My macro framework

FWIW. Since everyone else seems to be doing this.

1. There are n different types on labour.

2. Each individual has an endowment of one type of labour, and wants to trade some of it for some of the other types of labour.

3. But (double) coincidence of wants is rare, so they use money as a medium of exchange (and medium of account).

4. Output and employment are the same thing; prices and wages are the same thing.

5. Prices/wages are sticky. I don't really understand why, but I think it's probably got something to do with coordination problems.

6. Sometimes there is an excess supply of money, and money is a hot potato. It is easy to sell labour and hard to sell money. That causes prices/wages to rise.

7. Sometimes there is an excess demand for money, and money is a pleasantly warm potato on a cold night. It is hard to sell labour and easy to sell money. That causes the volume of trade to fall. We call that a recession.

8. Other economists with different types of labour can use different frameworks to talk about the long run, and other important things.

Comments

[jonathan]

It sounds like our basic models are quite similar, and quite similar to Krugman's, i.e.:
http://web.mit.edu/krugman/www/MINIMAC.html

"5. Prices/wages are sticky. I don't really understand why, but I think it's probably got something to do with coordination problems."

One thing that helped me to finally grasp price stickiness intuitively was when I realized that it's not stickiness of individual prices that matters, but stickiness of the overall price level. In other words, the problem is that the price of *money* is sticky, in terms of *all goods*.

Then it's easy to see why it's difficult to coordinate a general fall in prices of millions of individual goods, which all individually want to keep their relative prices unchanged, and why it's much simpler to increase the money supply instead. It further nicely dovetails with the evidence of price stickiness from exchange rates (the price of money in terms of other kinds of money moves around a lot more than the price in terms of goods!).

[Frank Restly]

Nick,

3. A double coincidence of wants is rare so they use money as a medium of exchange (and medium of account).

That explains the use of money to facilitate the exchange of labor that is simultaneously available. But what happens when one type of labor can only work during the summer months (crop harvesting) while another can work only during the winter months (snow shoveling)?

I want to trade my snow shoveling labor for my neighbor's crop harvesting labor. Money doesn't seem to be enough. Any trade of labor between myself and my neighbor involves one person taking time sensitive risks. Those risks include relative price (inflation) risk and default risk.

Bottom line, where does debt fall into your macro-model?

[Roger Sparks]

Rather than debt (Frank suggests the need for debt), I was thinking about "savings". Savings and debt are two parts of the same coin. Simultaneous exchange of valuable labor or material is unnecessary if a coin of enduring value is available for use (in exchange).

I think you need a point 9. I would suggest that it deal with the creation of money. You might even start with the easy creation of money by a local counterfeiter. Prices and the creation of money must be linked in some way.

[Frank Restly]

Roger,

"Simultaneous exchange of valuable labor or material is unnecessary if a coin of enduring value is available for use (in exchange)."

I disagree. And the reason is simple - with n types of labor and n-1 prices of labor relative to any coin, the question becomes what "value" should be enduring? In my example should the relative price of a coin and snow shoveling labor be enduring (1 coin is always and everywhere equivalent to 1 hour of snow shoveling labor) or should the relative price of a coin and crop harvesting labor be enduring? A coin that tries to fix the relative price of snow shoveling versus crop harvesting would be ill advised.

What should always and everywhere be enduring is the legal protection of a debt contract agreed to by both the borrower and the lender. The value of the time between when I shovel snow and when by neighbor harvests crops should be mutually agreed upon.

[Curtd]

1) Any change that forces reordering of the PSST (network of production) is a transaction cost that all seek to avoid, and avoid more so when risk increase from declining price pressure. People hold out. The entire chain gets more efficient. And they only switch when it's no longer possible. This is just what people do. Particularly if relationships are involved. The more complex the relations the worse it is.

2) The individual who lives with little savings and high cashflow demands interprets changing jobs as the highest transaction cost other than divorce or devastating illness.

3) An entire organization can come apart if you reduce pay, because it affects the entire network of responsibilities of each person.

4) As the marginal value of talent has increased, and the marginal value of fixed capital has decreased, the influence of shocks on talent places higher risk to the organization- people are very difficult to replace but the best are the first to leave.

5) Net is that the side effect of little savings and higher consumption at high velocity, is stickier everything and worse adjustment to shocks.

Here in the 'less advantaged world' it's not a problem. Oversupply of labor. Everyone is overqualified for everything. Lack of credit keeps everyone poor. Lack of credit because the government cannot be trusted not to appropriate anything and everything.

-Curt

[Ian Lippert]

If prices and wages are the same thing doesn't that mean that all costs are labour costs?

[Nick Rowe]

jonathan: it is indeed very similar. It's on the role of saving where we *might* part company...

Roger and Frank: savings are important for long run macro, but not for short-run macro. It is only saving *in the form of money* that matters.

Curt: maybe. I would have to see it worked out.

Ian: yep. That's a simplification obviously. I could easily add land to the model. And intertemporal exchange too, with a bit more difficulty. They won't change things much, so I left them out.

[Nick Rowe]

jonathan: I agree with you on the general price level coordination thing. It *helps* us understand it, but I don't think it's enough for a *full* explanation. What is it precisely that determines how difficult it is for individuals to coordinate to solve that problem, and what determines how long it takes?

[Tel]

Interest rates?

[Tel]

Roger and Frank: savings are important for long run macro, but not for short-run macro. It is only saving *in the form of money* that matters.

If you are talking about cash under the bed type savings (M1 money) I think you can safely presume it is zero. There might be a few drug dealers out there with shrink wrapped cash, and perhaps a few CIA helicopters flying around with a palette of USD, but other than those guys, everyone else uses a bank.

If you are talking about broad money, including account balances, credit cards, and possibly various bonds, then you are facing the job of modelling the financial industry.

[Roger Sparks]

Frank,

".........the question becomes what "value" should be enduring?"

The ratio of 'snow shoveling to coin' or 'harvest to coin' (in my opinion) should not be a fixed ratio. (it is certainly convenient when it is fixed) Instead, each is a separate transaction, complete and sufficient in itself. In each case, after the trade, the holder of coin is left with the responsibility of finding future value for the coins held.

(again in my opinion) A debt denominated in coin is a debt for coin, not material nor labor. When coin is returned to the debt holder, the now coin holder has the responsibility to find future value for the coins held.

Nick,

It seems to me that short term macro is macro divided by the number of transactions (that is 'transactions for money'). Savings is part of that even if we only count savings as where the money resides between transactions. Mathematically, if the velocity of a coin is 12 over the year, then the coin must have been in savings for one year but in the hands of twelve holders. Each holder of coin would have held savings for one month.

[Nick Rowe]

Tel: in my framework, interest rates don't matter except to the extent that they are one of the things that affects the demand and/or supply for money. And that depends on the differential between the interest paid on money and the interest paid on non-money assets.

[Roger Sparks]

"5. Prices/wages are sticky. I don't really understand why, but I think it's probably got something to do with coordination problems."

The stickiness may have something to do with saved money. If the velocity of coin is 12 (meaning one coin changes hands twelve times during a year), there are twelve opportunities for an unwelcome surprise if inflation occurs during that year. At least one of those twelve holders could balk at paying the increase, with the result that only 11 exchanges occur during the year. Would that be a case of excess demand for money? If so, would the excessive demand be on the part of the buyer or seller?

I would agree with you that this would be a coordination problem. I am ambivalent about who to blame for the lack of coordination.

[Frank Restly]

Roger,

"The ratio of 'snow shoveling to coin' or 'harvest to coin' (in my opinion) should not be a fixed ratio."

"Simultaneous exchange of valuable labor or material is unnecessary if a coin of enduring value is available for use (in exchange)."

I am not sure how you square one with the other. What is meant by a coin of enduring value if the value of that coin relative to any type of labor can float? A coin starts off buying one hour of snow harvesting labor and ten years later buys 1 minute of snow harvesting labor. Is that a coin of enduring value?

[Roger Sparks]

Frank,

"...........Is that a coin of enduring value?"

Yes, even a depreciating coin (in my view) is a coin of enduring value. Your example of snow harvesting is perfect. You might remember the 3 cent postage stamp (USA) about 70 years ago which has been replaced with the 49 cent stamp (USA today). Not as bad as your 1/60 reduction postulated over 10 years but still very much an example of a depreciating currency.

I have noticed that the identical product will exhibit cost differences between stores. Milk is a good example. Another commonly expressed example is that male and female workers doing identical jobs are paid differently. I use these two examples to illustrate that a coin may trade for the identical product at widely varying prices.

[Frank Restly]

Roger,

A little off topic, but functionally 3 cent (and other small denomination) stamps have little value. They have some philatelic value for collectors and in a pinch, a bunch of them can be used together for correct postage. But ever since the U. S. went to forever stamps, no one buys small denominations to make up the difference whenever postage rates change. I can still remember buying sheets of 1 cent stamps so that I could use older stamps after postage rates changed.

Back to the topic at hand. I can only guess what you have in mind when you say "enduring value", and it may be a waste of time to drag out a definition from you.

In any case, I offer my snow shoveling labor to my neighbor, my neighbor gives me coin for that snow shoveling labor. I offer the same coin to my neighbor for his crop harvesting labor, my neighbor refuses to accept my coin for his crop harvesting labor. It really doesn't matter how enduring the coin I get from my neighbor is - he can refuse to accept it back at a later date.

A system of legally enforced debts overcomes the time difference between the availability of different types of labor, regardless of whether a currency exists. If my neighbor and I agree to trade 1 hour of my snow shoveling labor now for 1 hour of his crop harvesting labor 6 months from now in a debt contract then both of us will ultimately get what we want (an exchange of labors). Adding coinage does not accomplish that goal.

[Tel]

Frank, if you are 100% sure you need crop harvesting labor in 6 months then the contract is more useful (lower risk).

If on the other hand, you don't know exactly what you might need in 6 months then the coins are better... you have more options as to how you spend them.

I see no reason why some people would prefer one asset, while other people prefer a different asset. Mind you, if there's a marketplace for labor futures contracts in this world then those who want such things could get them. Sounds reasonable to me.

It is possible that at some stage *EVERYONE* will refuse to take payments from you (i.e. the desire to hold money drops to zero) but that would imply systemic failure (e.g. hyperinflation).

[Jussi]

"money is a hot potato"

Take a small economy, let there be one bank (banking sector) and only government papers. Make the bank buy all the papers. Take the last paper, is its price higher (low interest rate) or lower (high interest rate) than before the purchases? How do you reconcile your answer with hot potato?

[Nick Edmonds]

It would be useful to know how you imagine money is in this model. Is it a commodity money? Is it an instrument issued by the government when it spends? Or maybe it's balances at a bank, which may be positive or negative, but where the aggregate supply is zero?

[Nick Rowe]

Nick E: It could be any of those, and which one it is may affect the demand and supply functions, but doesn't change the essentials of the framework. But my simplest default thought-experiment is it's just some bits of paper that drop from the sky.

[Ian Lippert]

If all costs are wage costs how do you account for productivity? Ie, consuming less resources to produce more goods. This seems like a big hole in Say's law.

[Nick Rowe]

Ian: I fail to see any relation between changes in productivity and the truth or falsity of Say's Law.

Suppose there are n different types of fruit, each one produced by one of the n types of labour. And suppose productivity doubles.

In a barter economy, where the supply of fruit *is* the demand for fruit, both supply and demand would double.

In a monetary economy, it may or may not cause an excess demand for money, so Say's Law may fail.

(And no, introducing debt into the model does not change this. Money is different because there are 2 ways an individual can get more money: buy more money; sell less money. So don't go off on that red herring. Yes that means you Frank.)

[Roger Sparks]

But Nick, there is a third way for the individual to get money. He can create it.

And please, do not say that only government can create money. Individuals control government. Granted that creating money by individuals through the government veil is more difficult, but it is occurring in a regular pattern.

[Ian Lippert]

What I am trying to get at is that saying all costs are wage costs implies that all inputs are ultimately labour inputs. But I believe there are costs to economic output that don't involve wages, ie how well the economy is using its scarce resources.

Starting from all costs are wage costs, it follows that aggregate income equals aggregate expenditure (Maybe this isn't Say's Law). But this is a tautology and true simply because whenever someone spends a dollar someone has to be there to receive that dollar. But dollar income is a meaningless metric removed from the real economy that we derive its meaning from.

Aggregate income may equal aggregate expenditure but aggregate wealth (the amount of goods that income can purchase) is going to correlate with how productive the economy is and not how many pieces of paper circulate through that economy, whereas aggregate income will correlate with velocity. I think ignoring the real costs of non-labour inputs leads us to focus on expenditure at the expense of wealth creation and leads our economy to be unproductive in the long run.

I may be misunderstanding your whole macro frame work but I have found over the years reading your posts (and many modern macro economists) that there is little interaction in their models between the monetary economy and the real economy. It seems that low interest rate policy is based on analysis that only looks at the short term benefits of incentivizing people to spend their savings in the short term without properly analyzing the long term negative effects on real savings.

[Roger Sparks]

Ian,

".........believe there are costs to economic output that don't involve wages,........"

I think you are recognizing an important omission with this comment (in it's entirety). I would suggest that the omission is related to the control of resources. Please let me amplify.

While individuals have control of their own labor (they control their own muscles and thoughts), government (which is collective control) has control of individuals (as a collection of people) and resources (land, development, trade). This control by government can be reallocated (as in capitalistic societies) or directly exercised (as in communist societies). In reallocated control economies, control is exercised by taxation or rent, or both sequentially. In directly exercised control economies, control is based on permits or permissions.

In either case, one individual will give permission to a second individual to utilize resources. It seems to me that the big difference between the two control procedures is in how the permission giving individual attains the power of control. That could be the basis of a political discussion.

[Frank Restly]

Tel,

"It is possible that at some stage *EVERYONE* will refuse to take payments from you (i.e. the desire to hold money drops to zero) but that would imply systemic failure (e.g. hyperinflation)."

Or it would imply a technological leap forward. Hyperinflations are not the primary destroyers of currencies (IMHO). Rather, currencies are often replaced by others that have advantages (sea shells, stone tablets, metallic coins, etc.). Even paper money today is being phased out with electronic account balances.

"If on the other hand, you don't know exactly what you might need in 6 months then the coins are better... you have more options as to how you spend them."

If I don't know exactly what I might need in 6 months, then I would attempt to be the borrower of labor rather than the lender. I would borrow the crop harvesting labor I need today for the snow shoveling labor that I am willing to offer six months from now. Obviously, this creates a dilemma - someone has to be decisive in their future plans.

[Nick Rowe]

Ian: "Starting from all costs are wage costs, it follows that aggregate income equals aggregate expenditure (Maybe this isn't Say's Law)."

1. we don't need to assume that all costs are wage costs to get aggregate income = aggregate expenditure. AE=Y would also be true if fruit required land only, with no labour, or if fruit just fell from the sky and people picked it up and sold it.

2. AE=Y is not Say's Law. Say's Law is that *desired* aggregate expenditure = *desired* aggregate sales. AE=Y is about *actual* expenditure = *actual* sales (of newly-produced goods).

[Ian Lippert]

How can fruit require land only? Someone still needs to pick it and receive a wage for it unless people were simply consuming what they picked.

I thought Say's law meant that aggregate supply created aggregate demand. Production creates jobs, which creates demand for production. Like I said I am probably thinking of something else since Say's Law isn't really strictly defined any where.

[Hugo André]

Because I don't want this to descend into another fruitless discussion about Say and the law named after him:

Say himself never formulated his theory into any kind of law. The term Say's law was (I believe) invented by Keynes and yes it means roughly what you've written Ian but the law does not accurately represent what Say wrote.

Nick is describing Say's actual theoretical reasoning. If I am allowed to be a bit pedantic he never wrote about it in aggregate terms the way Nick is doing here, preferring instead to focus on individual markets. The aggregate version comes from Leijonhufvud who calls it Say's principle.

[Ian Lippert]

Sounds good. If I refer to Say's law I will just refer to Nick's definition in point (2).

[Nick Rowe]

Ian: "Production creates jobs, which creates demand for production."

God no. That's not Say's Law. A defender of Say's Law would say "Production creates *income*, which creates demand for production." Whether that income is wage income or land rent income or interest income or 'I lucked out and this fruit fell into my hands' income.

[Ian Lippert]

You guys are really getting hung up on my incorrect use of Say's law. As I said, I was just wrong on the definition.

[Bob]

6. BIG problem with that.
The hot potato argument has been debunked thoroughly by the empirical evidence. Denmark and the Eurozone have *negative deposit rates* and yet there is no potato movement.

There is lots of QE going of already and there has been negligible potato activity. (Remember that current QE is functionally the same as *not issuing the Gilts/bonds in the first place*).

Inflation is due to the *flow* of money not the stock. If you and I have only £10 between us then there is a limit to how fast we can move it between us in exchange for goods and services. That's the natural friction within the system (and is lower in the financial sector which is how it appears it generates so much money. Really its just a velocity shift).

However if there is more money in the economy - say £1000 then we can each have savings and still have enough liquidity to move real goods and services between us as fast as a possible in the real sphere.

Which is actually what we need.

The belief that is wrong is that the system naturally has enough liquidity. It doesn't. The unemployed have insufficient liquidity to demand the goods and services they need, which if they could would actually result in them being employed.

And the paradox of thrift caused by financial saving just isn't automatically offset by sufficient loans from banks. The market doesn't 'clear' at full activity, the quantity wanders up and down dependent entirely upon its own dynamic and with little direct connection with the real activities that need financing.

Money is made round to go around. What matters in turnover of money stock, not the size of the money stock.

[Nick Rowe]

Bob: "The belief that is wrong is that the system naturally has enough liquidity. It doesn't. The unemployed have insufficient liquidity to demand the goods and services they need, which if they could would actually result in them being employed."

Which is exactly the point I made in a post last month

"Money is made round to go around. What matters in turnover of money stock, not the size of the money stock."

Or, in my language: MV=PT

[Bob]

If it is in your language then you've done the usual economist trick of redefining the terms to confuse everybody. I am surprised economic literature is not in Latin.

One of the reasons I say you can't discuss this stuff until you have a moving model in front of you. Could you do a post with that? Just for me please. It is so much easier than using words.

[Bob]

"Which is exactly the point I made in a post last month"
I am fairly new to this blog, should be interesting to go over older posts.
"Or, in my language"
Could you define it a bit more clearly. Define M. What is M? Base money, bank deposits, loyalty cards etc? Can I check the assumptions put into the equation it tends to hide a lot of things.
Inflation is based on the *flow* of money, you can't divide all prices by the stock of money and that apparently gives you price level (as some Monetarists do, not saying you necessarily.)

[W. Peden]

"you can't divide all prices by the stock of money and that apparently gives you price level (as some Monetarists do, not saying you necessarily.)"

Monetarists who can't do algebra?

[notsneaky]

Let me try to translate this into ... well, maybe not MY macro framework but at least my understanding of your macro framework.

1 + 4 = this is an endowment economy

2 = the endowment each individual receives is individual specific (does this matter?) but everyone has "love of variety preferences"

3 = there is a cash-in-advance Clower constraint

5 = the price vector is exogenously given. This sort of contradicts 3 since we appear to be talking about something other than a cash-constrained price equilibrium.

6 + 7 = I can't really make sense of (as in "I'm not sure in what they mean" not as in "they don't make sense") without understanding exactly what 5 is suppose to mean.

[Nick Rowe]

notsneaky: I'm genuinely surprised.

My 5 is very standard. Why can't there be two constraints: cash in advance and sticky prices?

My 6 is the old monetarist metaphor for MV=PT. A bunch of kids are sitting in a Wicksellian circle around a campfire, passing a potato (or several potatoes) clockwise around the circle, in exchange for goods. M is the number of potatoes, and V is how quickly each potato is passed on. If the potatoes are too hot, so everyone passes the potatoes on quickly, MV expands, causing a boom and inflation.

My 7 is just the counterpart of 6, when the potatoes are passed on too slowly.

The big difference between the medium of exchange and other assets is there's both a flow into our hands and a flow out of our hands, so there are two ways an individual can adjust the stock in his hands: adjust the flow in; adjust the flow out. If there's an excess demand for potatoes, everyone wants to increase the flow in, but can't, because trade is voluntary Q=min{Qd,Qs}. But each individual can reduce the flow out.

[notsneaky]

good surprised or bad surprised? If it's the "bad" kind let me make the excuse that this is my way of trying to think through it.

If you have "sticky prices" (a non-market clearing price vector), why do you actually need money for the framework? Wouldn't any good, whether it's medium of exchange or not, work? Or is it that you need one good which gives no utility but can be produced at zero cost, whose quantity can be changed to get that non-market clearing price vector to somehow mimic market clearing?

[notsneaky]

I guess what I'm wondering is what happens if you throw enough money into the economy so that the cash in advance constraint is no longer binding - the fact that the markets don't clear due to wrong prices is still going to be there.

[Nick Rowe]

notsneaky: neither good nor bad. Just surprised.

Suppose there were 100 different types of fruit, but no money, because barter is easy. If the price of apples is wrong, people will be unable to buy (or sell) as many apples as they want, but trade in all other fruits will be unaffected.

Now suppose barter is impossible, but people use apples as the medium of exchange. If the price of apples is wrong, so people can't buy (or sell) as many apples as they want, all trade in all fruit will be disrupted. Because you can't trade bananas for cantaloupe without buying and selling apples. Apples are like the hub, in a hub-and-spoke system of airports.

Plus, if apples are also the unit of account, you can't change the price of apples without changing all 99 prices. Which is a lot harder than changing just one price. There's a coordination problem.

Whether or not the medium of exchange gives utility, or can be produced at zero cost, is not essential.

[notsneaky]

But isn't the price here a relative price? Just ratio of exchange which will clear markets? So if the price of apples is wrong, then the price of oranges is wrong, no? This is like the opposite of Walras Law. If n-1 markets clear then n markets clear. If the nth market doesn't clear then the n-1th market doesn't clear. Or am I missing something?

[Nick Rowe]

notsneaky: yes, you are missing something big. But it's not just you. Most economists are wrong on those same things. I don't have the energy to go through it again. For starters, with n goods, there are n-1 markets in a monetary economy (every market is a "money market"), and (n-1)n/2 markets in a barter economy. And Walras' Law is just plain wrong (in a monetary exchange or a barter economy). Here's an old post.

[notsneaky]

I do feel like I'm missing something big and I really want to know what it is (lots of macro just doesn't make sense to me). Sometimes I feel like I need to kidnap a famous macroeconomist and chain'em up in my basement so that whenever something comes up and I get confused or have a specific question - and this happens often - I can engage them in some mutually beneficial trade of subsistence food for information. But that would be bad so I instead bug people on their blogs.

Your framework seems to have two "extra" features. The cash-in-advance constraint and the disequilibrium prices. I want to know which one is the really important one. Or do we NEED both? Of course you can have both if you want to, but are they both necessary? If you already assume non-market clearing prices, isn't the money thing redundant anyway?

I am not invoking Walras Law. I m saying the opposite, that when one market doesn't clear (so WL has no chance of holding) there's got to be at least one another market which also doesn't clear. And that's in a barter economy. So you can't separate the market for apples from the rest of the economy - which will still be affected.

If by "sticky prices" we mean "disequilibrium relative prices" then do we even need to talk about money? Only if somehow putting money into it means that these disequilibrium prices are a function of the money stock so they can be tweaked to eliminate the discrepancy between supply and demand in all markets at once.

But let's take a cash-in-advance economy with a "wrong" price vector and no money in utility function. Then flood this economy with money so that the cash-in-advance constraint is non-binding for anyone. You still got disequiilbrium prices and trouble.

Or put it another way:

"Whether or not the medium of exchange gives utility, or can be produced at zero cost, is not essential."

If you have a cash in advance constraint but money can be produced at zero cost then you don't really have a cash in advance constraint. So the cash in advance formulation is not equivalent to the money in utility function formulation unless you have a utility function which has some kind of a bliss point for money holdings (after a certain point money yields no further liquidity services). This is related to the fact that in the cash in advance formulation 1) "recessions" are asymmetric; not enough money and you have less trade, but "too much" money and you just get the Walrasian barter equilibrium which cannot be improved upon, 2) the reason they're asymmetric is that there's no costs of inflation. Why would your #6 be a problem? Why would we care that the economy is experiencing "inflation" (a re-indexing of all the relative prices)

[Nick Rowe]

Most macroeconomists get this wrong. Only those "of a certain age" remember this stuff (and maybe a few more in France, students of Malinvaud and Benassy). "Disequilibrium macro" got swept away by the New Classical revolution. Some important stuff got forgotten.

You are using Walras' Law, just in the opposite way it's usually used, but it's the same law. It's wrong. It doesn't even get the number of markets right.

2 goods: 1 market. Count em.

3 goods: either 3 markets (barter); or 2 markets (if one of the 3 is used as money).

4 goods: either 6 markets (barter); or 3 markets (if one of the 4 is used as money).

Etc. Count em.

If there are n goods, with the nth good used as money, there are n-1 markets. Each good is traded in 1 market, except for money, which is traded in n-1 markets. Each good has 1 excess demand (or supply), except for money, which has n-1 excess demands (or supplies). In each market, the value of the excess demand (or supply) of the non-money good traded in that market equals the excess supply (or demand) for money *in that market*. That is all we can say.

The above assumes that each market has 2 goods traded in that market; we exchange A for B.

Walras Law assumes 1 big market, run by the Walrasian auctioneer, where all n goods get traded simultaneously.

Consumer choice theory is wrong. If there are n goods, and so n-1 markets, there are n-1 consumer choice problems. In each of the n-1 markets, the agent maximises U st the budget constraint, and st any quantity constraints (rationing) in each of the *other* n-2 markets. (Benassy, based on Clower, which was an interpretation of Keynes).

We need both sticky prices and monetary exchange. We live in a monetary exchange economy. If the price of money is wrong, so there's an excess demand for money, that screws up all markets. In a recession, we see (nearly) all markets screwed up. It's a system-wide problem. Assume all relative prices between the n-1 goods are right, but the price of each good in terms of money is wrong. Then all n-1 markets get screwed up. Yes, changing the stock of M can fix the problem.

"but "too much" money and you just get the Walrasian barter equilibrium which cannot be improved upon,"

No. You get the Barro-Grossman supply-side multiplier. There's excess demand for both labour and output. Firms are unable to buy more labour, and households are unable to buy more output. Nobody wants to work, because they can't buy extra goods with extra money income, so output and employment spiral down. Cuba looked like that, in the 1990's. Barter can solve this problem too: "I don't want extra money because I can't buy extra goods with it, and nor can you, because all markets are in excess demand. But if I produce some extra apples for you, will you produce some extra bananas for me?"

[Nick Rowe]

And "Walrasian barter economy" is an oxymoron. Sorry.

A barter economy has (n-1)n/2 markets, in each of which 2 goods are traded. A Walrasian economy has 1 market in which n goods are traded.

[Kathleen]

@Nick: your model and comment at 6:04 are very clear. Makes total sense to me. Awesome.

[Nick Rowe]

Kathleen: thanks! Much appreciated.

[Paul Friesen]

"Prices/wages are sticky. I don't really understand why, but I think it's probably got something to do with coordination problems."

I don't think it has much to do with coordination problems. I think it's just real-world human psychology. It's rare for companies to reduce nominal wages. Krugman presents histograms on that once in a while, with a big spike at 0 wage change in recent years.

It's just that people get a lot more upset if you cut their nominal wage rate than they would if you kept their nominal wage the same while inflation cut its purchasing power by the same amount. They blame you. They are likely to slack off or quit. So companies mostly just don't do it. Better to lay people off than to reduce the wages of those who you keep.

Most companies don't have much of an idea where the optimum wage for them to pay is, or what the optimum price is. They are just guessing, and they are probably somewhere close, but there is also a lot of wiggle room in both.

[Roger Sparks]

We talk a lot about sticky prices but what about the price of oil? Nothing sticky about that until we get to the gas pump (at one gas station) where prices become very sticky. In this case, stickiness is a matter of convenience (it would drastically slow sale speed to haggle over price for each customer).

Money should be considered as if it were a commodity. Then we can consider that each exchange is really barter, even if we choose to allow sticky prices to set price levels so that speedy transactions can minimize the potential for negotiated (very slow) transactions.

[Nick Rowe]

Paul: that's probably part of the story, but we still observe stickiness even at fairly high inflation rates, where that shouldn't matter much.

Roger: OK, that too is probably part of the story, but at best there you have an explanation of stickiness that lasts for one day.

"Money should be considered as if it were a commodity."

What does that mean?

[Roger Sparks]

" "Money should be considered as if it were a commodity."

What does that mean?"

It would have been better for me to tie to your 6:04 comment by saying Money should be considered as if it were a *good*.

If we did this, we would also look for a money market . The money market would have it's own supply, storage, and consumption patterns. Your formula for number of markets (barter markets) " (n-1)n/2 " would be correct for monetary economies as well as barter economies.

(All of my past comments are rooted in this concept (money is a good or commodity).)

[Nick Rowe]

Roger: re-read what I wrote "3 goods: either 3 markets (barter); or 2 markets (if one of the 3 is used as money)."

Yes, I am already counting money as one of the n goods. No, that does NOT mean that the formula for number of markets (n-1)n/2 would be correct for monetary economies as well as barter economies. Count the damn things.

And looking for "*a* money market" is a waste of time. Every single market is a money market, in a monetary economy. Because money is traded in every single market!

yhub (That was me, smashing my head on the keyboard.)

[notsneaky]

Nick, I'm still confused but I think it's because at some point we started talking about two different things. I was originally questioning this statement:

"Suppose there were 100 different types of fruit, but no money, because barter is easy. If the price of apples is wrong, people will be unable to buy (or sell) as many apples as they want, ******but trade in all other fruits will be unaffected******."

There is no money. Your subsequent comments appear (again, this could be entirely my misunderstanding) to address economies with money. Or even with production (but I think that's a separate issue). And this confusion (again, very possibly mine) could be to do with what exactly are "sticky prices" or "disequilibrium prices" in an economy with no money.

Suppose there are three goods; apples, bananas and coconut. There are three individuals. Person A has 10 apples and no other fruit, Person B has 10 bananas and no other fruit and Person C has 15 coconuts and no other fruit (of course we can assume that they produce these with their labor). They all have the same Cobb-Douglas utility function with the weight on each good of 1/3.

In the Walrasian equilibrium then the exchange ratios are pA/pB=1, one apple for one banana, pA/pC=2/3, two apples for three coconuts, and pB/pC=2/3, two bananas for three coconuts. Everybody eats 10/3 apples and bananas and 5 coconuts.

Now suppose that the chief of this economy comes in and says "this is unfair to the coconut people, apple people are ripping them off! We must have a fair price of coconuts in terms of apples. From now on, all apple-for-coconut trades must be 1-for-1". The chief doesn't care about the terms of apple-for-banana trades or banana-for-coconut trades.

What will the apple-banana price be in this economy? Will it still be 1, which I understand to be what your statement says?

The short side of the market determines the actual quantity traded. The individuals still have the same desired (notional?) demands but something has to be constrained. If pB/pA is less than 1/2 then the total demand for apples is less than total supply of apples (10) and also total demand for coconuts is less than total supply of coconuts (15). Demand for bananas is less than the supply (10) but all 10 bananas get traded. If pB/pA is between 1/2 and 2, then total demand for bananas is less than total supply of bananas and total demand for coconuts is less than total supply of coconuts. All 10 apples get traded. If pB/pA is greater than 2 then total demand for bananas is less than the supply of bananas. All apples and all coconuts are traded.

It could still be true that apples trade for bananas at 1-for-1 but I don't think it's guaranteed. I'm guessing that here we need to specify a rationing rule which decides who gets what (although then we'd also have to re-maximize taking account of that rationing rule) and different rationing rules will lead to different outcomes.

So a "wrong price of apples" does affect other markets.

I'm purposefully not saying anything about money or Clower constraints in this comment.

In a way - and this is me probably misunderstanding you - you seem to be saying that in a Walrasian economy we can always pick our unit of account, so it doesn't matter what we set the "price" of apples to. This is true, but that isn't "disequilibrium prices". We can always pick pA=1 (or whatever) or pA^2+pB^2+pC^2=M, but we can not "normalize prices" by setting pA/pC=1.

Ok, here's the part about money. If you have the "wrong" pA/pC and you add money to the model then I'm not clear on how changing the amount of money in the economy will get rid of the problem. If the money price of apples is pA$ and the money prices of coconuts is pC$ but pA$/pC$ is still constrained to be 1 then...

Again, it could very well be that I'm just not getting this.

[notsneaky]

I also actually dug out my old General Equilibrium volume of the New Palgrave series which has a couple short entries by Benassy, one by Patinkin and one by Silvestre on Fixed Prices. I've actually read every entry in the volume before, except for exactly these, which means there's probably true to what you say about people not knowing about this stuff anymore. Unfortunately I've been way to busy to read these so I might have to get back to you on it in the future.

[Nick Rowe]

notsneaky: a few months back I actually set up a tiny macro model to explain better what I'm trying to say about money vs barter. It's sorta similar to the one you sketch above, except the endowments are different, and there's only 2 (types of) agents, which makes it simpler. It's better I refer you to that, than try to explain what I'm thinking here.

I've just done a new post on this, expanding on my comment above. We should maybe switch this discussion there. Please tell me if it's useful to you. Benassy is very good on this stuff. Patinkin had part of it, early on. I have only a hazy memory of Silvestre, so can't say. Clower, Leijonhufvud, and Malinvaud, are the other names.

[notsneaky]

Yes this is sort of related to that tiny macro model you posted before. That model is insightful but it's also a bit rigged, at least in the context of this discussion. Specifically this part:

"What happens if Pa=Pc=2, and prices are sticky and won't fall to the market-clearing level?

If this were a barter economy, it would make no difference at all, because the relative price Pa/Pc is still at the market-clearing level, and there is no trade in good B anyway. "

This is true but only because each type of agent has 100 B's, so there is no trade in good B anyway. What if one agent type had 50 B's and the other 150 B's? Wouldn't then Pa=Pc=2 make a difference?

(I really wish some of the old post comment threads remained active longer because sometimes it takes me a few days or weeks to think of something relevant, but I guess that's not the nature of blogs)

[Nick Rowe]

notsneaky: "What if one agent type had 50 B's and the other 150 B's? Wouldn't then Pa=Pc=2 make a difference?"

Yes, it would. But I don't think those sort of effects would be very big, in real life. It wouldn't disrupt all markets, to the extent that an excess demand for money would disrupt all markets.

[notsneaky]

Well, that's an empirical question but we're doing theory here. I'm sure it's possible to come up with some utility functions where one big disruption in a single market matters a lot more than a whole bunch of little disruptions in a whole bunch of markets. That's one thing about general equilibrium, lots of stuff can happen. And actually, *it would* potentially disrupt all markets through these very wealth-general-equilibrium effects.