Strategy space and the theory of monetary policy One

In ECON 1000 we teach that a monopolist picks a point on his demand curve that maximises his profits.  We can think of the monopolist as setting a price to hit that point, or we can think of the monopolist as setting a quantity to hit that point; and we teach that it doesn't make any difference which way we think of it. Economists normally think of the monopolist as setting a quantity, simply because it's easier for us economists to think that way, but if we set the problem up in math, and maximise with respect to price, or maximise with respect to quantity, we end up with the same answer either way.

Here's an example where it does matter whether the monopolist picks a price or picks a quantity:

Suppose the monopolist is selling a new communications gizmo. Some people are rich, or really like new communications gizmos, and are willing to pay a lot to buy one. Other people are poor, or don't care much for new communications gizmos, and aren't willing to pay very much to buy one. And there's a whole distribution of people between those two extremes.

But communications gizmos are different from other goods: the more people who own one, and the more people you can communicate with if you buy one, the more you would be willing to pay to buy one. There's a network externality. That's what creates the weird-looking demand curve I've drawn above.

The height of the demand curve at any given quantity shows the willingness to pay of the marginal buyer. That's standard. What's non-standard about the demand curve I've drawn is that the willingness to pay of every buyer depends positively on the number of other people who own a gizmo.

Start where nobody owns a gizmo, where Q=0. The very richest person, or the one who wants a gizmo more than anyone, and who has the highest willingness to pay, still wouldn't be willing to pay very much. Because there would be nobody he could talk to on his new gizmo. So the height of the demand curve for the first gizmo is very low. It might even be zero.

As the quantity increases, and the number of people you can talk to increases, the willingness to pay of the marginal buyer will increase. Sure, you are going down the list of potential customers, from the richest towards the poorest, and from the keenest towards the least keen, both of which would reduce the willingness to pay of the next buyer in line. But at the same time the number of people you can talk to increases, which raises the willingness to pay of everybody.

So as quantity increases, the height of the demand curve first increases, then eventually falls, as the market gets saturated. It's probably going to look roughly the way I've drawn it.

Suppose the monopolist sets a price of $100. There are three equilibria: Q=0, where nobody buys a gizmo so nobody is willing to pay $100 because there's nobody to talk to; Q=150, where lots of people buy a gizmo because there are lots of people to talk to; and Q=50, where only the richest and keenest buy a gizmo because there aren't many people to talk to.

Suppose instead the monopolist sets a quantity of 150. There is only one equilibrium: P=$100.

In this example, it does matter whether we think of the monopolist as setting a quantity or setting a price. We might get the same answer either way; but there again, we might not.

When I say it does matter whether we think of the monopolist as setting a price or setting a quantity, who's the "we" that does the thinking? It's not just the economist. It's the customers buying gizmos. If they think that the monopolist is setting a price of $100, they don't know whether to buy one or not. Each potential customer watches to see how many other people will buy a gizmo before deciding whether to buy one himself. But if they think the monopolist is setting a quantity of 150, exactly 150 customers will be willing to pay a price of $100 or more, just like in the normal case.

In this example, the monopolist will want his potential customers to think of him as setting a quantity, not a price. That way he can sell 150 gizmos at a price of $100 each. Even if he knows the exact shape and position of the demand curve, he can't be sure how many he will sell if he sets a price of $100. It could be 150, it could be 50, or it could be 0.

In 1970 William Poole wrote a classic paper on the theory of monetary policy under uncertainty (pdf). He set up an ISLM model, with unforecastable shocks to the IS curve and to money demand, and asked whether it would be better for macroeconomic stabilisation if the central bank set an interest rate or a quantity of money. His answer was that the optimal monetary policy instrument depends on the size of the shocks, and on the elasticities underlying the IS and LM curves.

In Poole's model, if there are no shocks, so the central bank knows the position of the IS and LM curves, it doesn't matter which instrument the central bank chooses. We can think of the central bank setting an interest rate, or setting the money supply (or base money), and we get exactly the same answer either way. We could even think of the central bank as setting NGDP, and we get exactly the same result that way too. It's exactly like the theory of monopoly we teach in ECON1000, where it doesn't matter whether the monopolist sets a price or sets a quantity.

That's because in Poole's ISLM model, and in the ECON 1000 monopoly model, there is a unique equilibrium whichever instrument the central bank/monoplist sets. If you know Q you know P, and if you know P you know Q. But, as I have shown above, it does matter whether the monopolist sets P or Q if you know P given Q but don't know Q given P.

Suppose we had an ISLM model in which equilibrium is not unique for some instruments. Suppose, for example, the IS curve wasn't always and everywhere downward-sloping. Suppose the IS curve looked something like the demand curve I have drawn above.

Why might an IS curve look like that?

The answer should be obvious. In my microeconomic example, each person's willingess to buy a gizmo depends positively on how many other people he expects to buy a gizmo. Hmmm. Maybe in macroeconomics each person's willingness to buy all goods and services depends positively on how many goods and services he expects other people to buy? Hmmm, that idea does sound familiar. Of course that idea sounds familiar! It's the Old Keynesian multiplier!

If the Old Keynesian multiplier effect is strong enough, the IS curve will slope up; just as if the network externality effect is strong enough, the demand curve for gizmos will slope up.

And there is nothing in theory to prevent the Old Keynesian multiplier effect being strong enough to make the IS curve slope up. All you need is for the marginal propensity to consume plus the marginal propensity to invest to exceed one. There is nothing to say that cannot happen.

The same price of gizmos may be too high if nobody expects anybody else to buy one, and too low if everybody expects everybody else to buy one.

The same rate of interest may be too high if nobody expects anybody else to spend, and too low if everybody expects everybody else to spend.

It does matter what we think of central banks as setting. But again, we need to ask: who's "we"? And the answer is: people, not economists, or central banks. But where do people get their ideas from, when it comes to how to think about monetary policy? From economists, and central banks.

Should we economists think about central banks setting a nominal rate of interest or a target for NGDP? Should central banks think of themselves as setting a nominal rate of interest or a target for NGDP? How should we best communicate to the public what it is that central banks do? It matters.

It's just like when the monopolist sets a price of gizmos, and each person can't decide whether to buy one or not, and waits to see whether other people are buying before buying one himself. When the central bank sets a nominal rate of interest, each person can't decide whether to buy or not, and waits to see whether other people are buying before buying himself.

[Addendum: Off-topic ECON 1000 test: Draw the Marginal Revenue curve associated with that demand curve.]

Comments

[Greg Ransom]

in the real world you can't know _any_ of these elements, they aren't known by anyone and they aren't ever "given" to anyone, as they are to the economist at the Black Board stipulating these things as "things which exist & things stipulated as known things".

This is the fallacy of mistaking a theorist's stipulated "data" invented for the sake of teaching economics as "given" and knowable "data" for people adjusting their judgments and activities in the real world.

Call in Coase's Fallacy after Ronald Coase, who belittles the economist who falsely assumes his Black Board "givens" limns

None of this "knowledge" is given to anyone, none of even exists anywhere, and to pretend that it does or can exist as a known and given "data" in someone's head is the Coase Fallacy.

[Greg Ransom]

The set up of "the problem of the monopolist" presumes the knowledge and existence of things which exist nowhere but on the economist's Black Board.

Call this Coase's Fallacy after Ronald Coase, who belittles the economist who falsely assumes his Black Board "givens" limns what actual is knowable and what actually exists somewhere besides on his Black Board.

[Greg Ransom]

"In ECON 1000 we teach that a monopolist picks a point on his demand curve that maximises his profits."

There is no economist in the world who possesses this "demand curve" as something given to him the way economists fool themselves and their students into believing this "demand curve" exists for the monopolist to pick and choose points up.

The significance of this fact for macroeconomic science is suggested by Hayek all of his work on price signals & the use of formal economic models, a point first made by Hayek when discussing the difference between formal analysis & the significance of relative price signals such as interest rates for the coordination of real people adjusting their judgments in the real world of real changing relative price signals, in his 1929/1933 _Monetary Theory and the Trade Cycle_, the origin of Hayek's landmark papers on the signaling role of relative price changes, insights which have yet to be fully grasped by the economics profession, despite how they have transformed everything. The insight has more work to do before it is done remaking everything.

[Nick Rowe]

Greg: slightly more on-topic than Dan Kervick. My point is that *even if* the position of the monopolist's demand curve were known, there would be an irreducible uncertainty from the difficulty of coordinating under the P-strategy space.

[Nick Rowe]

Dan: I have unpublished your comments, and my responses to them.

If you wish to write a new comment, saying there is something you do not understand in my argument, or that my conclusions don't seem to follow, then go ahead, but keep it short and on-topic.

[Jacques René Giguère]

I'll stay on the micro side of it...
Network effects exist but exclusivity is also valuable.Yogi Berra once said about a restaurant "Nobody goes there anymore. It's too crowded."
Remember the first bulky cellphones? Part of their appeal was how few people had one. I remember my time in politics when the use of the devices was restricted and Important People had a cellphone assistant. Prestige crashed when truck drivers replaced their CB's with cells. Rich and/or powerful people (not necessarily the same) enjoy eating in exclusive restaurants but they don't want to be totally alone. I don't have the time to properly draw a new curve but it could be far weirder than the one you propose ( and it's a real nice one!)

IIRC, in my grad student days(late 70's-early 80's) we used Hal Varian Microeconomic Analysis 1st ed. and it had a whole chapter on weirdozoid suppy-and-demand systems.(I am on vacation and so can't browse my library.)

[Dan Kervick]

No thank you Nick. I thought my views on what I thought was wrong with your argument were expressed quite well in my proposed central bank communication in my original comment. I'll post them elsewhere.

[Nick Rowe]

Jacques: In those examples, I think those "negative network effects" would make the demand curve steeper than it otherwise would be. Might even make it backward bending?? On second thoughts, I don't think it could. Hang on, it might, depending on *who* bought the gizmo. At a high enough price, only the rich would buy one, but all the rich would want to buy one. At a low price, those who bought would be rich and poor, so nobody would want to by one, because it's not exclusive any more.

In which case, setting a quantity could give (say) 3 equilibrium prices, but setting a price would give a unique quantity. The exact opposite of my case.

[Greg Ransom]

Yes. Morgenstern's point. Hayek used the point as an "even if" argument -- "even if we falsely assume the God's eye view perspective of the Black Board economist exist or is knowable, there is still the source of 'uncerainty' which forces you into my perspective, ie out of the false world and back into the actualprice signal/individual changing judgments world."

See Hayek's footnote to Morgenstein's Holmes-Moriarty paper in one of Hayek's famous price signal papers.

"Greg: slightly more on-topic than Dan Kervick. My point is that *even if* the position of the monopolist's demand curve were known, there would be an irreducible uncertainty from the difficulty of coordinating under the P-strategy space."

[Gref Ransom]

This expectations, uncertainty, price signals stuff (usually in the macro context) was at the core of paradigm articulation and the development of alternative explanatory strategies in economics in the 1930s.

It's where the famous Hayek 1937 and 1945 papers were from. Hayek has an earlier 1933 paper in the same series adressing the Swedish macroeconomists on expectations which is part of the same fleshing out and division which took place across the 1930s.

You've moved the game with your example to back where it was before Samuelson etc turned Hicks/'Keynes into "the world as it exists and is given to us just like we stipulate it to freshmen on a Black Board."

[Greg Ransom]

Just to be give basic background about Morgenstern, the issue is the consistency / coherence of 'perfect expectations' between actors, and how this on Morgenstern's account can become a hall of mirrors that produces uncertainty.

The issue was how to think about modeling equilibrium across time -- which grew out of macroeconomics in the 20s and 30s.

[Kevin Donoghue]

"And there is nothing in theory to prevent the Old Keynesian multiplier effect being strong enough to make the IS curve slope up."

That's not enough to give you multiple equilibria, is it? In textbook theory I've only ever seen a unique equilibrium, which is unstable if slope_IS>slope_LM.

[rsj]

The middle equilibrium is not stable. And the first equilibrium point is going to be very hard to hit, if the firm's expectations of demand are fuzzy.

[Nick Rowe]

Kevin: Imagine an IS curve that looks *roughly* like the demand curve in my diagram.

(It won't look exactly the same because if Y falls below some point gross investment will presumably drop to zero, so we can ignore the marginal propensity to invest, so the IS curve will probably be downward-sloping again at very low levels of Y.)

Now take the LM curve straight off Poole. With the central bank setting an interest rate, the LM is horizontal, so if mpc+mpi exceeds one over some range, the IS curve will slope up over that range, and there will be multiple equilibria within that range. But yes, outside that range there won't be multiple equilibria. And if the LM slopes up (Poole's M-target) there may not be multiple equilibria. And if the LM is vertical (NGDP target) there won't be multiple equilibria (Though I am fudging there on the distinction between NGDP and RGDP).

rsj: "The middle equilibrium is not stable."

That sounds right to me. And it's usually the case that where there are multiple equilibria you get an unstable equilibrium between two stable equilibrium. But I am a little wary of speaking of stability in what is essentially a one-period model with no adjustment process specified. I think my toy models work at some heuristic level, but I wouldn't want to push them beyond what they can manage. For example, are gizmos durable goods? Do customers line up to buy them, so they can see who else is buying? Etc. Such questions might (or might not) matter for which equilibrium we get to. Under some circumstances, we might not even get to any equilibrium. Suppose half the customers expect the Q=0 equilibrium, and the other half expect the Q=150 equilibrium (neither expectation is irrational). Then we would go to Q=75, which isn't an equilibrium. Which (I think) is related to Greg's point.

"And the first equilibrium point is going to be very hard to hit, if the firm's expectations of demand are fuzzy."

By "first equilibrium" I take it you mean Q=150? Which (let us assume) is the profit-maximising point.

Yes. This is exactly related to Poole's point. Ignore the upward-sloping bit of my demand curve. Poole's point (translated into micro) is that if the monopolist can't forecast the demand curve exactly, then he won't know either the profit-maximising price and output exactly. But, depending on the precise nature of the uncertainty about demand, and the elasticity of his cost curve, either setting a P or setting a Q could get him closer to that profit maximising point. It depends.

For example, if the MC curve is flat, and the elasticity of demand is known, but the location of the demand curve isn't. Then the monopolist should set P. Make the opposite assumptions, and the monopolist should set Q.

[BSF]

It's easy to set up dynamic versions of the ISLM model - the IS and LM curves then become stationary loci, your assumptions about what's in the various behavioural equation, what their magnitudes are and how the adjustment process works (which have to be set out explicitly when you're working with a mathematical expression of the model)determine existence and dynamic stability of the equilibrium, and the IS-LM diagram becomes a phase diagram with phase arrows summarizing the dynamics of the system. Then, for example, it's easy to show that if you have linear IS and LM curves with an IS curve which is upward sloping and steeper than the LM curve, the equilibrium is a saddlepoint. That way of setting the model up also makes it easy to show how the location of the equilibrium changes in response to policy changes (it's best to think of the IS curve as shifting up or down, not left or right) under various assumptions about the parameters and the dynamics of the adjustment to disequilibrium in the two markets.

[Nick Rowe]

BSF: "It's easy to set up dynamic versions of the ISLM model..."

Not for math-klutzes like me it isn't!

But yes, mathematically competent New Keynesian macroeconomists do (their own New Keynesian version) of that sort of thing all the time. But what worries me about those NK versions, AFAIK, is that they duck a lot of these interesting questions by imposing a unique RE path.

"...(it's best to think of the IS curve as shifting up or down, not left or right)..."

Yes! That is something that I stumbled upon too, when I was writing about the fiscal policy multiplier in New Keynesian models. But notice something that brings us back to the main topic of this post: it matters which way we think about the IS shifting, and thus it matters how we think about fiscal policy too. Does "expansionary" fiscal policy mean shifting the IS up, or right?

[Zorblog]

Very interesting!
The communication gizmo is a convincing example of hill-shaped demand curve. Other products may see the demand of a given consumer affected by that of other consumers (luxury brands, blockbuster movies, etc.). Overall, they might even account for a significant share of the consumer's budget.

The IS-LM analogy may not be so important. The point is that the investment, saving and consumption decisions of any given individual are indeed affected by those of all other individuals. Whatever model you're using, you should then expect to have multiple, and possibly unstable, equilibrium.
It looks like this has indeed huge implications for monetary and fiscal policies...

[Nick Rowe]

Zorblog: "The IS-LM analogy may not be so important."

Yep. This point should generalise beyond ISLM. I chose ISLM because: Poole used it; I'm familiar with it; lots of people are familiar with it; it's simple.

Many economists build models with multiple equilibria. But I'm trying to make an additional point: that whether or not there are multiple equilibria may depend on something so....unconcrete....as the strategy space, which is all about how people think about what other people are doing.

[marris]

Wow, that demand curve is very weird. The quantity dropping as price falls is Veblen, right? But at some low price, the network benefits overcome the status loss?

[Gregor Bush]

Brilliant post Nick.

So to take your monopolist mode to IS-LM would you have nominal GDP on the x axis and the nominal policy rate on the y axis? Are there IS-LM models that use nominal instead of real variables?

[Joseph]

As a resident of the periphery of the "concrete steppes", I would speculate that the private monopolist can't simply "choose" the higher quantity equilibrium, but has to take some actions to get to that level, which I think you do see. Often certain technology manufacturers will subsidize their items through sales and promotions through certain retailers to gin up buzz over the products so they can point to the massive momentum their product has and have evidence to back up "predictions" of large sales which helps shapes exceptions onto the higher quantity equilibrium.

I think the same lesson applies to central banking. If you're on the stable equilibrium, markets will tell you what you need to do to meet their expectations. It should be obvious how much money needs to printed and how many bonds need to be brought to support a stable growth trajectory. Doesn't mean that the central bank doesn't have a job a do, it still needs to do what the markets are telling it to do, just like the monopolist still needs to produce enough product. When expectations get off track though then the central bank needs to reform expectations, like the monopolist does when he first releases his product.

This is my one quibble with the expectations view exposed by those like you and Sumner. Central banks need to tell their economies and markets what they want before they can give their markets what they want.

[Nick Rowe]

marris: the shape may look like Veblen, but I think the reasoning behind it is different from Veblen. (It's a long time ago I read Veblen, and I may have forgotten, but I don't remember him talking about network effects.)

"But at some low price, the network benefits overcome the status loss?"

It's not status loss (in this case). The demand curve doesn't *necessarily* have to look the way I've drawn it (if there is a network externality), but it *probably* does. At a Q near 0. the willingness to pay must be very low, since there's nobody else to talk to. At Q near total population saturation, the WTP must also be very low, if there are some people out there (recluses) who don't value a gizmo at all, or if nobody wants two gizmos. So if there's a point somewhere between those two extremes where the WTP is a lot higher, that means the demand curve must look roughly like the way I've drawn it. So it's plausible.

[Nick Rowe]

Gregor: Thanks! (I confess I was rather pleased with it myself ;-))

"So to take your monopolist mode to IS-LM would you have nominal GDP on the x axis and the nominal policy rate on the y axis? Are there IS-LM models that use nominal instead of real variables?"

I fudged a lot there.

The ISLM ought to have RGDP on the x axis, not nominal (for reasons it would take me a little time to explain); and it should have both real and nominal interest rates on the y axis, with a wedge equal to expected inflation between the IS and LM curves.

I would have needed to introduce a Phillips Curve, and expectations, to have done this properly. I cheated. But actually, if I had done that, I could have introduced additional tendencies for multiple equilibria. For example, assume Real GDP is constant. The same nominal interest rate is both too high, and deflationary, if expected inflation is low; as well as being too low, and inflationary, if expected inflation is high.

In my opinion, the Keynesian multiplier effect is the most important force here, in the short run. Scott Sumner simply adds the two effects together (though he might not think of it precisely this way) to say that the same nominal interest rate is both too high if expected NGDP growth (=real GDP growth + inflation) is low; and too low if expected NGDP growth is high.

Oh God, but nominal interest rates are such a bad way to think about what central banks set!

[Nick Rowe]

Joseph: "As a resident of the periphery of the "concrete steppes", I would speculate that the private monopolist can't simply "choose" the higher quantity equilibrium, but has to take some actions to get to that level, which I think you do see."

I partly agree with you. You can think of this as a sort of concrete pre-commitment strategy, sort of like Ulysses tying himself to the mast. For example, simply produce 150 gizmos first, show everybody you have produced them, and then go ahead and start selling them at whatever the market will bear. Or some sort of advertising/promotions strategy, as you suggest.

But in the real world most people simply "use their words", and make promises, and others usually believe those promises, unless they have reason to disbelieve them. And once people believe what you say, and think of what you are doing the way you want them to think of it, all you have to do is not violate their expectations, and they will keep on thinking the same way.

In other words: it's a lot easier to keep an existing "institutional structure" (way of thinking about what people are doing) going than it is to create a new one from scratch. Revolutionaries know this, I think.

Here is you saying the same thing, and very nicely put: "I think the same lesson applies to central banking. If you're on the stable equilibrium, markets will tell you what you need to do to meet their expectations. It should be obvious how much money needs to printed and how many bonds need to be brought to support a stable growth trajectory. Doesn't mean that the central bank doesn't have a job a do, it still needs to do what the markets are telling it to do, just like the monopolist still needs to produce enough product. When expectations get off track though then the central bank needs to reform expectations, like the monopolist does when he first releases his product."

[Gregor Bush]

Thanks Nick,

"Scott Sumner simply adds the two effects together (though he might not think of it precisely this way) to say that the same nominal interest rate is both too high if expected NGDP growth (=real GDP growth + inflation) is low; and too low if expected NGDP growth is high. Oh God, but nominal interest rates are such a bad way to think about what central banks set!"

"the money rate of interest is, in reality, very often low when it seems to be high and high when it seems to be low" - Knut Wicksell

When I first started reading Sumner I thought of trying to create a variable to capture the current the stance of policy that was the SPF expected NGDP growth relative to the nominal Fed funds rate. So if the Fed funds rate was low relative to expected NGDP policy was easy. But then as I continued to read Sumner the more it became clear that, to him, expected NGDP (relative to trend) WAS the stance of monetary policy. If expected NGDP growth is weak, policy is tight, regardless of the level of rates. So the level of the policy rate is extraneous.

I don’t know if you take requests but, if you do, I would be interested in the follow-up post it which you flesh out the IS-LM model that you described in your response to my first question. It seems to me that most NK models would tend to see only minor differences between NGDP targeting inflation targeting using the policy rate as the instrument. Your idea that there is a portion of the IS curve that slopes upward and, because of this, that the choice of instrument and target variables matters a great deal, seems like it could be quite important.

[Scott Sumner]

Great post. When I read your best posts I realize how much I'm not able to do because of my inferior knowledge of models.

Nick and Gregor, I'm increasingly interested in figuring out how much we lose (if anything) by combining P and Y into one variable, and using some completely different variable for cyclical effects---say hours worked relative to the natural rate of hours worked. Real wages become W/NGDP, the value of money is the fraction of NGDP that can be purchased with each dollar (1/NGDP), etc. Do we lose anything of importance in that sort of model of business cycles?

[Nick Rowe]

Scott: thanks! But I wrote my second post, "published" just a few mintes ago, especially for you. It's much more up your street.

Good question. I'm going to have to think about it. I don't think we lose much qualitatively. In other words, since a lot of units are arbitrary anyway (e.g. log transformations don't really change anything of substance), we could probably find some way to rig the units so that combining P and Y would be legit.

[Greg Ransom]

Hayek's case against Keynes was that what economics loose when they do this sort of thing is the very the mechanism of change that causally coordinates or causally leads to discoordination (and non-economic goods without an economically viable function) in the economy.

"Do we lose anything of importance in that sort of model of business cycles?"

Yes, you lose the ability to even see / speak / notice the very stuff that makes up the business cycle. (Compare Kuhn on how scientific paradigms can prevent scientists from seeing phenomena staring them in the fact that is right in front of them, e.g. dust particles bounding off a charged balloon.)

Think about it. Or put the king size horse blinders back on and ignore the point.

Scott writes,

"I'm increasingly interested in figuring out how much we lose (if anything) by combining P and Y into one variable,"

[Dan Kervick]

At New Economic Perspectives, I have expanded upon my original comment on Nick's closing series of questions.

{edited to embed link to Dan's post here. NR]

[Nick Rowe]

Gregor: "When I first started reading Sumner I thought of trying to create a variable to capture the current the stance of policy that was the SPF expected NGDP growth relative to the nominal Fed funds rate."

I have read David Beckworth doing the same thing. I like it. I think it's a useful approximation.

"But then as I continued to read Sumner the more it became clear that, to him, expected NGDP (relative to trend) WAS the stance of monetary policy."

It might be that the "Beckworth gap" is an index of AD, and the "Sumner gap" is an index of AD relative to the Short-Run AS?? I don't know. My mind is not clear on this yet.

[Edeast]

Last time I tried to figure this out, I think the IS curve looked like a U. Just saying. It'll be another month before I can think about it.

[david stinson]

" The same price of gizmos may be too high if nobody expects anybody else to buy one, and too low if everybody expects everybody else to buy one."

Apologies if you have already addressed this but how this does relate to an externality argument for price stickiness?

[Nick Rowe]

Edeast: There are two ways to derive the IS curve:

1. Start with the Keynesian Cross model of Y, and change the rate of interest.

2. Start with the loanable funds model of the rate of interest, and change Y.

In this case, it's easiest to use the second method. Suppose Y drops. And suppose that causes (is associated with) a fall in expected future Y too. The standard model says the S curve shifts left if y falls. But it might not, especially if expected future Y falls too. Plus, the I curve will probably shift left too, and may shift left more than S, in which case r falls, so the IS curve slopes up. But when Y gets very small, gross I drops to zero, and can't drop further. And when Y gets very big, and hits capacity, people know that future Y can't rise any more.

So the IS curve probably looks like an S that has fallen over on it's right side.

david: "Apologies if you have already addressed this but how this does relate to an externality argument for price stickiness?"

I haven't addressed this. I don't know.

[david stinson]

Nick: "david: "Apologies if you have already addressed this but how this does relate to an externality argument for price stickiness?" I haven't addressed this. I don't know."

I asked because it has always struck me that the externality argument ran the other way - i.e., if you know where your new (reduced price) equilibrium is, presumably because one is aware of excess money demand, the recognition that others have not yet moved to their new equilibrium by reducing their prices would presumably make it even more urgent that you reduce your price, probably to a level below the "everyone moves together" equilibrium. In other words, I had assumed that the externality, if anything, would accelerate downward price changes.

[Nick Rowe]

david: Ah! OK, I follow you now.

The answer to your question is: it depends. If there's a shock that reduces the equilibrium price level by 10%, but everyone else holds his price constant, my optimal price may fall by either more or less than 10%. Roughly, there are two effects:

1. The unemployed resources and fall in real incomes due to everyone else not cutting prices mean I want my real price to be lower (relative to the new equilibrium).

2. But if all my competitors and suppliers have raised their real prices (relative to the new equilibrium), that makes me want to raise my relative price too.

Damn. That's not very clear.

Here's another attempt. It depends (inter alia) on the slope of the AD curve. And of the individual firm's demand curve. If AD is very steep, it would take a big cut in all prices to get to the new equilibrium. But if my individual firm's demand curve is fairly flat, I only need to cut my price a little below other firms' in order to sell all I want.

[david stinson]

Thanks Nick. I see the dynamic.

I don't want to belabour this (you're guessing that I probably will anyway) but there's something about it I don't find terribly convincing. I am not speaking of your explanation which I am sure is correct but rather the argument itself as a plausible basis for sticky prices. I am not sure precisely what bothers me about it. Perhaps, a few things:

a) not all prices are sticky, so even if there were a bunch that were sticky, you would be potentially raising your price relative to non-sticky-price stuff;

b) the likely presence of non-sunk costs that are invariant to demand and the risks they pose,

c) the notion that in the midst of a general glut, even an incipient one, producers would raise prices relative to their customers' incomes seems counter-intuitive, and

d) on the assumption that all agents know where the new equilibrium is, and given that the previous equilibrium relative prices represented an optimum or at least the result of an ongoing process of market coordination, why would there be an assumption of reluctance on the part of all agents to move immediately to the new equilibrium? Does that not require an assumption either of ignorance on the part of some agents or, at least, the assumption on the part of some agents that some of the other agents are uncertain or unaware of the new equilibrium?

BTW, although I always enjoy your posts when I have time to read them, you seem to have really been in the sweet spot of late.

[Nick Rowe]

david: Thanks!

"Does that not require an assumption either of ignorance on the part of some agents or, at least, the assumption on the part of some agents that some of the other agents are uncertain or unaware of the new equilibrium?"

I like that assumption.

Think how hard it would be for all of us to change our clocks in spring and fall if there weren't someone to tell us "everyone put your clocks forward exactly one hours.....now!"

Think how hard it would be for 8 oarsmen to increase the speed at which they row if there weren't a cox calling out the new time.

The orchestra without a conductor.

Those aren't perfect analogies, but give some idea of the coordination problems involved. We don't know where the new equilibrium is, and won't know till we get there (by which time it will have moved again). We don't know what others know, and what others know that we know. We don't know when the others will move. Everyone wants to wait and see what the others are doing before moving themselves.

[david stinson]

Me: Does that not require an assumption either of ignorance on the part of some agents or, at least, the assumption on the part of some agents that some of the other agents are uncertain or unaware of the new equilibrium?

Nick: I like that assumption.

It seems obvious that there is such a thing as monetary disequilibrium so I am presuming that there is such a thing as sticky prices. However, I am easily confused by the sticky price rationales. They seem a little woolly (not woolley).

If one is thinking inside of a rational expectations model, then everyone has the same expectations, uses the same model, has the same info, etc., and knows where the new equilibrium is, particularly if the shock is monetary. They just don't want to immediately adjust to the new equilibrium because it is costly or something. Given the RE world, I wouldn't have thought the argument that there is now the potential for discoordination was permitted. Discoordination suggests that valuable collective information was lost and has to be rediscovered through re-coordination. Plus, everyone was happy with the old equilibrium, knows that coordination is costly, if we do try the re-coordination thing (and we're lucky) we will just probably end up at the new equilibrium. But since we already know where it is, why not just avoid the cost and hassle and go there right away. If the driver of all this is the assumption set out above (in either form), I am not clear how that assumption can be squared with rational/consistent expectations.

The timing who-goes-first thing I find a bit weak because, in addition to the above, it suggests that firms believe they are better off waiting, even at the risk of too high a price. Casual empiricism would suggest that while firms obviously want to optimize their price, in the presence of uncertainty, they are likely to be more concerned about pricing too high than they are about pricing too low. In any case, if they decide that have made an error they can always correct it immediately, unless menu costs are present, in which it seems to be really about menu costs not the externality (?). Finally, if the response of agents under uncertainty to discoordination is a kind of paralysis, how did we ever get the original equilibrium?

[BSF]

Nick: Re whether we should think of expansionary fiscal policy as shifting the IS curve to the right or up, the important thing for teaching purposes at least is to get across the idea that it's an equilibrium locus, not a behavioral curve, and that one of its prime functions is to show how the goods market will behave when it's not in equilibrium. An increase in government spending disturbs the equilibrium. Assuming you have an investment function which is a negative function of the interest rate, one way to characterize the shift of the equilibrium locus is to say that it takes an increase in the interest rate to hold equilibrium income unchanged at the original value, by bringing investment demand down. Hence an upward shift of the equilibrium locus. This covers off shifts in positively sloped as well as negatively sloped IS curves. It runs against all our instincts, though, which say that with Y on the horizontal axis, an increase in demand increases income. When we think that way, we're implicitly merging the two distinct issues of the location and dynamic stability of the equilibrium.

[Nick Rowe]

BSF: "It runs against all our instincts, though, which say that with Y on the horizontal axis, an increase in demand increases income."

I see what you are saying, and sort of agree. But perhaps this does say that our instincts are wrong.

Think of it this way: the IS curve only makes sense in a monetary exchange economy. The goods market is a market where goods are bought and sold for the medium of exchange. The bond market is a market where bonds are bought and sold for the medium of exchange. The "money market" is an oxymoron. Bond-financed deficits affect the bond market, driving up the interest rate. Which makes people want to turnover money more quickly. Which is expansionary for AD.