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.
Worthwhile Canadian Initiative 
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.
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?
” “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).)
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.)
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.
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.
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.
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)
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.
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.