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I think this is a brilliant article , and I hope you are joking about burn out or get over it quickly !

I have a question on:

'This teaches students that Investment and Saving are central to understanding recessions. This teaches them something that is false. It is monetary exchange, not Investment and Saving, that is central to understanding why monetary economies sometimes suffer from recessions. It is possible to have a one-period model, where by definition "Investment" and "Saving" are meaningless, which has exactly the same sorts of recessions that we observe in the real world'.

I see that in your minimal model it is possible to have a recession even with one period and no investment. IS/LM is not very useful to understand a this model.

However it is also possible to imagine a world with multiple periods and investment where people just sometimes want to invest less than in other times and this could lead to a fall in income that could be defined as a recession even with no excess demand for money. IS/LM does shed some light into this world.

What empirical evidence or theoretical confusion would you point to to show that your model more accurately describes real world recessions than the model in which IS/LM does have explanatory power ?

> Thinking of macro in this way integrates macro into micro in a way that "microfoundations", as commonly understood and practised in e.g. New Keynesian macro models, can never do.

Is this because of the representative agent paradigm, or do you think that microfounded models with heterogeneity would also fail at this? Would agent-based modelling have a better shot at explaining this facet of recessions?

MF: Thanks! But I'm not joking about burnout. Maybe it's just I've been teaching for 35+ years, and blogging for 7? years, feel like I'm just repeating myself, and am overdue a sabbatical (but won't take one because I know if I did I would never come back). Plus I'm getting old. Or it might just be the usual Spring doldrums.

Suppose people decided to invest less. If they decided to consume more leisure instead, that would lead to a fall in output and employment. But it wouldn't lead to that increased difficulty of selling goods & labour for money (and increased ease of buying goods & labour for money) that to me is a signature of a recession. And we wouldn't see people desperate enough to resort to barter.

Harry. My simple model can be thought of as a representative agent model. Even though some agents have an endowment of apples, and others an endowment of bananas, we can think of this as a model where each agent has "fruit", but wants to eat some of other agents' fruit as well as his own. They are symmetrical, rather than identical.

Nick, if you're feeling that you're getting a burnout you should definitely take a break and consult a physician. A burnout, as I understand it, is when you deplete all your energy reserves and rebuilding these can take a very long time during which you will for a while not be able to do anything: e.g. no reading, no watching television, little to no movements etc. Recovery times here can vary between 6-8 weeks to even years. Definitely not worth the risk if you can avoid it.

Why not spent a sabbatical to organize some of your blog posts into a book that could accompany an undergraduate intro and advanced macroeconomics class? There is more than enough material there. Furthermore, you could then keep teaching what you have been teaching all these years or even Olivier's new suggestions eventually whilst also telling students what's wrong with it. You would be equipping students to think in models and skills to critically evaluate these models. More cannot really be asked of you, and it seems that that is what a good economist needs if Rodrik is to be believed.

P.S. For what it's worth, thanks to you and some others (e.g. Sumner) I have the feeling I understand much more of macro than I did as an undergraduate in economics. I could move the curves up and down, and reproduce the relevant bits from the book, but I never had the feeling that I understood what I was doing. If you ever come out with a book based on a collection of your blog posts I'd definitely be buying it.

Well, whatever you do - please don't stop blogging ! For people like me who are genuinely trying to learn economics from the blogosphere - your posts have the status of Shakespearean Sonnets.

Toby: thanks, but my physical energy is OK. Just economics, or maybe just macro/money. I was trying to write one more post on helicopter money, got halfway through, and got sick of it.

MF: Thanks!

I teach macro at very basic level to people who won't become economists, a level suitable from a humble IO guy. I never tell them that recession are about Investment. Saving in a monetary world yes but not I.
Collect your blogs in a book. You could time it with Stephen's "Columns written from an airport departure lounge". It would make a nice one-two punch from the best bloggers-colomnists in town.
If it's not simple end-of-term doldrum, take it seriously.


It seems you have a clear idea of why you are depleted.

I hope you will excuse me for possibly offering gratuitous advice, I would say there is only one remedy, as Shakespeare said, "To thine own self be true."


Which of the Clower Howitt papers are you referring to?

Recessions are not about GDP. I can imagine a world where GDP is exogenous and never changes (all goods fall like manna from heaven) and yet we still get recessions for exactly the same reason we get recessions in the real world because people fail to trade enough of those goods, and are stuck consuming too much of their own endowment and consuming too little of someone else's endowment.

AFIK consuming ones own endowment / home production does not count towards GDP. Only selling new output to another legal entity counts.

The fourth problem with the ISLM model is the vertical axis. This teaches students that the rate of interest is central to understanding recessions, and that recessions are caused by the rate of interest being too high. This teaches them something that is wrong, and it is wrong whether we are talking about the real or nominal interest rate. It is wrong because we can get recessions even in a one-period model, where interest rates do not exist.

I don't know about New Keynesians, but in a credit economy where money is not given but rather must be borrowed to cover the cost of production / wage bill, an interest rate makes perfect sense even in one period without investment.

But I don't want to bore you, I assume you've heard the above often enough to have convinced yourself it's quackery.

Rather I'll join in with the other compliments. Your blogging should count towards Canada's development aid.

Jacques Rene: sometimes I think about putting some posts together and writing something longer. But blogging gives you ADD, and Twitter makes it worse!

Henry: Peter Howitt was one of my macro teachers, and I view the Clower and followers approach to Keynesian macro through his lens.

Oliver: There's (at least) two exceptions to that. The services of owner-occupied housing; and inventory accumulation. Both are included in GDP. It's a bit of an arbitrary mess, once you start looking at it closely.

If people borrowed money, I would need a 2-period model, with them paying back the money in the second period.

As far as GDP goes, I'll take your word for it and let the accountants defend the concept. But assuming it were not quite as messy as you claim it is, say by squinting very hard, is GDP not a natural ally to your theory of recession? It measures not how much is produced but how much of one's production is consumed by others (or meant to be consumed by others in the case of inventory since firms do not consume their own output).

And as far as I've understood the basic credit model, money is essential within the period as a means of transferring purchasing power from the firm to wager earners and its owners to buy back their own output but all money balances are back to 0 at the end of the period, with or without an interest rate (or investment, for that matter). The model does however require a division of the economy into firms that produce but don't consume and individuals who consume the firms' output.

I was about to buy the new text by Blanchard because I am trying to better udnerstand macro and Blanchard is an acknowledged expert. Now I am not so sure. Where do I go? What do I read?

I have a feeling I'm cementing you despair...

I'm sorry to hear about your burn-out. I hope you will continue to continue to grace this blog with at least the occasional post since I think they are some of the very best econ blogging out there.

On topic:

I think you're being a bit too harsh on the horizontal line. It's true that one could conceive of a situation where you get a recession without a fall in GDP (as in your example). However in any real recession, the most important coordination failure is in the labour market where people consume too much of their own endowment of labour and THIS IS THE SAME THING as a fall in GDP. The GDP decline is not a result of the failure to sell labour and other things, it is the same thing (more precisely it's how we measure the same thing).
(I know writing in all caps makes me look like a madman but I don't think there's any way to use bold in the comments section)

I'm also surprised to see you arguing against a change from LM curve to Taylor rule curve. Didn't you yourself write that you use this approach when teaching the IS-(whatever) model?

Surely there must be a way to build a modified IS-LM that goes some way towards incorporating your objections.

"It is possible to have a one-period model.."

The only reason saving is meaningless in that model is that you have made money a consumption good, so by definition acquiring more money is not saving. But we're normally concerned with money that is a financial asset, so accumulating it is indeed saving. If you somehow managed to have an excess demand for a (financial asset) medium of exchange without having an excess demand for savings, I'm not sure you'd get the same result.

Hugo Andre (and this is perhaps a response to Oliver too): Well, let's say that GDP is an *empirical proxy* for recessions. But I would like us to focus theoretically on *trade*, as opposed to *production*. We can at least imagine a world where self-employed workers produce goods, and in a recession they go on producing exactly the same amount of goods, but must consume their goods themselves. One real world example of this (though it's not included in GDP) is increased investment in human capital during a recession, where the student's own labour is the biggest input.

Nick E: Let's consider 3 cases where our little model is changed to introduce saving:

1. Mangoes are storable, but apples and bananas aren't.

2. Apples and bananas are storable, but mangoes aren't.

3. All 3 fruits are storable.

Start in full equilibrium, then hold all prices fixed, and let's ask what happens if time-preference falls (people become more patient).

In case 1 I think we get a recession. But in case 2 I think we get a boom. And in case 3 I think nothing happens.

It's a bit like saying "But if money is gold, an increased preference for gold jewelry will cause a recession".

Egmont: you have not read my post, your comment has nothing to do with my post, and you are just repeating the same spam that you post everywhere. So I deleted it.

Derek: buy Blanchard's text. It will be good, and you need to know that stuff anyway. But understand there are other ways of looking at it.

Recessions are transaction crashes. The question "what causes recessions?" is "what causes transaction crashes?". Or, more specifically, "what in a monetised economy causes transaction crashes in lots of industries at once?".

Which is another way of saying focus on trade, not production.

So much of analytical progress is asking the right questions.

(Deirdre McCloskey has written that Marx was wrong on almost every substantive point but was still the greatest social scientist of the C19th. A friend sceptically asked how can he be a great social scientist if he was so wrong. My inferred answer was: because he asked really good questions. The problem with Marxism is people believed his answers. If you want examples of analytical inertia, consider how much of academic life is still infected with those wrong answers.)

Great post.

Thanks Lorenzo. Yep, I agree that getting the question right is at least half the battle.


You variously said:

" I can imagine a world where GDP is exogenous and never changes (all goods fall like manna from heaven) ...."

The last lot that tried this took 40 years to find an equilibrium. Every recession I've seen (and I've seen a few) has been accompanied by a fall in GDP (in fact, as you know, that's how recession is defined). What's your imagined world got to do with the real world?

" "Money buys goods, and goods buy money, but goods do not buy goods", to quote Clower, IIRC. If unemployed workers could easily barter themselves back to full employment, they would do so."

What about income effects?

" It is an excess demand for the medium of exchange that prevents mutually advantageous exchanges being made that we call "recessions"."

How does this excess demand arise?

" It is possible to have a one-period model, where by definition "Investment" and "Saving" are meaningless, which has exactly the same sorts of recessions that we observe in the real world. "

So what? What has this do with the real world?

Hicks says he developed ISLM (sounds like a religion the West is having some trouble with currently, I guess it conforms to the Bibical line you have taken)in 1935, before Keynes had published the GT. It was a model based on neoclassical precepts. Hansen developed it further, calling it Keynesian. How he came to do this I am not sure. In his "Guide to Keynes" he asserts that Chapter 17 of the GT was superfluous and could have been omitted even though Keynes titled it "The Essential Properties of Money". The ESSENTIAL...Obviously Hansen didn't get the essential part, leaving one to ask what exactly did he get of the GT.

Henry: a "fall in GDP" is not in fact how recessions are defined. (If we did define "recession" as "2 consecutive quarters of declining GDP", then agricultural countries would have recessions every Winter.) "Recession" has no agreed-on definition. Falling GDP is just one of the symptoms that economists look at when they try to date recessions.

It's a bit like defining the disease in terms of one of the common symptoms.

"What about income effects?"

If I could sell my labour and buy all the goods I normally buy through barter instead of monetary exchange, my (real) income would be exactly the same.

"How does this excess demand arise?"

By a failure of the monetary system to respond to shocks to demand or supply of money correctly.

"So what? What has this do with the real world?"

The whole point of modelling is to figure out what features of the real world matter and do not matter for understanding the phenomenon (in this case recessions) in question.

Nick Rowe

You wrote: “OK Nick, but if you don’t like teaching IS-LM, what would you teach instead? Which is a perfectly reasonable question. Which is why I despair. Because what could I teach instead?”

The answer is in my post ‘Getting out of IS-LM = Getting out of despair’. With the structural axiom set A1 to A3 you get the CORRECT FORMAL MINIMUM. These macrofoundations fully replace both the obsolete Walrasian microfoundations and your apples-bananas-mangoes equilibrium model.

It seems that you cannot see the solution for your self-inflicted despair when it is right before your eyes. While it is perfectly understandable that you deleted my post in your analytical agony it would have been perhaps helpful for others if you had at least left a link standing, e.g.

After all, other desperate IS-LMers should also have a fair chance to make up their minds. It is of utmost importance to terminate IS-LM teaching once and for all.

Egmont Kakarot-Handtke


You said:

"It's a bit like defining the disease in terms of one of the common symptoms."

That's a good place to start isn't it? Symptoms? Diagnosis? Every recession I've seen has been accompanied by output and employment reduction. It's of course beginning to sound tautological. OK, there might be other kinds of recession which don't exhibit these features, if so, they appear to be missed and of no consequence anyway. Recessions only feature because of the damage that is evident to output and employment and asset values. Output/employment loss are not just symptoms - they become "stimulants" for further dislocation and decline in spending.

"If I could sell my labour and buy all the goods I normally buy through barter instead of monetary exchange, my (real) income would be exactly the same."

Given it's a one period endowment model you have assumed away output and employment retrenchment, so there can be no loss of income. So of what use really is your model? It's fine to model stuff but when your model looks nothing like reality of what use is it? Why construct a model in the way you have? Couldn't models with other (unreal) characteristics be defined and formulated that result in other (unreal) ways of looking at the world? It seems to me you have constructed your model the way you have because it gives the result you want to assert is a feature of real world economies. The fact is that real world economies do have saving and investment, with some arguing, believe it or not, that how decisions are made around these features, impacts on output and employment.

"By a failure of the monetary system to respond to shocks to demand or supply of money correctly."

Sounds like a circular argument to me.

" "Y" is (real) GDP. Recessions are not about GDP. I can imagine a world where GDP is exogenous and never changes (all goods fall like manna from heaven) and yet we still get recessions for exactly the same reason we get recessions in the real world because people fail to trade enough of those goods, and are stuck consuming too much of their own endowment and consuming too little of someone else's endowment. Which is exactly what happens to unemployed workers in recessions; they are stuck consuming too much of their own labour services and too little of some other workers' labour services "

Well, since the good "leisure" (produced with own labor) is not counted in GDP, I think it's okay to put GDP on the x-axis. But it's a good point and being explicit about it can help the student understand better what is really going on. It would also make explaining why "too much GDP" can also be a bad thing easier, which is always left out of the textbooks.

Henry: if you define "income" as "quantity of fruit sold", then there certainly is a drop of income in a recession in my model.

notsneaky: yep. There's a "right" amount of trade, to maximise welfare.

Nick, you and the others Market Monetarists need to get together and build up a research program.

I feel what you need to make a neat MM model that can compete with IS-LM is a simple 3 equations model:

Philips Curve
Monetary Authority response function
Money demand

Philips curve is easy. Monetary Authority response function is also easy. So we're left with money demand.

The easiest model is money demand as NGDP=k*M in an NGDP x M space. It interacts with a monetary authority response function, and gives us a NGDP and a money quantity. So we use de NGDP to build an Aggregate demand function to interact with our Philips curve and get a Price and Employment.

This is simple and easy, but we really should have a more developed money supply. First some tentative functional form, then we can go from comparative statics to dynamic, include things like expectations influence on money demand, so some interesting results can be found. Something like the money demand is higher if an NGDP targeting bank overshot its target, because it implies lower NGDP grow in the future.

Anyway, the way I see it you guys need an interesting money demand function.

Hi. I read some old krugman column/article pretty much saying the same as your one period minimalist model -- that the ISLM is just a 3 good model and that its possible to demand too much of one good in equilibrium (that good is money).

in the same way, your manoes, apples and bananas model is the same, right?

Arthur. You may be right. But I think I will leave it to the young guys.

Gabby: if we are thinking about the same article, and if my memory is correct, there's a problem in it. Paul talks about 3 goods and *3* markets. If one of the 3 goods is the medium of exchange, there are only *2* markets.

Ok, I know I have this tendency to comment on some of your posts long after they've "expired" in terms of blog-time, but that's because sometimes I have to turn over something in my head a bit before something occurs to me. And yes, usually, it's something not all that important.

Given that disclaimer, I want to back track on my comment above - but also make a point. If you insist on having a one period model, with no saving or investment or any kind of intertemporal stuff, then it's actually impossible to have "too much GDP". I was wrong in my comment above. In a one period model it's basically impossible for there to be "too much money". Yes, you can have an excess supply of money, but since the only purpose of money is to carry out transactions, the Central Bank can just flood the economy with it, the right amount of transactions take place and people put any excess balances in their back pocket. They wouldn't mind getting rid of it, but since we're also assuming good prices are fixed (that's what preventing the economy from achieving an optimal outcome) there's no variable that can adjust to eliminate it. Or, alternatively, if some variable can adjust (say, there is more than two goods in the economy) then it adjusts but it makes no difference. In a one period economy only excess demand for money is a problem, not excess supply.

So I guess one argument for putting some saving in there and making it more than one period is because you want to consider the possibility of utility loss due to too much money - i.e. costs of inflation.

Here is a sort of informal proof/exposition of the above, with the qualifications that actually it's about the number of goods vs. the number of prices you keep fixed:

In a one period model with a Clower constraint, and money NOT in the utility function, the amount of money in the economy constraints the transactions which can take place. But it is the relative price of the goods which determines allocations. So if the good prices are flexible, the Clower constraint is just a particular normalization of the relative price. The allocation is the same as if it was in a pure barter economy and it is optimal.

But suppose that one of the good prices is given. Now we have two constraints - the Clower money constraint and the fact that one of the prices has to equal some fixed level. The thing is, the Clower constraint may be non-binding while the fixed-price constraint is always binding. Suppose both constraints are binding. Then you get the "recession" and a sup-optimal amount of trades. There's not enough money in the economy. But suppose only fixed-price constraint is binding - at that particular fixed price, individuals have enough money balances to carry out desired transactions. Then the relative price adjusts to the Walrasian level and you get the optimal allocation. Excess money is not a problem.

To make excess money a problem you need, at least:
a) More than two goods
b) Fix the prices of more than ONE good.

In Macro when people say "fixed prices" or "sticky prices" they are implicitly fixing more than one good price. Usually they do that intertemporaly - prices are fixed today and tomorrow (or, equivalently, the price of a good tomorrow is a function of the good today).

notsneaky: an excess supply of money will also reduce the volume of trades below the optimal. I show this in my little model. It's the Barro-Grossman supply-side multiplier.

Nick, I know, but I think that's because in that model (that's the "Another tiny money/macro model for microeconomists" right?) you stick money - good B - in the utility function, which I think is sort of cheating. Because in that case if you have Central Bank which truly controls the money supply then why not just provide a crapload of B?

notsneaky: I don't think that's right. Remember the "Short Side Rule" Q=min{Qd,Qs}. We can have an economy where Qs is the binding constraint, and if people have more money they demand more goods and supply less goods. (Why work to produce goods if you don't need more money, and can't spend more anyway because there's an excess demand?) Cuba looked a lot like that in the 1990's.

I'm not seeing it. Although it does get a bit weird if you think about it.

In your "Another tiny money" model, take good B out of the utility function. It still remains as a medium of exchange. A still has to be traded for B and C still has to be traded for B but A cannot be traded directly for C.

First, as a baseline consider a non-monetary exchange economy with flex prices where you can exchange A for C directly. Then there's a relative price (in this case I believe 1) pA/pC which leads to an optimal allocation.

Now, impose the constraints that A and C have to be exchanged for B. And fix the B-price of A to, I dunno, 50. Say there's only a little bit of B in that economy. Then the B-price of C cannot adjust to 50 so the relative price is off and you get the recession. But suppose there's a ton of B in that economy. Agents exchange A for B then B for C etc the money price of C is 50, so the relative price is 1, so you get the optimal allocation. Yes, people will sit there with cash (B) on hand that does them no good. But so what? Will they try to spend it? They can try (I think this is where it gets into the nitty gritty of what the concept of equilibrium is and how the competition actually takes place). But the marginal utility of money, of B, at this point, is zero. So the price of B in terms of other goods should be zero.

This is a bit weird though because we have the money price of each good equal 50 up to the point that money is necessary to carry out the transactions to achieve optimality but after that the money price of each good is infinite.

So if we assume that at that point, agents are not willing to trade their A and C goods for B anymore, we get that excess of money doesn't cause any problems. If we assume instead that in the model agents have to accept any offered exchanges made at given prices, then we get that the agents just pass the excess supply of B amongst each other in a circle - there is no equilibrium.

Here is my version of your tiny model, which I think is more "macro-ish". There are two goods, output and leisure, with the latter measured as disutility of labor. Labor is only factor of production, constant return to scale, in fact, let's just make one unit of labor produce unit of output. There are two Betrand firms which can produce the good and hire labor. There is a third object called "money" which is necessary to carry out trades. That is, labor can only be exchanged for money, and output can only be exchanged for money, but labor cannot be exchanged for output directly. Initially, the firms are endowed with some money holdings. There's only one period but there's a sequence to moves made within the period.

Firms first announce the money wages that each of them will pay to workers. Having observed each other's wage offers they announce prices at which they'll sell their output. They hire labor up to the point necessary to produce demanded output subject to the constraint that they can finance this hiring with their initial money holdings. Employed workers demand output and pay for it with their money wages.

Worker's utility is U=(wL/p)-.5*L^2. So each worker (and let's just assume there's a mass 1 of them) wishes to supply w=pL labor. This is the labor supply curve. It's a ray from the origin in w/L space.

Firms are subject to the monetary constraint wL=M where M is their total initial money holdings (that's actually a "less than or equal"). So w=M/L which is a downward sloping curve in w/L space.

Finally, given these are Bertrand competitors, prices equal marginal cost and firms make zero profit, which means that w=p. Which is a horizontal line in w/L space.

With flexible prices the three lines, w=pL, w=M/L and w=p all cross at the same point, equilibrium and optimality everywhere.

But suppose we fix the output price p=p'. We have two cases. Either the labor supply curve w=pL crosses the zero profit condition w=p to the left or to the right of the crossing between the monetary constraint w=M/L and the zero profit condition. (we could have of course get the same outcome as the flexible price equilibrium by accident or if there's "just enough" M in the economy)

Suppose the crossing point between w=p' and w=p'L occurs below w=M/L. Labor supplied is 1. Firms hire 1 unit of labor. Spending equals value of production. Equilibrium and optimality everywhere *despite* the fact that p' is fixed and there's a monetary constraint. Firms wind up with left over money but so what? How could they get rid of it? They could try to hire more workers. But to do that they'd also have to raise wages (since we're at labor demand = labor supply). Which, given p', would mean they make negative profits. So they won't.

The case where the crossing between w=p' and w=p'L occurs above w=M/L is giving me a bit of a logical headache, mostly because this is a model of "double Bertrand competition".

notsneaky: Make a small change to your model: assume the households who supply labour also own the firms, and so own all the money the firms own.

In your model the money is all owned by people who supply no labour (or other goods), so you get a distribution of wealth effect. You also have a perfectly inelastic (wrt everything) labour supply curve.

I am assuming that firms own the firms - that's the standard assumption so I just wasn't making it explicit. I don't think that makes a difference though. However, the firm decision making is separate from the household decision making (again, standard) - firms try to maximize profits, individuals try to maximize utility.

I'm not sure I get the perfectly inelastic labor supply curve part either. If the utility function of person i is Ui=(w/p)*l(i)-.5*l(i)^2 (I've now made it explicit that labor supply is an individual decision) then the first order condition is (w/p)=l(i). What am I missing?

err... assuming that *households* own the firms

I think your analysis of your own model - http://worthwhile.typepad.com/worthwhile_canadian_initi/2015/06/a-second-tiny-macro-model-for-microeconomists.html this one - is incorrect. If you make the additional assumption that agents can only travel to exchange once, it's then half right. The part that is still wrong is precisely the part about booms and excess supply of money. There is also the additional problem of having money (good B) in the utility function. What does that mean? I'll leave that alone for now because it's a separate issue.

Let's refer to agent types with capital letters (A agents, C agents) and endowments/quantities trade by lower case letter (a,b,c). There are two mistakes in the analysis, one of them in the comments, by Max. The first one is the fact that you appear to rule out some trades on the basis that "promises are not credible". But that only means that any trades have to be incentive compatible. I will trust your promise, even if you have no way of committing, as long as I know it will be in your interest to keep your promise. Second, in the comments, where Max says "we can leave off log(C) because he doesn't have any and won't purchase any in his initial trade of A to B". You can't do that. Utility is utility and if you're comparing two utilities where one of the arguments is zero then you're comparing two utilities that both equal -infinity so utility is same in both cases. And all that matters is final utility not any kind of "intermediate utility", as long as that final utility is achieved via a sequence of incentive compatible trades.

So first let's make the model a bit more precise. The way that trade happens is that there are two camps, a-camp and c-camp and agents travel between them to engage in trade. They cannot take their non-b endowment with them to the other camp. And they are prohibited from trading non-b endowments even when they have both in their camp. It's all got to be b for other stuff.

Once you follow the logic through then you get the following result:

* If each agent can only make one trip to the other camp, then
** If there's "not enough money" (p(a)=p(c)=2) then you get the recession.
** But if there's "too much money" (p(a)=p(c)=1/2) then it doesn't matter, the agents can achieve the optimal allocation.

* If agents can make as many trips as they like between camps, then the only thing that matters is the relative price and as long as p(a)=p(c), whether it's 1/2 or 2, you get the optimum.

Consider the case where p(a)=p(b)=1/2 ("too much money"). Agents C go to A's camp and trade 200 a for 100 b. Agents A are willing to accept this trade because their utility is -inf before and after. Agents C are willing to offer that trade because their utility is -inf before and after. So now A's have 200 b and C's have 200 c and 200 a. A's go to C's camp and trade 50 b for 100 c and 50 b for 100 a. They are willing to offer that trade because it changes their utility from -inf to the optimal amount. C's are willing to accept the trade for the same reason.

So there's no inefficiency with too much money even when agents are allowed only one trip.

Now consider the case where p(a)=p(c)=2. C's go to A's camp and trade 100 b for 50 a. This doesn't decrease anyone's utility so it's acceptable trade. Now A's have 150 a and 200 b and C's have 200 c and 50 a. Then A's go to C's camp. They trade 100 b for 50 c. Now A's have 150 a, 100 b and 50 c, and B's have 50 a, 100 b, and 150 c. Trade is acceptable because both groups' utility increases as a result. They both now have utility log(50)+log(100)+log(150).

This is the point where you stop and call it a recession. And this will indeed be true if there are no more trips permitted (this is like restricting the velocity of money). But suppose the agents are allowed more trips.

So now we start with an endowment {150,100,50} for A's and {50,100,150} for B's. C's go to A's camp again and trade 100 b for 50 a. A's are willing to accept that because now they'll have {100,200,50} which gives them higher utility. But it may be a problem for C's since now they'll be back to -inf for their "temporary utility". However, this trade is still incentive compatible because C's correctly anticipate that A's will visit their camp again and offer another mutually beneficial trade. Indeed, that's what happens. A's go to C's, and trade 100 b for 50 c. Everyone winds up with the optimal amount of goods.

To sum up. In your model. If we assume that:
1. There's money in the utility function
2. There's also a cash-in-advance constraint which necessitates that exchanges are made with money
3. Money prices are "wrong" (although the relative price of non-money goods is right)
4. There's a restriction on the number of events of exchange that can take place


I. If there's "not enough money" then we get a suboptimal outcome.
II. If there's "too much money" we still get the efficient outcome.

If we drop assumption 4. then

You always get the efficient outcome anyway.

And like I said, this is keeping assumption 1. in place, that money is in the utility function, which means that either i) this is not a 1-period model where the presence of money in utility represents "future liquidity services of money" or ii) this is a commodity money economy in which case whatever monetary authority exists doesn't really have control over money supply so the whole point of it being a monetary recession is sort of moot.

I apologize for bringing this up again. Just once I start thinking about it it gets in my head and I need to get the logic right.


Let's switch to my second version of the model, where I *think* I got it right:


P=1 is the market-clearing equilibrium price for apples and bananas. Assuming P < 1 (so there's excess demand of apples and bananas):

In the apple market, alphas choose A to maximise U = log(200-A) + log(B) + log(100+PA-PB) taking B as given.

In the banana market, betas choose B to maximise U = log(A) + log(200-B) + log(100-PA+PB) taking A as given.

The answer I get is (from the post):

"[For completeness, we can solve the model for P < 1, where there is excess demand for apples and bananas, so it is buyers of apples and bananas who are constrained in how much they can buy. The Nash Equilibrium is A = B = 200 - 100/P ]"

If I'm right, we get too little trade if P < 1.
But, as you know, my math is not to be trusted.

Alright, I see what you're doing there. You also have the assumption that essentially the goods have to be "consumed on the premises". So, going with the camp analogy, when one group visits the other group's camp and trades, they can't take what they got with them. Ok. But then these aren't apples and bananas. They're folk dances and poetry readings. Services. So you have an economy which has only services and a physical good which serves as money, money in the utility function and wrong prices. I'm not sure if this is a model you can still call "minimalist".

But there's another problem. Suppose P=2/3. There's "too much money". Each agent's utility is log(150)+log(100)+log(50). Which is inefficient because if prices were flexible they'd have 3*log(100).

But then what is the "right" amount of money in that economy that will ensure efficiency. 200/3 mangoes per person. In that case P=2/3 is the market clearing price. And each agent gets utility of 2*log(100)+log(200/3)

But log(150)+log(100)+log(50) is greater than 2*log(100)+log(200/3). So agents are better off in the "inefficient" economy with "too much money" than in the efficient economy with "optimal money"

If prices are stuck at P=2/3 and there's someone out there that has control over money supply (even though it's commodity money) why would they ever choose the efficient economy? And it's strange to say that that "too much money" economy, inefficient though it is, is "in a monetary recession"

notsneaky: "But then these aren't apples and bananas. They're folk dances and poetry readings. Services. So you have an economy which has only services and a physical good which serves as money, money in the utility function and wrong prices."

True. It was a quick and dirty way to get money in the model.

We rarely observe the "too much money" case in market economies (but we do see it in communist countries with price controls a lot). I think that is because of monopolistic competition, so that prices are "too high" on average, so it takes a very big shock to create too much money. And yes, the decline in trade in the "too much money" case is very different from a normal recession, and deserves a different name.

And yes, given that I've got M, and not (M/P), in the utility function, calling it "too much money" instead of "too low a price level" is not the best choice of words.

But this isn't about whether we observe "too much money" in the real world. It's about the fact that "too much money" improves welfare in the model. It's confusing two things

*Given the amount of money, if prices are wrong then the outcome is inefficient
*Given that prices are wrong, more money, even above the "equilibrium amount", increases welfare

And I'd like to see a model like this without the money in utility function, which is partly what creates this problem and the confusion around it. It is hard to get an equilibrium in such a model (that's what I was trying to do in my model above) since if there's only one period everyone tries to dump their money balances.

I don't know, if you are going to have money in utility - maybe as a sort of reduced form for "future liquidity services" - then a different utility would work better? One with some kind of satiation point? Maybe something like log(A)+log(B)-(M-Mbar)^2

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