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The interesting thing is not only disruption occurs but that it is bound. If I had to guess, eventually current income falls below acceptable consumption and assets, investments, and liquidity are liquidated to prevent further decline. Those with liquidity are forced or tempted to part with it and those without raise it to sustain minimal consumption, while those without either income or assets are forced on their creditors and public and private charity.

Lord: yep. As long as the supply of money is prevented from falling, there should be a lower bound, and the economy won't collapse to zero trade. But we may see some resort to barter, despite the costs of barter, if the decline in monetary trade is bad enough. And, empirically, it seems we do see some resort to barter. Which is hard to explain in non-monetary theories of recessions.

There are estimates that Amazon has 100 million products.

Humans can't solve a 100-million dimensional consumer choice problem -- n-1 -- and a fortiori can't solve a 10-quadrillion dimensional problem -- n(n-1)/2.

Since we are probably reducing that exact consumer choice problem to a few dimensions, does it matter that the full problem is 100 million or 10 quadrillion dimensional? Both seem like infinity relative to what humans likely do.

So is there really a difference between a barter economy and a monetary economy?

http://informationtransfereconomics.blogspot.com/2015/11/is-there-difference-between-monetary.html

1. Let's count the number of markets.

Let's do, your count falls short, I guess you missed a few. Bundled offers, my friend! You want fries with that? We have meal deals.

Let's say you have one live sheep and I want it (alive) so I offer a crate of apples, but you think the sheep is worth more than a crate of apples, and that's all the apples I can spare, so I decide to throw in a couple of chickens to round out the deal. Am I dealing in the sheep to apple market, or the sheep to chicken market? I just don't know any more.

Oh no, combinatorial explosion in the barter economy! She's gone factorial Captain. Wonder how those macho stats men are going to deal with that?

Money does clean it up a bit, but maybe people disagree on what is money and anyway, we still have those meal deals to contend with. Buy any two types of chocolate bar, get a free drink! Retailers seem to understand this a lot better than economists, which suggests the two groups don't take a lot of interest in each other. As far as I'm concerned, real economics starts in the supermarket and ends in the kitchen.

Nick have you looked at the general equilibrium work of Herb Gintis and co-authors? see here http://people.umass.edu/gintis/papers.html#get

I don't know that it has anything interesting to say about money - although this paper looks at role of financial constraints

http://www.umass.edu/preferen/gintis/Price%20Dynamics%20J%20Econ%20Dynamics.pdf

I don't know if it looks at money in the sense you are interested in here

Never ever use the words "the money market". All (n-1) markets are money markets.

Yeah well never use those words *UNTIL* someone puts a gun in the back of your neck and says, "Have you tried some of my IOU notes? They aren't redeemable for anything except another identical IOU note; but in my line of work, we say this is backed by the full faith and credit of I just might blow your freaking head right off."

After that's happened a few times (and sooner or later it happens to most of us) you can go right ahead and start talking about "the money market".

Jason: IIRC, John Hicks (he of the ISLM model) wrote an interesting related paper once, maybe 40 years ago. I can't remember the title, but a tech-savvy young person like you should be able to find it. It went roughly like this:

When you set up a Lagrangian constrained optimisation problem, let lambda be the shadow price on the constraint. In economics terms, lambda is the Marginal Utility of money income. It's the increase in utility when a dollar falls out of the sky, relaxing the constraint, and you spend it optimally.

Hicks said that, instead of solving the consumer choice problem simultaneously, we solve it sequentially. It's an easier heuristic. We have some rough idea of how big lambda is, and buy apples until the Marginal Utility of a dollar spent on apples equals lambda. Then do the same for bananas, etc. Then we slowly adjust lambda up or down over time depending on whether we are running out of money or the opposite.

If Hicks is right, money doesn't just make it easier to trade; money makes it easier for normal people to find an approximate solution to a very complex problem.

And if Hicks is right, you can sorta see how inflation would really mess with that heuristic, because it means lambda is falling over time, even if you are making the right choices.

Luis: Herb Gintis normally strikes me as someone doing interesting stuff. But I haven't read him on GE theory.

In this framework, we have money involved in every trade. Money is also a good, like every other good. This combination can be diagrammed as a wheel, or more accurately, just an axle and spokes.

Money (as a good) would be located at the axle (axis). Every other good is located at the end of a spoke.

Now introduce trade into the framework. Trade is between any two goods. Except for a trade in money, the path for every exchange is from tip-of-spoke to tip-of-spoke (which includes passing through the axis). By your definitions, it takes two spokes to complete each market but every market is a "money market" because the path passes through the axis.

Now add a ban on the term "the money market". This would imply a denial that one possible trade is from a good on the spoke-end to the axis (where money-as-a-good is located) and back to the originating good. I doubt that this is what you intended.

The axle-spoke depiction of your framework should carry over to the Walrasian model. Walrasian theory would be an attempt to model the axle-spoke framework as a single entity, trading simultaneously.

One trouble with this extension is that in the Walrasian model, there is a need to label each good as it's own market. Of course, that desirability takes us back to the need to label the money center as "the money market".

Closing comment: The real economy moves real goods, including money-as-a-good. Movement implies a path-of-movement which should be traceable. The axis-spoke model should be labeled (including path labels) in a manner adaptable to other models such as the Walrasian.

Roger: there's hub (money), rim (other goods) and spokes (markets) connecting hub and rim. Every spoke is a money market.

"Roger: there's hub (money), rim (other goods) and spokes (markets) connecting hub and rim. Every spoke is a money market."

OK. Then how do you label (describe) an event such as an apple producer going to the hub (to get money) and returning to the rim?

Lots of good stuff here. Likewise, lots of points I might comment on, but I'll limit myself to one.

"Start in full market-clearing equilibrium. Now double all prices in terms of money. So there is an excess demand for money."

One thing about money, is that we like to use it for loans. So, if the dollar is used as money, then we are likely to find that there are many people who have short positions in dollars, just as there will be many who have long positions. So a doubling of all dollar prices has complex wealth effects and we can't in general say that it will lead to an excess demand for money.

Nick E: thanks!

You may be right.

Comment away!

Roger: he sold apples for money, in the apple/money market. And we usually call the apple/money market simply "the apple market", since it is taken as understood that you buy and sell apples for money.

What about recessions in Diamond's coconut plucking model? Or recessions in Bryant's QJE 83 paper, "A Simple Rational Expectations Keynes-Type Model"?

I believe some version of "animal spirits/expectations" causes a coordination-failure driven recession in both those non-monetary models...

primed: pretty sure I've read both those papers (definitely read Diamond) but my memory is hazy. But didn't they both have the feature of some sort of extreme discouraged worker effect? Workers don't go looking for jobs, because they figure there's no employers looking for workers, and employers don't go looking for workers, because they figure there's no workers looking for jobs? Which doesn't seem quite right to me.

Plus, the fact that barter seems to increase in (big) recessions does suggest a monetary problem.

But yes, there is more than one way to think outside the Walrasian box. The way I'm doing it here does seem most "realistic", since we do in fact use money, so it seems like a good idea to start there.

Thanks for the reply Nick; that will keep me busy for awhile. It seems that formulation turns the n-1 dimensional problem into a factorized set of n-1 sequential 1-dimensional problems which would achieve an o(n^2.5) speed-up.

Just to be clear, though: I wasn't saying money doesn't help make economic decisions easier, I just had an issue with there being a difference between problems with dimensions n(n-1)/2 (barter) and n-1 (monetary) when n is very large ... so large that dimension of both is approximately infinite. There has to be some kind of heuristic/simplification being used (such as the one from Hicks) so the original difference between the two does not obviously carry over to the simplified problem.

I have my own wild ideas about how money helps solve the economic allocation problem ... :)

http://informationtransfereconomics.blogspot.com/2015/06/the-definition-origin-and-purpose-of.html

Jason: any given individual need not solve the whole optimization problem. Say n = ~10 for any given individual, chosen from the 100 million you cite above. Then aggregate over a few billion individuals.

Patrick: I get your point, and it's correct. But it's a bit more than 10, I think. Plus, there are lots of goods we don't even consider, because it takes too much time to research or even think about them. Which is why advertisers keep trying to attract our attention.

But that's an argument that's not really the main point of this post. Which is about the number of markets, and the number of excess demands, and how Walras' law is horribly wrong, and how most economists simply don't get some very basic stuff about money and exchange.

In this economy, why would excess SUPPLY of money ever be a problem?

Suppose that everyone in this economy has a portable money printing machine which they carry with them. When they arrive at one of the n-1 money markets they print whatever money they need to carry out the desired transactions. Or more if they wish.

notsneaky: "In this economy, why would excess SUPPLY of money ever be a problem?"

Barro-Grossman 71 answered that one. I will give a simplified version.

Self-employed service providers, who sell one service and buy many. Start in competitive equilibrium. Then M doubles, holding all P's fixed (or all P's halve, holding M fixed). There's an excess supply of money. Everybody wants to buy more services, but nobody wants to sell more, so they fail to buy more. They can't increase the flow OUT of their pockets. But they can reduce the flow INTO their pockets. They decide to sell less services ("buy" more leisure). Output falls. But that makes the excess demand for services even worse, and causes a supply-side multiplier effect, where output falls still further.

Barter could solve this excess demand for services. ("OK, I will only agree to cut your hair if you agree to give me a massage in return, because I don't want more money, because I can't spend any more money, because nobody will sell me any more goods")

I saw this problem in Cuba in the 1990's. Communist countries called it "monetary overhang".

The reason it rarely happens in capitalist countries is because equilibrium is monopolistically competitive, not perfectly competitive, so firms always want to sell more at current prices, since P > MC. That's why a loosening of monetary policy causes output to temporarily increase in New Keynesian models, which assume monopolistic competition.

"Suppose that everyone in this economy has a portable money printing machine which they carry with them. When they arrive at one of the n-1 money markets they print whatever money they need to carry out the desired transactions. Or more if they wish."

Then nobody would produce or sell anything, if they could print money instead to buy things they wanted, so they wouldn't be able to buy anything with that money.

"Then nobody would produce or sell anything, if they could print money instead to buy things they wanted, so they wouldn't be able to buy anything with that money."

I have to think about the first part. But for this part: money is NOT in utility function. It's just a (non-binding, given the existence of personal money printing machines) constraint on transactions. You still want to produce and sell stuff because it takes BOTH money and goods to trade.

My understanding is that it is a general given that recessions cannot occur in a barter economy.

Is that correct?

(i.e. as a "general given")

If so, what is the logical proof of that?

(It is relatively easy to see how recessions occur in a monetary economy. And it is vacuously obvious that recessions cannot occur in a barter economy in the same way that they occur in a monetary economy, because there is no money in a barter economy. So that sort of argument won't do as any type of proof. What is the proof/logic that excludes any reference to the functioning of a monetary economy?)

If that is not correct, what is a more precise statement about the logic of recessions in a monetary economy versus a barter economy?

Separate but related question; this is even more basic I think: Can Walrasian economies be either barter or monetary as a type? Or are they considered one or the other or neither?

JKH: "Can Walrasian economies be either barter or monetary as a type?"

Some (many?) economists may think that a Walrasian economy is a barter economy, because it doesn't have money. I would say it is neither barter nor monetary. It only has one market, so a monetary economy, with n-1 markets, is somewhere between a Walrasian economy with 1 market and a barter economy with (n-1)n/2 markets.

"My understanding is that it is a general given that recessions cannot occur in a barter economy."

Many (most?) economists don't see the connection between recessions and whether an economy is barter or monetary.

For example, Real Business Cycle models normally work exactly the same way whether they are barter (they usually are) or monetary. And many (most?) economists think that New Keynesian models are "cashless", where money is only the unit of account (they are wrong).

So I think I'm maybe in a minority, and part of a weird alliance of monetarists and old/post keynesians. You can get falls in output and employment in a barter (or Walrasian) economy. But they won't look like the recessions that we normally see.

notsneaky: suppose I were the only person who had a money-printing machine (I'm a counterfeiter). I would print money to buy the goods that other people produced, but wouldn't bother producing any goods myself. Now take the limit as more and more people get their hands on a money printing machine. Even if prices were fixed by law in terms of money, that money would still become worthless, because there would be nothing to buy with it. Sort of like Venezuala, only worse. So even the people who didn't have a money machine would stop producing goods for sale for money, because they would be unable to spend the extra dollars. The (indirect) MU of holding paper money drops to zero, if you think you can never spend the extra money.

Sorry to be late with this further comment, but Nick, your post and further comments deserve careful thought, even if late.

Turning to the axis-spoke model of markets and money, we obviously see that money is the common element in every trade. Equally obvious, every market trades with every other market using the common money-pathway. Each market has n-1 possible trades with other markets. The total number of possible trades is (n-1)n/2 which is the result when all possible market-to-market trades are counted.

In a monetary economy, all of the (n-1)n/2 possible trades would use money as a common, time-bridging, mechanism to facilitate the exchanges.

Now, very important, money itself has a origination, a storage mechanism, and a death or destruction. As a result, market disruptions such as counterfeiting can occur. In the axis-spoke model, this disruption is at the hub, the axis, the very center of the system. Disruptions at the center cause disruptions throughout the entire economic system.

All models are built to better demonstrate the components of the whole. The time-bridging aspect of money is difficult to model because it is not a physical element. So how can time be modeled in a physical construction? My suggestion is that the spokes of the axis-spoke model represent time. I call the spokes a "pathway"--it takes time to traverse a pathway.

If we use my model, the axis is the money market, the spokes are time (and perhaps distance) and the end of the spokes are markets. I allow the markets to interact, with each interaction in the monetary economy being through the axis and using money over a time displacement. Thus, it takes two spokes to connect between any two markets except that only one spoke is needed for connection to the money market.

This model differs from yours by including the time element, time being displayed by length of spoke if time scale became important.

It seems to me that the Walrasian economy can be represented by the axis-spoke model. Each market would make a portion of supply available for sale each day. One day's sales would involve a measurable quantity of money, which may or may not be the same quantity of money used the previous day.

Excess demand for any product (including money) would require analysis of inventories held by each market. Like beauty, excess is judged in the eye of the beholder.

Hayek made a version of this argument in 1929.

This is an interesting post. And one of the few I can relate to + think I understand :-).

You write: Start in full market-clearing equilibrium

What does equilibrium mean in this context? How can you assume equilibrium if there is a separate market for every product and no mechanism by which disequilibrium in one market is resolved by flows from offsetting disequilibria in others? Does general equilibrium not require the Walrasian autioneer? That's a methodological question, I guess.

And how does a change in monetary policy affect general equilibrium / market clearing in all markets? Or is nobody saying that it does? I can only imagine it having an impact on the average of all markets. Which is fine of course, but I'm having trouble relating monetary policy to the concept of general equilibrium within this framework.

Or is it something like the own rate for each goods market I'm missing? And if so, how does that square with an assumption that money is a commodity with a purely positive value, as opposed to being thought of as credit with equal positive and negative values?

Hope I'm making sense here.

Greg: that doesn't surprise me much. Hayek was the sort of guy to think about things like this. But can you be more specific? 1929?

Oliver: thanks.

"Equilibrium" in this context can mean 2 things:

1. Standard market-clearing. All prices are at exactly the right levels so that quantity demanded = quantity supplied in all n-1 markets.

2. For any arbitrary set of prices, the quantities that buyers expect to be able to buy match the quantities sellers are willing to sell, and the quantities sellers expect to be able to sell match the quantities buyers are willing to buy.

If you had a perfectly symmetric model (except for money), an excess demand for money (caused by bad monetary policy) would cause the exact same excess supply of goods in all n-1 markets. The real world is more complicated, of course. A recession might cause an excess demand for Kraft Dinner.

I understand 2. as saying that there cannot be a build up of inventories because fluctuations in relative prices prevent that.

But that rests on the assumption of symmetry which can be relaxed within your framework to cause say excess demand for Kraft Dinner but not in a walrasian world where markets always clear, even when output falls / there is excess demand for money?

Oliver: that's not what 2 means. And it's best not to think of inventories at all. Inventories are just a fudge factor that some keynesians introduced to avoid having to think clearly about what is happening. Assume all goods are services, like haircuts and massages, that cannot be stored. Or are produced to order, so you never produce goods that cannot be sold. If Qd < Qs for haircuts, then Q = Qd, and there is an excess supply. Hairdressers who want to produce and sell more haircuts than they actually produce and sell.

Let's think about "2. How many excess demands are there?".

At any one time, in a monetary economy, representatives of n markets can stand at the axis (hub) with the money market product in hand. In a monetary economy, this represents excess demand for each of the n-1 markets. (we could also say that one market, the money market, has an excess supply.)

We could ask "Where in the measuring period is this moment in time?". In the Walrasian world, the moment would be at the beginning of the measuring period. At the end of the Walrasian measuring period, money would have moved from the money center into each of the markets. At the end of the measuring period, the money market would hold n-1 goods in some quantity and the sum of the markets (n) would hold money (the product of the money market) in some redistributed quantity.

At the end of the Walrasian measuring period, excess demand would have been matched with excess supply so that excess demand less excess supply equals zero across all n markets.

I think this is an alternative analysis to the analysis you penned.

"Hairdressers who want to produce and sell more haircuts than they actually produce and sell."
Again the fixed capacity myth. Work harder, faster with better machinery (not so much hairdressing on that last one, can you think of any hairdressing machines) and you improve that.
And of course no business operates at maximum capacity because of the natural variation in the order cycle. There is always room for more output.
And even if you hit maximum output what you actually do is delay your customers (aka queueing!).
The mainstream economic myths are clearly created by people who have never operated in the real world.
The job of government is to make it really, really difficult for price rises to stick - by improving competition and lowering barriers to entry in all markets.

... can you think of any hairdressing machines?

Comb and scissors would be the first things that come to mind. Seems like hairdressers will get more done with the right equipment.

http://www.remingtonproducts.com/

Presumably those gadgets do something, the company stays in business at least. I admit I use one. Sorry to get randomly off topic, there is an important point under all this:

Hairdressers who want to produce and sell more haircuts than they actually produce and sell.

Agree with Nick on this one, inventories are pretty much an internal part of the business, some business may find it worthwhile to keep large inventories, while other business may have a "just in time" management philosophy and build on demand... nothing to do with boom and bust, and probably a bad idea for a bunch of economists to start trying to base macro-economic policy on what is trendy in management philosophy at the time. Much better to regard the business as a black box from a macro perspective.

However, I wonder if the full implications of that phrase "want to produce and sell" have been appreciated here. Coming from an empirical background in engineering, I'm a lot happier to take measurement from an observable event, than I am attempting to take measurement based on an internal "want" inside someone's head. Of course, in a way that "want" must be a real thing, but it would only become observable real thing in an alternative universe where more customers come to buy haircuts.

The "supply" and "demand" curves that economists draw are necessarily hypothetical imaginary constructs. In the real world we have transactions, and only transactions... credits and debits must balance at all times (both in money, and in goods, or "stock" as accountants prefer to call it). Conjecture about what else might have happened must necessarily remain unmeasurable, although there are various ways to estimate what the local region of supply and demand curves might look like (i.e. estimate the slope).

The reason it rarely happens in capitalist countries is because equilibrium is monopolistically competitive, not perfectly competitive, so firms always want to sell more at current prices, since P > MC. That's why a loosening of monetary policy causes output to temporarily increase in New Keynesian models, which assume monopolistic competition.

There must be something wrong there, a monopolist has an incentive to create artificial scarcity precisely because it keeps prices up.

Suppose I sell expensive handbags which are (to the best examination of a heterosexual male scientist) pretty much identical to the cheap handbags, other than the label attached... now government provides a monopoly privilege to me as the owner of the label, but does *NOT* provide a monopoly privilege on who can produce handbags. The owner of the expensive label can apply this label to more handbags at very low cost (thus "producing" more of their branded handbags) but someone smart won't do that because the whole idea of the exclusive label is to be exclusive... that's what people are paying top dollar for!

" I would print money to buy the goods that other people produced, but wouldn't bother producing any goods myself. "

Hmm, ok. But maybe let's try something different.

Two agents, A and B, two goods X and Y. Person A can produce only X and person B can produce only Y. Upper cases {X,Y} denote productions. Lower cases x and y, {xA, xB, yA, yB} denote respective demands. Actual consumptions of physical goods are {cxA, cxB, cyA, cyB}. Production is linear with labor, {lA, lB}, only factor so X=K*lA and Y=H*lB. K and H are productivity constants (I'm not sure if these even matter here). Each agents has the same Cobb-Douglas utility amended to include disutility of labor supply

U_A= ln(cxA)+ln(cyA)-(r/K)*X
U_B= ln(cxB)+ln(cyB)-(r/H)*Y

r is some parameter related to leisure.

In this economy there's no Walrasian auctioneer. There is no "equilibrium", except by chance. There is perfect information. But choices are made sequentially.

First both agents decide how much of their outputs to produce. They then take these outputs to a "central clearing house" which buys these outputs from them for "money", at prices m for each unit of X and a*m for each unit of Y. A bit hokey, but no more so than a Walrasian auctioneer. These prices are known in advance. After they've sold their outputs they can buy back outputs from the central clearing house for consumption, at prices nx for each unit of X and ny for each unit of Y. These prices are also known in advance and they don't "clear" anything, they're just exogenous "sticky" parameters. Supply doesn't have to equal demand. So we need a rationing rule.

If xA+xB (total demand for X) is less than or equal to X (total supply of X) then each agent gets their demand. Any surplus X gets thrown away. Same for yA+yB vs. Y.

If xA+xB is greater than X then each agent gets their *share* of demand in total demand. I.e. Person A gets (xA/(xA+xB))*X and person B gets (xB/(xA+xB))*X. There is some assumption here about how agents don't get to misrepresent their demands. But I'm sure there's a lot of rationing rules that will work here, this one's just simple.

Same for yA+yB greater than Y.

We can have equilibrium in both markets, excess supply in both, excess demand in both, excess demand in one and excess supply in the other. The outcome depends on how much X and Y both agents produce which in turn depends on the parameters (which include both the "buy" and "sell" prices).

Oh, one more thing, both agents take total money supply, mX+amY, as given (i.e. there's really 1000's of each type of agent) when maximizing.

The relevant parameter we want to think about is the m, which can be thought of as money supply (central clearing house could also choose a, how money is distributed). Can m ever be "too high"?

(I haven't worked out all the cases but the one of excess demand in both goods is a bit weird)

[edited by NR to fix typo]

notsneaky: "U_B= ln(cxB)+ln(cyB)-(r/H)*X"

Typo? Should be U_B= ln(cxB)+ln(cyB)-(r/H)*Y I think. (I will edit your comment, if you agree.)

notsneaky, some thoughts on your model:

1. If m =/= n, your clearing house is imposing a tax (or subsidy) on trade. The seller's price is not equal to the buyer's price. I'm not sure why that's in there, but it's not the same as money. And a tax on trade will reduce the volume of trade.

2. We could delete production from the model to simplify without changing it much. Give A an endowment of X, and B an endowment of Y.

3. With two goods, we can't distinguish between barter, monetary, or Walrasian exchange. There is only one market. If I added a third type of agent (C who produces good Z) to your model, then I would describe your central clearing house as Walrasian with a lazy auctioneer, who chooses an initial price vector at random, and can't be bothered to change it. Which is an OK model, but not monetary. And if the auctioneer sets m=n, and a =/= 1 (and a similar price for Z, b =/= 1) then we would observe 2 of the three goods in excess demand (or supply) and the third in excess supply (or demand).

notsneaky: "(I haven't worked out all the cases but the one of excess demand in both goods is a bit weird)"

I'm not sure how you can get that case in your model. If both agents are trying to buy more goods than they sell, how do they plan to pay for them? (Unless the clearing house is giving them a subsidy).

Tel: "There must be something wrong there, a monopolist has an incentive to create artificial scarcity precisely because it keeps prices up."

Suppose the monopolist is currently selling apples at a price of $10, because that maximises his profits. And $10 > MC (because P > MR = MC). Now suppose his demand curve unexpectedly shifts right, but he cannot increase price (because he has already advertised $10 as the price). He wishes he could increase the price, but is still very happy to sell more apples than he had planned to. He will increase production in line with demand, until his MC rises to equal $10.

notsneaky: but I should probably write a post on "Walrasian clearing house as central bank).

Yes, that was a typo

And the reason there's production is so that utility can vary. Otherwise, if there's excess demand then just the endowment gets traded. Given the rationing rule, the outcome will actually be the same as in the Walrasian version (I think), so utility will be the same. That was sort of the earlier point I was trying to make about "too much" money in an endowment economy not making a difference.

Also, can't we consider leisure as the third good here?

Anyway, I thought it up last night but was too tired to fully go through all the possibilities.

I'm not so sure that m=/=n is a tax. Suppose that the "buy back" prices are Walrasian/flexible - they clear markets. In that case nx/ny=H/K. Both agents get exactly their demands. So (1/2)*m*(X+aY)=nx*X=ny*Y. The agents' utility functions are then

U_A=2*lnX+stuff-(r/K)*X
U_B=2*lnY+stuff-(r/H)*Y

So the choice of labor gives X=2*K/r and Y=2*H/r. This is the same production (and allocation) as would occur without all the rigmarole of going through the clearing house. m and a don't matter. Fix ny=1 and suppose H=K. Then nx=1. We can have m=1/3, a=2 - so that the "sell to" price is greater than the "buy back" price to both agents and the outcome is still the same as Walrasian equilibrium.

Of course if the "buy back" prices don't clear markets then m and a do matter and they can act as a sort of tax/subsidy but I think that's sort of the point

(I think I've gotten to where I'm arguing your point for you. I just had to get there my own way)

"If both agents are trying to buy more goods than they sell, how do they plan to pay for them?"

If there's excess demand the goods are allocated according to the rationing rule. The share in total output is given by ratio of your money balance to total money. You increase your money by producing more good, but the other guy's doing the same. All we need is that they are able to pay only for what they actually receive

Suppose for simplicity that H=K=1 and a=1. There's excess demand in both markets if xA+xB > X and yA+yB > Y. The Walrasian demands are xA=(1/2)*(m/nx)*X, xB=(1/2)*(m/nx)*Y, yA=(1/2)*(m/ny)*X, yB=(1/2)*(m/ny)*Y. So excess demand in both markets if (m/nx) > 2X/(X+Y) and (m/ny) > 2Y/(X+Y). , or m > (2/(X+Y))*Max(X*nx,Y*ny).

Agents anticipate there'll be excess demand. The actual consumptions will be cxA=(m/M)*X^2, cyA=(m/M)*X*Y, cxB=(m/M)*X*Y, cyB=(m/M)*Y^2. M is total money M=m*(X+Y) but agents take it as given. Utility functions then are

U_A = 3 ln X + stuff - r*X
U_B = 3 ln Y + stuff - r*Y

So X=3/r and Y=3/r. So the condition for excess demand in both markets is m > Max[nx,ny]. Since nx and ny are given, there's no reason why we couldn't have that.

Hi Nick,

Suppose the monopolist is currently selling apples at a price of $10, because that maximises his profits. And $10 > MC (because P > MR = MC). Now suppose his demand curve unexpectedly shifts right, but he cannot increase price (because he has already advertised $10 as the price). He wishes he could increase the price, but is still very happy to sell more apples than he had planned to. He will increase production in line with demand, until his MC rises to equal $10.

OK, so now with the imposition of a price control, there may be something of an issue for the monopolist. I'm going to have to say that genuine sticky prices don't happen very often in capitalist economies, when they do happen they are temporary, and the monopolist has a strong incentive to figure out a way to get around whatever type of price control they are up against (incentives matter, so if he wishes he could increase the price, then somehow or other he will increase the price). You no doubt expected me to say that.

Mind you, I would also argue that in a more competitive market there will be less of an issue, because the seller in a competitive market knows that choosing not to supply will just make a bigger opening for other sellers to step into. Your original argument was that "the reason it rarely happens in capitalist countries is because equilibrium is monopolistically competitive, not perfectly competitive" but this just doesn't make sense... the closer to perfect competition you can achieve (I accept that truly competitive markets are idealized), the less concerned the seller will be about protecting the high market price. It's the opposite of your argument.

If you want to look at what real monopolists do, they go to great lengths to avoid that situation you described where they find themselves advertising a lower than optimal price. They *ALWAYS* advertise high RRP, and then offer discretionary discounts to feel the shape of the demand curve. They never advertise low and then get themselves stuck wanting to raise the price (OK, never say never: it sometimes happens, like the famous 5c bottle of Coke, but that's the exception that proves the rule, and was generally considered a business management blunder, not something to aspire to).


H&M's 'Brand Integrity': Destroying Surplus Winter Clothes in New York Instead of Donating Them to the Needy

There's an example of a real monopolist... actually destroying perfectly good clothes when they don't sell.

The destruction costs money so MC is *NEGATIVE* but they are still reluctant to sell. In the same article it describes similar practice by Anthropologie destroying unsold merchandise, so it isn't just a random isolated incident.

Your theory is that artificial scarcity does not exist in business, but more than one observation shows that it does exist all over the place. You really have to adapt the theory to fit the facts, rather than trying it the other way around. There's more examples in the computer games industry...

Consider that I'm selling a new release game for $100, but what is the marginal cost of producing one more copy of that game? Well marginal cost is about 20c including printing, shipping, distribution, etc. It costs next to nothing to print off a DVD, but yet the monopolist knows that if they seriously push the volume based on MC then profits will be demolished. Indeed, I'd say that the MC is just about irrelevant, call it zero, just ignore it because it has no effect on economic calculation here. With the games industry, they do gradually drop the price of a given game over time, so older games will sell at a discount. The discount is discretionary, so they can adjust it without following any particular pre-commitment that they have made. You will also find plenty of examples where excess game stock is simply destroyed (just like the clothing example above).

Now in the article linked above, they also throw in a bunch of hand wringing about "Oh those poor homeless people" (evil evil capitalism) and that's kind of obligatory these days to spend some time bashing capitalism, because bashing it is much better than explaining how it works. Thing is plenty of cheap clothing is available (thanks to competitive markets), just not the fancy "brand integrity" stuff, homeless people can buy the unbranded clothing available everywhere, and this type of clothing (i.e. the non-monopolist, highly competitive end of the market) does regularly sell at a discount. Those tight margin retail chains simply cannot afford to destroy stock.

Here's another excellent example of how real-world monopolists behave. The OPEC cartel, as dominated by Saudi Arabia, for a long time would reduce the volume of oil shipments deliberately to keep the price of oil high. It worked while OPEC were large enough to be able to dominate world prices (i.e. "equilibrium is monopolistically competitive" to use your terms; OPEC never was a full monopoly, but they had a lot of influence). So then producers like Russia got into the oil market, and just cranked any volume they could achieve, benefiting from the high price OPEC was providing for them. Each year Russia would crank up production, and OPEC would reduce their production to compensate. Then USA started fracking and the market got more competitive. After the Iraq War finally settled down and those Iraqi oilfields came back online into the world market, it was yet more competitive. So the market shifted from that "equilibrium is monopolistically competitive" situation, over to a much weaker OPEC position. Saudi Arabia understood that they could choose to keep reducing supply, and thus keep prices up, but the people to benefit from this would be all the other sellers. Eventually, OPEC said "enough!" and slammed oil prices, rolled up sleeves and went full trade war, to see who will be the last man standing. There are rational reasons why markets do not settle down to nice clean equilibrium situations.

notsneaky: "If there's excess demand the goods are allocated according to the rationing rule. The share in total output is given by ratio of your money balance to total money. You increase your money by producing more good, but the other guy's doing the same. All we need is that they are able to pay only for what they actually receive."

Ah! I *think* I now understand your rationing rule. E.g. If I know I will only get half the apples I ask for, I will ask for double the apples I can afford to buy?

Suppose wage is $10 per hour, and price of apples is $1 each. Workers start the period with $0 money. They want to sell 10 hours of labour and buy 100 apples. But they can only sell 6 hours of labour, so only buy 60 apples. There is an excess supply of 4 hours labour. What is the excess demand for apples? The "notional" excess demand for apples is 40. The "constrained" (or "effective") excess demand for apples is 0. (The Keynesian consumption function is a constrained demand function.) The words "notional" and "constrained/effective" are from Clower, IIRC. Walrasian demands are notional demands. They ignore quantity constraints in other markets.

It's a weird sort of "excess demand" if the people who have that excess demand couldn't actually pay for that excess demand.

Nick said: "Self-employed service providers, who sell one service and buy many. Start in competitive equilibrium. Then M doubles, holding all P's fixed (or all P's halve, holding M fixed). There's an excess supply of money. Everybody wants to buy more services, but nobody wants to sell more, so they fail to buy more. They can't increase the flow OUT of their pockets. But they can reduce the flow INTO their pockets. They decide to sell less services ("buy" more leisure). Output falls. But that makes the excess demand for services even worse, and causes a supply-side multiplier effect, where output falls still further."

Let’s change this a little. There are service providers who are all firms. Workers buy services from firms and work for firms. All workers want 70 units of each different service but no more.

Start in competitive equilibrium where 70 units of each different service are supplied. Every entity runs a balanced budget. There are no savings. Profit is zero for each firm. M = 10,000.

I believe Q demanded = Q bought = Q sold = Q supplied for each service here.

Then one firm decides to save 50 for a really long period of time. That same firm wants to balance its budget after the initial 50. All P’s are fixed. It pays its workers 50 less. The workers maintain a balanced budget. They spend less on services. National income falls. Eventually, national income stabilizes at a lower level.

Does that sound correct?

notsneaky, do you allow for zero or negative marginal utility?

"Suppose wage is $10 per hour, and price of apples is $1 each. Workers start the period with $0 money. They want to sell 10 hours of labour and buy 100 apples. But they can only sell 6 hours of labour, so only buy 60 apples. There is an excess supply of 4 hours labour. What is the excess demand for apples? The "notional" excess demand for apples is 40. The "constrained" (or "effective") excess demand for apples is 0. (The Keynesian consumption function is a constrained demand function.) The words "notional" and "constrained/effective" are from Clower, IIRC. Walrasian demands are notional demands. They ignore quantity constraints in other markets."

I think a better way to say that is Q demanded without MOE = 100 apples and Q demanded with MOE = 60 apples.

Suppose H=K=a=r=1. The price that the clearing house pays for each good is two units of money, m=2. The price it sells each good back to the agents at is one unit of money, nx=ny=1. Agents anticipate that there'll be excess demand and the good will be rationed. The notional (Walrasian) demand for X by agent A is (1/2)*m*X/nx=X. For X by B is (1/2)*m*a*Y/nx=Y. By symmetry (and by maximizing utility) X=Y. So total Walrasian demand for X is 2X. Supply of X is X, so 2X > X.

Each agent does have enough money to pay for their respective demands (agent A has X units of money and so does agent Y) but just not enough X has been produced to satisfy both demands.

Why doesn't agent A produce more X? They know the good will be rationed and that they'll get half of whatever's produced. They could increase production but that would cost them more in terms of disutility of labor (in fact, with excess demand they're already producing more than under the Walrasian equilibrium, essentially for strategic reasons)

notsneaky:

"U_A= ln(cxA)+ln(cyA)-(r/K)*X
U_B= ln(cxB)+ln(cyB)-(r/H)*Y"

I find myself fumblingly following your Cobb-Douglas mathematical logic. You are introducing some concepts that are new to me, slowing my comprehension and necessitating some mental realignment. That takes time.

I think one strength of your math model is that both capital and labor are traded in the central exchange. Your model also adds time (or sequences) to Nick's mechanical model of money at the center of markets.

Have you considered placing this entire chain of mathematical logic into a blog post of your own? [If you have a blog (of your own), it is not linked via the comment attribution (as are Nick's and my comments).]

Thanks for sharing this logic and the sequential development of it.

TooMuchFed

Marginal utility of what? In terms of X the marginal utility is (k/X)-(r/A) where k, constant, depends on whether there is excess demand or not.

Roger, Cobb-Douglas is easy because it just means that agents always spend a constant share of their income on each good. So here, each agent will always want to spend one half their money on one good and one half on the other good. It's about as simple as you can get.

I don't think capital is being trade, everything is produced with labor, just it has to be produced before any kind of exchange takes place.

I used to have a blog once upon a time

To explain the above more simply. Suppose agent A produces 3 units of X and agent B produces 3 units of Y (these are in fact Nash-equilibrium quantities for the game with excess demand). A brings 3 units of X to the clearing house and gets 6 dollars for it. B gets 6 dollars for their Y. The Cobb-Douglas utility just means that A wants to spend 3$ on buying back X and 3$ on buying Y, same for B. The buy-back price of X and Y is 1$ per unit. So total demand for X (and Y) is 3$ from A and 3$ from B, so demand for 6 units. But only 3 have been produced. So the clearing house just splits the 3 units among them, 1.5 and 1.5.

In Walrasian equilibrium where prices (trade ratios) adjust so that supply equals demand, A would only want to produce 2 units of X and same for Y. This is because producing the good is costly in terms of disutility of labor. But suppose B produces only 2 units of Y. They'll get 4$. Then X can do better than producing 2 units by producing just a bit more and shifting the share of money in their favor, getting more than 1/2 of each good. Y of course knows this and thinks the same, so they respond by increasing their production a bit more as well. X increases back in response. Y increases. They both increase until each is producing 3, which is "over production"

"Marginal utility of what?"

All the services.

See my comment above at 2:10.

"All workers want 70 units of each different service but no more."

TMF, in the model, the marginal utility of good x is 1/x, the marginal utility of y is 1/y and the marginal utility of leisure is r (more or less, the marginal disutility of labor is -r)

"The "supply" and "demand" curves that economists draw are necessarily hypothetical imaginary constructs. In the real world we have transactions, and only transactions... credits and debits must balance at all times (both in money, and in goods, or "stock" as accountants prefer to call it). Conjecture about what else might have happened must necessarily remain unmeasurable, although there are various ways to estimate what the local region of supply and demand curves might look like (i.e. estimate the slope)."
At market level they aren't necessarily curves. They can be any polynomial shape you can draw in a straight line.

Those are the SMD conditions that Steve Keen keeps going on about. There *are* no market demand curves.

"TMF, in the model, the marginal utility of good x is 1/x, the marginal utility of y is 1/y"

Quick glance.

It appears 0 and negative marginal utilities of good x and good y are not possible in that model. Is that correct?

If you mean marginal utility of consumption of either x or y then yes that is correct.

Bob, you realize that none of that actually makes any sense?

notsneaky: I'm still trying to get my head around your model.

Let me work with your 3.13 example, which clarifies things a lot. I have two problems with it:

1. Why does the apple-producer take apples to the market, and then buy back his own apples? Why not just keep the apples he wants to eat? (If all markets are clearing, and there are no taxes or subsidies or transactions costs, it won't make any difference, of course).

2. In your example, they start out with no money, and the clearing house starts out with no fruit. They are selling fruit to the clearing house at $2 each, and buying fruit from the clearing house at $1 each. So, OK, I can see why there would be an excess demand for fruit, that the clearing house cannot satisfy. And this explains my question 1 above, because it's like a subsidy. But it's like a fruitbroker/marketmaker who has no inventory of fruit setting his bid price above his offer price. He is wide open to arbitrage losses. And the Walrasian auctioneer always has the same bid and offer prices.

Bob's presumably been reading that Steve Keen paper on perfect competition. Steve Keen actually does sometimes do some interesting stuff. But his paper on perfect competition is not an example of that. It's just plain wrong. Here is Chris Auld on the subject, but it's off-topic for this post.

And too Much Fed is still stuck on an example where people are satiated in consumption, which is why he thinks there's excess supply. He doesn't get that they would stop wanting to work if they are satiated in consumption (or are living in the Garden of Eden), even though I have explained it to him. It's also off-topic.

1. Well, why do agents take their goods to the Walrasian auctioneer and let him compute the trade ratios? Why do the coconut-pickers in Diamond's Island model just not eat their own coconuts rather than waste their time searching for someone to trade with? It's an abstraction. Just a way to have a model with disequilibrium prices and excess money demand/supply. I guess what might make it more confusing is that the clearing house is actually playing two roles here, one as a money-issuing central bank and one as a non-Walrasian auctioneer. But we could separate out these two functions.

2. Yes, but see 1. above. The way to think of the "sell to" prices, m and a*m, is that they're just a way of carrying out monetary policy in a one period model. The way to think of the "buy back" prices is that they're the sticky, disequlibrium prices that exist because... because we assumed prices are sticky.

We could add an extra move by the clearing house, either before agents decide how much to produce or after, right before they trade in their production (depending on what we want to focus on), where, taking the "buy back" prices nx and ny as given (prices have already been set in advance) it decides on the "sell to prices" m and a*m.

Then we can add in shocks, timing, strategic considerations and get most of the issues of monetary macro.

And I think Bob's referring to Keen's "exposition" of the Sonneschein-Mantel-Debreau "anything goes" theorem. It's just as wrong as Keen's imperfect competition stuff.

Bob, the SMD theorem is really just about the uniqueness of the general equilibrium - it's hard to guarantee that there's only one (though every example of multiple equilibria I've seen tend to be fairly contrived). It doesn't say anything about market demand not existing or anything like that. Keen also confuses the SMD theorem with the Gorman Form Representation theorem (which is about when you can write aggregate demand as a function of aggregate wealth, rather than a vector of individual wealths, IIRC). I have no idea what "any polynomial shape you can draw in a straight line" means.

Hi Nick

Fascinating post. I often wonder about what I would have learned had I done a PhD in an earlier era, what got swept off the curriculum to make room for what we study now. So thanks for giving us a glimpse. Sometimes, when I am feeling particularly rowdy, I go to the library and take out an old, unfashionable economics book and attempt to read it. A few weeks ago I read the first hundred or so pages of Franklin Fisher's "Disequilibrium Foundation of Equilibrium Economics." I thought it was very interesting but had a hard time seeing how it fit into modern economics. I know people call the searching and matching models disequilibrium, but they don't resemble the model Fisher writes down (at least to me). You mention stability in passing in this post (thought I don't get the reference), what do you think of that stuff?

notsneaky:

1. OK. Let's run with Diamond's tabu on eating your own coconuts (and it works fine for haircuts, since you can't cut your own hair).

2. OK. Let's think of it this way. Your central clearing house is also a central bank, that prints or burns money, and uses the money it prints or burns to finance percentage subsidies or taxes on sales (or purchases) of goods.

"And I think Bob's referring to Keen's "exposition" of the Sonneschein-Mantel-Debreau "anything goes" theorem. It's just as wrong as Keen's imperfect competition stuff."

Ah. You are probably right.

Sam: Thanks!

I haven't read Franklin Fisher (or if I did, I don't remember). Brad DeLong knows the stuff I am talking about in this post, and has also, IIRC (but don't trust my memory), done a post on Franklin Fisher. He could give a better answer than me. The two key questions are these: when Fisher does his stability analysis, does he assume agents take quantity constraints into account, and is he talking about a monetary exchange economy with n-1 markets? If no to both, ignore it. If yes to both, read it.

“Self-employed service providers, who sell one service and buy many. Start in competitive equilibrium. Then M doubles, holding all P's fixed (or all P's halve, holding M fixed). There's an excess supply of money. Everybody wants to buy more services, but nobody wants to sell more, so they fail to buy more. They can't increase the flow OUT of their pockets. But they can reduce the flow INTO their pockets. They decide to sell less services ("buy" more leisure). Output falls. But that makes the excess demand for services even worse, and causes a supply-side multiplier effect, where output falls still further.”

“The reason it rarely happens in capitalist countries is because equilibrium is monopolistically competitive, not perfectly competitive, so *****firms***** always want to sell more at current prices, since P > MC. That's why a loosening of monetary policy causes output to temporarily increase in New Keynesian models, which assume monopolistic competition.”

“And too Much Fed is still stuck on an example where people are satiated in consumption, which is why he thinks there's excess supply. He doesn't get that they would stop wanting to work if they are satiated in consumption (or are living in the Garden of Eden), even though I have explained it to him. It's also off-topic.”

Nope. When firms are added, the scenario changes.

There are service providers who are all firms. Workers buy services from firms and work for firms. All workers want 70 units of each different service but no more.

Start in competitive equilibrium where 70 units of each different service are supplied. Every entity runs a balanced budget. There are no savings. Profit is zero for each firm. M = 10,000.

I believe Q demanded = Q bought = Q sold = Q supplied for each service here.

Then one firm becomes more productive. It does not increase output although it would rather do that. Instead, the firm reduces hours worked becoming profitable. It saves 50 for a really long period of time (there is the excess demand for money making this on-topic). All P’s are fixed. It pays its workers 50 less. The workers maintain a balanced budget. They spend less on services.

"Then one firm becomes more productive. It does not increase output although it would rather do that. Instead, the firm reduces hours worked becoming profitable. "
Why you need JG and strong demand.

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