rate of interest that was much too low. In general, because of imperfect competition, so that firms set prices above the competitive equilibrium, the quantity of apples sold will equal the quantity demanded, and will be less than quantity supplied. I will return to this point later.)
The solution to the above model will be identical to the solution to the standard New Keynesian model. Each firm will set price as a markup over marginal cost, where the markup depends on the elasticitity of its demand curve.
For simplicity, I want to consider only the solution where all firms set the same price. This would happen in a world where there were no real shocks, where the central bank had always targeted zero inflation, and where it had always set the nominal interest rate at exactly the right level in the past, and was confidently expected to set exactly the right interest rate in future.
In that long-run symmetric zero inflation equilibrium, the solution for the representative firm would be where the marginal rate of substitution between labour and the consumption basket (the shadow real wage) would equal (1-(1/e)) times the marginal product of labour (where e is the elasticity). Call the solution to that equation C*, or the natural rate of output.
MRS(C*,L*)=(1-(1/e)).MPL(L*) and C*=F(L*) if you want it in math.
(In the third stage of the auction, the firm asks each firm how much it would like to produce and sell. Since prices have already been set, the firm will answer this question exactly like a perfectly competitive firm, which takes the price at which it can sell its output as given. Because that price is now a pre-determined given. The answer to that question will be where the marginal rate of substitution between labour and the consumption basket (the shadow real wage) equals the marginal product of labour. Call the solution to that equation C^, or output supplied. C^ will be greater than C*, unless the labour supply curve is perfectly inelastic, or the firm's demand curve is perfectly elastic (e is infinite). Actual output and sales will be whichever is less, equilibrium quantity demanded, or quantity supplied. Since the natural rate C* is less than C^, the supply constraint will only be binding if a very big positive shock to demand causes demand to rise a long way above C*.)
MRS(C^,L^)=MPL(L^) and C^=F(L^) if you want it in math.
The above defines the solution if the central bank sets exactly the right rate of interest.
Now suppose that, after all firms have set prices, the central bank announces a nominal interest rate that is too high. And, to keep it simple, let's suppose that everyone is confident that this is a one-time mistake by the bank, so that output will return to the natural rate C* in the following period, and firms will choose to keep their prices constant next period. What happens?
Each firm will regret not having set a lower price. But by the time they get the news, it's too late to change price. The higher nominal and real interest rate gives every person an incentive to postpone consumption. In the fourth stage of the auction, if the auctioneer initially guesses that sales will equal the natural rate C*, and tentatively announces credits accordingly, he finds that demand is less than C*, because verybody wants to save some credits. So he learns his initial guess is wrong, and guesses again.
The solution will be where the Consumption-Euler equation is satisfied. The marginal rate of intertemporal substitution between current and future consumption, evaluated where future consumption equals C*, must equal (one plus) the (real and nominal) rate of interest set by the central bank. Call that solution Ci. Ci will be less than the natural rate C*.
(And if the central bank had set too low an interest rate, Ci would instead be above C*. And if the central bank had set a very low rate of interest, Ci would be so far above C* that C^ would be a binding constraint on supply.)
If you want math, the solution Ci is defined by MU(Ci)/MU(C*) = (1+r)B
where MU is marginal utility of consumption, B is the subjective discount factor, and r is the real rate of interest. Or something like that.
So far, my model is exactly like the standard New Keynesian model (except for a couple of trivial simplifying assumptions.) Now I'm going to introduce "barter".
"Barter".
Let's introduce a second auctioneer, who only opens for business after the first auctioneer has closed his books. (We can assume, if you like, that there is some trivial cost of using the second auctioneer, so everybody will try to do as much business as possible with the first auctioneer before resorting to the second auctioneer.) The second auctioneer is exactly like the first, except that he enforces Say's Law, at the individual level. No individual can carry a positive or negative balance of credits. Each individual can only swap fruit for fruit. He cannot sell fruit without buying fruit of equal value. He cannot buy fruit without selling fruit of equal value. (And by "value" I mean at the same prices that each firm had previously set, so I am not introducing price flexibility in this second auction.)
Again, let's assume for simplicity we start in a symmetric equilibrium, where all firms have set the same price. When the first auction closes, all firms have contracted to sell Ci, which may be above or below the natural rate C*, but is below the competitive equilibrium C^.
The apple producer maximises U(C,L) subject to the production function A=F(L) and the budget constraint P(C-Ci)=Pa(A-Ai), where Pa, the nominal price of apples, is pre-determined, and is equal to P, the price of a basket of fruit, in symmetric equilibrium.
Each firm will sell (and buy) an additional (C^-Ci) units in the second auction. The equilibrium after the second auction closes will be the competitive equilibrium C^, regardless of the rate of interest seat by the central bank. The proof is obvious. If the marginal rate of substitution of labour for fruit is less than the marginal product of labour, and it is less for any Ci less than C^, the firm/worker would prefer to eat more fruit even if it means working longer to produce it. Now the apple producer doesn't want to consume just apples, but he can swap his apples for bananas and all the other fruits in the second auction. If C is less than C^, there are unexploited gains from trade.
So, at the end of the second auction, C=C^. The economy gets to the competitive equilibrium, regardless of imperfect competition, and regardless of any mistake made by the central bank in setting the rate of interest too high.
Let me try to give the intuition.
First, Say's Law applies in barter. Both the apple producer and the banana producer want to sell more fruit. Each wants to sell more and save part of the proceeds. But neither is willing to borrow from the other. Barter allows both to undertake the mutually advantageous trades that can be made. "I will buy your bananas, but only if you buy my apples in return".
Second, under imperfect competition, each firm sets price above marginal cost. But if there's perfect symmetry (as there is here), that means the relative price of apples and bananas is equal to their relative marginal costs. So we still get the competitive equilibrium volume of trade in direct barter of apples and bananas. The (relative) price is right.
Just to avoid potential misunderstanding, I am not saying that money is the root of all problems. What I'm saying is that barter is very costly, and using monetary exchange is much less costly, so people use monetary exchange. The root of all problems is not money; the root of all problems is the cost of using barter, which means we have to use money.
Worthwhile Canadian Initiative 
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.