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You have specified two agents here: A and C.

Both have maximum possible utility from good B. They have 100 each.

Do we now need an agent for B who can be a middle trader between the two sides (who are forbidden to trade directly)?

Roger: the agents can trade directly. They just can't trade A for C directly. A-types can travel to C-land, carrying B, buy C with B, and consume C on the spot. The C-types can travel to A-land, carrying B, buy A with B, and consume A on the spot.

Nick, I think that your initial endowments of (200,100,0) and (0,100,200) at Pa=Pc=.5Pb (your boom case) completely fail to exchange any of good A for good C. It illustrates your point, but much more strongly than you think.

The key is to focus on the intermediate step of Endowment A (just for example, Endowment C has the same issue) considering the sale of ANY units of A (of which he has 200) for units of B (he has 100). At Pa=.5Pb and U=log(A)+log(B) (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), ANY trade of A to B results in lower utility. The math:

Initial endowment = log(200)+log(100)= 4.3010
Trade for ONE unit of B = log(198)+log(101)= 4.3009
Sale consistent with your example endstate of 150, 100, 50; but at the intermediate stage of 150, 125 (before A uses B to purchase C)= log(150)+log(125)= 4.273

Without assurances that he will be able to trade B for C, he won't trade any A for B when the price of good A is so low.

Max: I think you are right. (Damn! That's the same conclusion I came to at midnight last night, in my reply to John Hawkins! Why did I mess it up today?) Post being corrected.

Max: But if 1 > Pa=Pc > 0.5, there will be *some* trade in A and C, right?

Hi Nick,

Yep: you'll get increasing amounts of trade as Pa=Pc increases from 0.5. You can also stimulate trade by decreasing the initial endowment of good B in both (or, I guess, either) of the actors. Or, you could increase the amount of Good A.

The problem is that the ratio of prices (Pa=.5Pb) is equal to the ratio of goods (200:100 is equivalent to 1:.5) so they're already at a stable equilibrium with your given utility function.

That "non-trading" equilibrium holds at all higher initial values of B (or lower values of A) as well, so there's no trade if the ratio of Good A to Good B is less than or equal to the ratio of Price A to Price B (No trade: Qa:Qb<=Pa:Pb). I'm not really sure what that means in the real world: adding money when prices are already depressed obviously doesn't work but one solution seems to be letting A and C endowment holders produce themselves out of (this non-utility maximizing) equilibrium. They'll start trading A (or C) for B once their endowment exceeds 200. Hmm.

Max: thanks. That sounds right to me.

The policy when Pa=Pc < 1 is to reduce the money supply. Communist economies have precisely this problem; they call it the "monetary overhang". People already have too much money, can't buy anything with extra money, so stop working to earn money, which makes things even worse. Saw this in Cuba in the 1990's.

Nick,

Sorry, this is off subject to a degree, but I think you're a good person to ask this question:

Looking at simple IS-LM, suppose you start out with IS intersecting LM at 2% and \$17 trillion.

Then LM shifts sharply to the right. Now it intersects IS at negative 5% and \$22 trillion.

Of course, you can't get a negative interest rate, the ZLB. But, as you would normally read a supply and demand model, if the price has a floor, then you just can't have equilibrium. There's no, we change the curve; we draw it differently so it's now a flat line with an elbow where it becomes diagonal. No, you just say, sorry, there will be no equilibrium in this market. There's going to be a surplus of widgets; lots of them are going to pile up in warehouses and not get sold.

So, you'd think that when you get into ZLB with the IS-LM model, you get disequilibrium.

But what exactly does that cause? What exactly is now in surplus and piling up? Labor of the unemployed?

And what level does the model tell us that GDP will adjust to? In a typical supply and demand model, if you have a price floor, the horizontal-axis-variable, supply, ends up where the supply curve is, where that curve intersects the price-floor. Not where the other curve, demand, intersects the price-floor.

Where does the horizontal-axis-variable, GDP, end up in IS-LM when there's a price-ceiling on the vertical-axis-variable, interest?

Thank you very much.

Richard: It's sort of on-topic!

You really have two questions there.

1. If there are large storage costs of holding currency (but no storage costs of holding bonds) then the LM curve would continue down into negative nominal interest territory. (and we actually have observed this recently, in some countries, a little.) But if there are no storage costs, the LM cannot go negative; it can only go flat at 0%.

2. Assume perfect competition, for simplicity. Draw a vertical LRAS curve and downward-sloping AD curve in {P,Y} space. A fall in P causes the LM curve to shift right. The ISLM intersection tells us what point we are at on the AD curve. Draw a horizontal line at that point to illustrate the idea that P is stuck. (Macroeconomists call that horizontal line an "SRAS" curve, but that's a misnomer.) If that point on the AD curve is to the left of the LRAS curve, we have excess supply of goods and labour, and actual Y=Yd, because Y=min{Yd,Ys} just like in micro. If that point is to the right of the LRAS curve, then actual Y=Ys, and the economy is not at the ISLM intersection. (It's different if we assume monopolistic competition, because we can then go to the right of the LRAS curve.)

3. If the LM curve is horizontal, that makes the AD curve vertical.

Does that help?

I'm trying to think how to modify my tiny model here to get a ZLB.

This comment is a look at the basics of the model. I wonder if the author and commentators agree with my perception of what the basic limits are?

We have two decision makers (owners) who can trade goods for money (money is good B) but can not directly trade goods A and C.

The two owners are initially allowed endowments of 100 B and 200 A or 200 C. Thus, the initial wealth of the owners is 200 A plus 100 B or 200 C plus 100 B.

We have an underlying preference (utility) that becomes a goal. The goal is for each owner to have equal amounts of each of three goods (A, B, and C). A mathematical description of the goal is U=log(A)+log(B)+log(C).

Now let the model run to completion. Can the two decision makers devise a method of trading good B for A and C that will accomplish the goal of equal distribution of all three goods?

The owners have an initial condition of equal stock of money (100 B). It is automatic that any initial trade of money for goods A or C will unbalance that basic equality. It is also automatic that any trade of B for A or C will improve the distributional equality of goods A or C.

This limitation of initial automatic imbalance forces a decision by the two owners: Does the improvement in balance between A and C warrant the assumption of increased imbalance in good B? (The initial trade results in one party having too much B and the other party in having a deficiency of B.)

If the two decision makers can surmount this initial imbalance hurdle (and subsequent similar hurdles), it is possible to achieve equal distribution of all three goods. It will require more than a single trade between owners.

The ratio of B to be exchanged for A or C is not important UNLESS the ratio would change during the trading process. If the ratio changed after the first trade, final equality of goods distribution could be much more difficult (or even impossible).

As in my comment on the previous note, the case where Pa = Pc = 2 and each person starts with 200 A's plus 100 B's or with 200 C's plus 100 B's acts like the case Pa = Pc = 1 and each person starts with 200 A's plus 50 B's or with 200 C's plus 50 B's.

Min: correct.

Roger: almost correct.

1. It's better to think of there being 2 thousand people, rather than 2 people. Because I want to think about an economy where each individual is small, relative to the whole economy.

2. "The ratio of B to be exchanged for A or C is not important UNLESS the ratio would change during the trading process."

That bit is wrong. For example, in the case where Pa=Pc > 1, the A-type's demand for C (and the amount of C he buys) will be determined by the equation Ca = 100/Pc

Min in another post said: "Or, as the case with 150 B's indicates, there is not enough money."

Min, if the assumption "They all have preferences U=log(A)+log(B)+log(C)" is discarded, can there be a scenario where the situation is not about a shortage of B (MOE), but about a surplus of A and/or C?

Let's say barter is allowed, but trade in A/C does not occur. Would that be a good test of whether there is a shortage of B (MOE)?

Too Much Fed: "Min, if the assumption "They all have preferences U=log(A)+log(B)+log(C)" is discarded, can there be a scenario where the situation is not about a shortage of B (MOE), but about a surplus of A and/or C?"

First, the equivalence relies upon the equation. Drop that assumption and I don't know what happens.

Second, historically, recessions seemed to be general gluts, with a surplus of everything, which did not make sense. John Stuart Mill in 1829 showed that you could consider recessions to be a shortage of money.

Min, I believe "recessions" can be "general gluts" (aggregate supply shocks) or shortages of "money" (aggregate demand shocks).

The details matter to decide which one.

Most economists just assume the most common definition of economics is true (unlimited wants/needs and limited resources) so "general gluts" are not possible. I think Nick has assumed away a general glut by how utility is described here.

Nick,

"2. "The ratio of B to be exchanged for A or C is not important UNLESS the ratio would change during the trading process."

That bit is wrong. For example, in the case where Pa=Pc > 1, the A-type's demand for C (and the amount of C he buys) will be determined by the equation Ca = 100/Pc"

Can we think about this further?

No doubt your correction is correct for any one trade. But:

I made the observation that any initial trade would be less than optimum for holders of B. After trading, one party to the trade would have too much B and the other not enough. The only way the initial trade could occur would be for both parties to decide that the improvement in A (or C) preference was more important than the decrease of B preference.

Once that hurdle was cleared, trade could continue multiple times to reach the final goal of equality.

While the ratio of A to B (or C to B) is important to one trade, I can not see why it makes a difference if multiple trades are allowed. The holders of excess B would try to trade with deficient holders of B no matter what the exact ratio to the other goods until the goal of U=log(A)+log(B)+log(C) was reached.

I think the model is now correct (even though technically log(0) is not defined) and well presented. I think the idea is important it seems to match very well how recessions feel. Nick didn't say but how widely this stuff is known / taught? Can we say more about New Keynesian models and DSGE models in light of this model?

Roger,

All trades are between individuals that are small enough (one out of thousand) to just care about their own utility. Thus the only hurdle is to find a swap that will improve utility for both.

So "improvement in A (or C) preference was more important than the decrease of B preference." as Max wrote this is not true for "Pa=Pc=0.5" but is true for "Pa=Pc=2" given this utility function (and is true for some 1 > x > 0.5).

And "Once that hurdle was cleared, trade could continue multiple times to reach the final goal of equality." is true only to a point where "Marginal Utility of A/Marginal utility of B" as Nick posted. So the stop condition will depend on price difference and shape of the utility function.

Min, this will probably not be right the first time. It is hurried. The point should stand.

I want a scenario where each entity wants 50 to 70 of each of the 3 goods. 70 is the max.

Now have the (thousand) A-type agents each have an endowment of 200 A's and 100 B's. The (thousand) C-type agents each have an endowment of 200 C's and 100 B's.

Next, the A-types have 150 A's, 100 B's, and 50 C's, and the C-types have 50 A's, 100 B's, and 150 C's with no barter. Looks like not enough B (MOE).

Now allow barter. A-types have 100 A's, 100 B's, and 100 C's, and the C-types have 100 A's, 100 B's, and 100 C's. Everybody has more than the 70 they want.

TMF: your comments aren't making sense. Stop commenting now, please.

Roger: A has a reaction function, where his choice Ca depends on his initial endowment 100, on Pc, and on C's choice of how much A to buy.

And C has a reaction function, where his choice Ac depends on his initial endowment 100, on Pa, and on A's choice of how much C to buy.

Solve the two reaction functions simultaneously.

If Pa=Pc=P > 1, then at the point where Ca=100/P and Ac=100/P, neither has an incentive to change, so that point is the solution (Nash equilibrium).

Jussi: " Nick didn't say but how widely this stuff is known / taught?"

Good question. Explicitly taught? Not very widely at all. But most good macroeconomists understand it intuitively, I think.

"Can we say more about New Keynesian models and DSGE models in light of this model?"

Yes. They don't make sense, except as (implicitly) models of monetary exchange economies.

Nick,

Ok, I just don't have a good explanation or understanding of the IS-LM model. So, first off, what textbooks explain the IS-LM model really well – and *precisely*. I will buy them, and over time read them.

Online, nothing very good I've found, lots of vaugey-vauge, fuzzy. What the hell exactly is supplied and demanded in the LM market? Currency? How can that ever *not* be in equilibrium?! The government just decides however much it wants to supply, not limited by interest rates. And consumers will take as much as they can get no matter what the interest rates or price level.

Is it how much currency is kept in storage? It depends on the interest rates available, but as prices go up, just the velocity of money goes up, there's no equilibrium to speak of. There's always some velocity of money, it just gets higher or lower.

Is IS-LM the supply of, and demand for, money in very liquid vehicles like checking accounts? How can that ever get out of equilibrium?

Next, what the hell exactly is supplied and demanded in the IS market? Investment and savings, the amount people want to save to put into investments, and the amount business actors want to borrow to put into productive investment projects at the current interest rate. So, if a person saves money and puts it into currency under his mattress that's not "savings" as defined here. If they put it into a stock then it is, I'm assuming. What if they buy a corporate bond with it, is that part of the "money", IS market, or the "savings" LM market? What if the put it into a checking account at a bank, is that "money" and part of supply in the LM market, or "savings" and part of the supply in the IS market, as it will be loaned out to some home builder in a housing investment project?

The whole thing is just horribly unclear, imprecise, and fuzzy, and no one nails it down concretely that I've seen, and I have several intermediate macro books, and have spent a lot of time googling.

Can you recommend any book, or other source, anywhere that really explains this well in a non-fuzzy, precise way?

Thanks a lot,

Richard

Richard:

Start here with the Keynesian Cross: http://worthwhile.typepad.com/worthwhile_canadian_initi/2015/02/keynesian-cross-as-simultaneous-moves-symmetric-nash-equilibrium.html

Then the IS curve: http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/05/the-is-curve.html

See if you get anywhere with that.

Min seems to understand what I am saying.

Why can't I talk to Min about this?

TMF: "I want a scenario where each entity wants 50 to 70 of each of the 3 goods. 70 is the max."

Here is your scenario:

Each agent wants 70 of each of the 3 goods, max, which is enough to make him blissfully happy. So A-types throw away 130 A's and 30 B's, and C-types throw away 130 C's and 30 B's. The A-types pick up 70 C's off the ground, and the C-types pick up 70 A's off the ground. Everyone consumes 70 of each good, and is blissfully happy.

See? It's a stupid question. Recessions don't look like that. Market economies don't look like that. The Garden of Eden looks like that.

Now stop wasting my time, and stop cluttering up my comments and wasting my readers' time. You have been reducing the quality of my threads for far too many years, ignoring my polite requests to stop.

If you want to talk to Min, and if Min wants to talk to you, you can. Somewhere else.

Dear other readers: don't worry. None of the rest of you come anywhere close. And some stupid questions are allowed, if you actually pay attention to the answers.

So DSGE might be microfounded but not monetaryfounded! Maybe we one day have Rowe critique taught in econ101!

I hope this is also sort of on-topic:

Summers, just as an example, writes:

“The essence of secular stagnation is a chronic excess of saving over investment. (http://larrysummers.com/2015/04/01/on-secular-stagnation-a-response-to-bernanke/)

Does this mean we also have too much investments as I == S or how should this be deciphered? It might mean, as often said also on secular stagnation, that productivity is down by too few innovation and thus IS is steepened (less Y given r) but why then say it is about savings?

Is the (key?) take away here that excess savings doesn't need to be an explanation for falling interest rates?

In my 'June 09, 2015 at 10:11 AM' comment, I used the phrase "We have an underlying preference (utility) that becomes a goal. The goal is for each owner to have equal amounts of each of three goods (A, B, and C). A mathematical description of the goal is U=log(A)+log(B)+log(C).".

Based on several comments (but without direct challenge), that phrase must be incorrect. If incorrect, what is the purpose of the preference formula "U=log(A)+log(B)+log(C)" as it is used in the model under discussion?

Jussi: I have done a few posts criticising NK macro for not making monetary exchange explicit.

Roger: Micro 200 says: solve this problem:

Max U=log(A)+log(B)+log(C) subject to the constraint Pa(A-200)+(B-100)+Pc.C <= 0

That's for person A, and there will be additional constraints, if he is unable to buy or sell as much A or C as he wants. Person C's problem is similar, except the budget constraint is Pa(A)+(B-100)+Pc(C-200) <= 0

That gives you the individual's demand functions.

The goal is to get as much utility as you can. You will only try to get equal quantities of the 3 goods if you face a budget constraint, and if Pa=Pc=1, and if you can buy and sell as much of each as you want.

Roger: the First Order Conditions are MU(A)/Pa=MU(B)/Pb=MU(C)/Pc etc., where MU(A) means Marginal Utility of good A, which means dU/dA, which equals 1/A with a log utility function.

The purpose of me assuming U=log(A)+log(B)+log(C) was to create a model with simple well-defined demand functions.

This is very basic micro. And I wrote this post for microeconomists. You ought to learn this stuff. Microeconomists are good people, and they have figured stuff out over the years. The only part of this post that is not very basic micro is my assumption of monetary exchange.

Nick,

Once I grasped the importance of the utility function to the model I finally think i understood it and liked it.

I have a slightly off-topic question.

In this model the goods all arrive via endowment. Tweek it so that an additional stage is that agents have to decide how much A,B and C to produce. Assume that what they produce is correlated to expectations of what they will be able to sell. If a recession in the model is measured by trade in A for B, and C for B, then could you get a recession in this modified version of the model even if prices were all in equilibrium if the agents are pessimistic about the future so produce and trade less ?

MF: Totally on-topic.

Yes, you could tweak the model like that, fairly easily.

Make the utility function U = log(A)+log(B)+log(C)+log(L) where L is leisure.

Give A a production function A=24-L, and C a production function C=24-L, where 24 is total hours in the day. (Or rig it so that 24 gets replaced by some other number to give me the same equilibrium as above.)

Then you have a first stage, where they choose how much to produce, given their expectations of prices, and how much the other will produce. Then a second stage just like mine above.

And you are right that (irrational) pessimism could result in lower production, even if prices are right, and expected to be right. But in the second stage of the game we would see an excess *demand* for A and C.

***And recessions don't look like that.***

Roger: you could say that the *social planner's* goal is to give each individual equal quantities of the 3 goods. But that's not the *individual's* (selfish) goal. The game (except at competitive equilibrium) is a Prisoner's Dilemma, where each acting in his own self-interest makes both worse off.

I'm flattered that you liked my model enough to do this and I agree with pretty much everything you've said here (but then, you didn't include the usual comment about recessions being an excess demand for the medium of exchange.)

Nick E: yours is a good model. Now we just need Kevin Donoghue to draw a 3D picture to illustrate it, in particular the bit about only being able to move in the AB plane and BC plane, but not in the AC plane. You have to move along two sides of the triangle and can't move directly long the hypotenuse.

"(but then, you didn't include the usual comment about recessions being an excess demand for the medium of exchange.)"

It didn't need saying. It's obviously true in this model!

Nick

Thanks for the extra information on the utility function. It helped. I will follow up with more study.

"(but then, you didn't include the usual comment about recessions being an excess demand for the medium of exchange.)"

It didn't need saying. It's obviously true in this model!

I'd be interested to see Nick E's reply to that last statement / or why it isn't implied in his own model.

Oliver,

It is true in my model, but my model (and Nick R's) is very simple and I don't think you can extrapolate every consequence to the real world. I'd agree there is a sense in which you can say that any recession is an excess demand for money and I can see how that fits with Nick R's world view, but to me that sense is somewhat trivial. In particular, whilst I think that more money can reduce a recession, I think it is critical how that extra money gets into the system. There's not enough going on in my model to show that. It's also the case in my model that flexible prices will solve the problem, and that's another result I'm dubious about extrapolating to the real world.

But, there's so much that Nick R and I agree on here about the relevance of monetary exchange, that maybe I shouldn't nit-pick.

Nick E: what is your view on Jussi's question: " Nick didn't say but how widely this stuff is known / taught?" ?

I found that a tricky one to answer. I said I though most good macroeconomists understood it intuitively, but now I'm not sure.

An excellent question. I was on the verge of offering an answer along with my earlier comment and then didn't for some reason.

I see this distinction between a monetary exchange economy and a barter economy as being an essential part of Keynes's break with the classics (although by no means the only essential part). I may be wrong on this - I'm rubbish on the history of economic thought - but it's how I understand what Keynesian economics means anyway. But I find it very frustrating that whilst many old Keynesians and post-Keynesians want to emphasise the importance of monetary exchange, they don't really seem to come up anything I find very convincing. And amongst most mainstream economists, I don't think the issue even occurs to them. I found the discussion with Stephen Williamson rather odd, frankly.

So I don't think this stuff is well known, really. As to whether it's taught, I'm afraid I haven't been near what's taught for years, I'm afraid, but I don't recall being taught it.

Nick E: good answer. I agree with a lot of it. I too see it as absolutely essential to Keynes' economics, and any sort of Keynesian economics. They just don't make any sense otherwise. Though I think that's true of many "classical" monetary theorists too. But you don't find any sort of clear statement, until maybe Clower and his followers, but that whole "disequilibrium" school sort of disappeared.

I had really hoped that Steve Williamson would get it, because the whole idea behind new monetarism is supposed to be understanding monetary exchange. But I got precisely nowhere when I tried to argue that Woodford only makes sense as a model of (implicit) monetary exchange.

Nick & Nick

Thanks for your answers!

re: I think it is critical how that extra money gets into the system

This has always struck me as important, too. And I suspect this is where your respective opinions differ most. I for one would also be interested if either of you found the time to flesh out this gap.

And if I may add my own 2 cts.:
While adding in the markets of AB and BC certainly seems a step forward from ignoring them completely, either by assuming barter or by becoming obsessed with B in isolation (money cranks), I'm not at all sure whether treating these markets analogously to AC trades (barter) cuts it either. It seems to me that B, at least under certain circumstances, is an altogether different creature from A and C. So, tying in with Nick E's quote from above, one needs to isolate these circumstances, that is those under which the creation of new money and new goods coincide or influence each other. Starting out by assuming that both are just there and that external forces exist which can change them at will seems to me to be missing the (or at least an important) point.

So we cannot ignore money, we cannot treat it in isolation, nor can we just compare the two. To me an integrated approach is called for which acknowledges the essence of each but also captures their respective paths from cradle to grave and puts them into relation.

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